BRIGHAM EXPLORATION CO
8-K, 2000-02-29
CRUDE PETROLEUM & NATURAL GAS
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<PAGE>   1
================================================================================

                                  UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

                                 ---------------


                                    FORM 8-K

                                 CURRENT REPORT

     PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES EXCHANGE ACT OF 1934


                                 ---------------


       Date of Report (Date of earliest event reported): FEBRUARY 17, 2000




                           BRIGHAM EXPLORATION COMPANY
             (Exact name of registrant as specified in its charter)



         DELAWARE                   000-22433               75-2692967
(State or other jurisdiction       (Commission             (IRS Employer
      of incorporation)            File Number)          Identification No.)


                            6300 BRIDGEPOINT PARKWAY
                             BUILDING TWO, SUITE 500
                               AUSTIN, TEXAS 78730
          (Address, including zip code, of principal executive offices)

       Registrant's telephone number, including area code: (512) 427-3300

================================================================================
<PAGE>   2


Item 5. OTHER EVENTS.

         On February 22, 2000, Brigham Exploration Company (the "Company")
announced that it entered into a series of financing agreements that provide
funding for its planned 2000 capital expenditure program and working capital
obligations. These transactions include (i) a restructuring of its senior credit
facility to provide from $14 million to $19 million in borrowing availability,
(ii) amendments to the terms of its senior subordinated notes to provide for the
restructured credit facility and additional financial flexibility, and (iii) the
issuance of $4.5 million of common stock and warrants to purchase common stock
in a private placement.

         A copy of the Company's press release regarding the financing
transactions contemplated thereby is attached hereto as Exhibit 99.1. The
following summaries of the financing transactions are qualified in their
entirety by reference to the related financing agreements, copies of which are
attached hereto as Exhibits 10.1 through 10.15, and are incorporated in these
summaries by reference.

         Amended Credit Facility. On February 17, 2000, Brigham entered into an
amended senior credit facility with its existing lenders, Bank of Montreal and
Societe Generale, and a new lender, Shell Capital Inc. This amended facility
provides the Company with $70 million in borrowing availability for a three-year
term, an increase from the $56 million in availability under the existing
facility. If Brigham exceeds certain asset value and interest coverage tests in
the second or third quarters of 2000, the total borrowing availability under
this credit facility will increase to $75 million. Borrowings under the senior
credit facility in excess of $45 million are convertible into shares of Brigham
common stock in the following amounts: (i) the first $10 million of borrowings
is convertible at $3.90 per share, (ii) the second $10 million is convertible at
$6.00 per share and (iii) the final $10 million is convertible at $8.00 per
share. If the credit facility is repaid at maturity or is prepaid prior to
maturity without payment of cash premiums, the Company must issue to Shell
Capital warrants to purchase Brigham common stock. All borrowings under the
senior credit facility bear interest at annual rates of LIBOR plus 3.00%, or
approximately 8.875% based on current LIBOR rates. In addition, certain
financial covenants of the senior credit facility have been amended or added. In
connection with this amendment, the Company has agreed to reset the price of the
warrants to purchase one million shares of Brigham common stock previously
issued to the Bank of Montreal and Societe Generale from a current exercise
price of $2.25 per share to $2.02 per share.

         Amended Senior Subordinated Notes. On February 17, 2000, Brigham
entered into an amendment to the terms of the indenture related to its
outstanding senior subordinated notes due 2003 (the "Notes"). In this amendment,
the holders of the Notes have agreed to waive the minimum consolidated interest
coverage ratio covenant through June 30, 2000 and to adjust subsequent levels
under this test. In addition, the amendment to the Notes provides the Company
with an extension of its right to pay interest through the issuance of
additional Notes in lieu of cash (or "in-kind") through the third quarter of
2000 and potentially through the fourth quarter of 2000 if certain conditions
are met. In exchange for granting these amendments, the Company has agreed to
(i) reset the price of the warrants to purchase one million shares of Brigham
common stock previously issued to the holders of the Notes from a current
exercise price of $3.50 per share to the average market price of Brigham common
stock during the twenty day period beginning February 22nd and ending March
12th, and (ii) grant to holders of the Notes a term overriding royalty interest
that provides for



                                       2
<PAGE>   3


the limited right to receive 4%, or 3% if certain conditions are met, of the
Company's net production revenue to reduce any outstanding Notes issued as
interest paid in-kind.

         Private Equity Placement. On February 22, 2000, Brigham entered into an
agreement to issue 2,195,122 shares of common stock and 731,707 warrants to
purchase common stock for total consideration of $4.5 million in a private
placement to a group of institutional investors led by affiliates of two members
of the Company's board of directors. The equity sale consists of units that
include one share of common stock priced at $2.0525 per share and one-third of a
warrant to purchase Brigham common stock at an exercise price of $2.5625 per
share with a three-year term. Pricing of this private equity placement was based
on the average market price of Brigham common stock during a twenty trading day
period prior to issuance.

         Disclosure Regarding Forward-Looking Statements. The Company or its
representatives may make forward looking statements, oral or written, including
statements in this report, press releases and filings with the SEC, regarding
estimated future net revenues from oil and natural gas reserves and the present
value thereof, planned capital expenditures (including the amount and nature
thereof), increases in oil and gas production, the number of wells the Company
anticipates drilling in its planned capital expenditure programs and the
Company's financial position, business strategy and other plans and objectives
for future operations. Although the Company believes that the expectations
reflected in these forward looking statements are reasonable, there can be no
assurance that the actual results or developments anticipated by the Company
will be realized or, even if substantially realized, that they will have the
expected effects on its business or operations. Among the factors that could
cause actual results to differ materially from the Company's expectations are
general economic conditions, inherent uncertainties in interpreting engineering
data, operating hazards, delays or cancellations of drilling operations for a
variety of reasons, competition, fluctuations in oil and gas prices, the ability
of the Company to successfully integrate the business and operations of acquired
companies, government regulations and other factors set forth among the risk
factors in its filings with the SEC. All subsequent oral and written forward
looking statements attributable to the Company or persons acting on its behalf
are expressly qualified in their entirety by these factors. The Company assumes
no obligation to update any of these statements.



                                       3
<PAGE>   4


Item 7. FINANCIAL STATEMENTS AND EXHIBITS.

         (c) Exhibits

                    Item                Exhibit

                    10.1*               Amended and Restated Credit Agreement
                                        dated as of February 17, 2000 among
                                        Brigham Oil & Gas, L.P., as Borrower,
                                        Bank of Montreal, as Agent, and the
                                        Lenders signatory hereto.

                    10.2*               Amended and Restated Guaranty Agreement
                                        dated as of February 17, 2000 by Brigham
                                        Exploration Company in favor of Bank of
                                        Montreal, as Agent, and each of the
                                        Lenders party to the Amended and
                                        Restated Credit Agreement.

                    10.3*               Partial Assignment of Notes dated as of
                                        February 17, 2000 by and among (i) Bank
                                        of Montreal, (ii) Societe Generale,
                                        Southwest Agency, (iii) Shell Capital
                                        Inc,, and (iv) Brigham Oil & Gas, L.P.

                    10.4*               First Amendment to Warrant Agreement
                                        dated as of February 17, 2000 between
                                        Brigham Exploration Company and Bank of
                                        Montreal.

                    10.5*               First Amendment to Warrant Agreement
                                        dated as of February 17, 2000 between
                                        Brigham Exploration Company and Societe
                                        Generale, Southwest Agency.

                    10.6*               Equity Conversion Agreement dated as of
                                        February 17, 2000 by and among Brigham
                                        Oil & Gas, L.P., Brigham Exploration
                                        Company and Shell Capital Inc. and its
                                        successors and assigns.



<PAGE>   5


                    10.7*               Warrant Agreement dated as of February
                                        17, 2000 by and between Brigham
                                        Exploration Company and Shell Capital
                                        Inc.

                    10.8*               Registration Rights Agreement dated as
                                        of February 17, 2000 by and between
                                        Brigham Exploration Company and Shell
                                        Capital Inc.

                    10.9*               Letter dated as of February 17, 2000
                                        regarding certain fees pursuant to
                                        Credit Agreement dated as of February
                                        17, 2000, among Brigham Oil & Gas, L.P.,
                                        Bank of Montreal, as Agent, Shell
                                        Capital Inc. and the lenders signatory
                                        thereto.

                    10.10*              Second Amendment to Intercreditor and
                                        Subordination Agreement dated as of
                                        February 17, 2000 by and among ECT
                                        Merchant Investments Corp., Joint Energy
                                        Development Investments II Limited
                                        Partnership and Bank of Montreal, as
                                        agent for each of the lenders that is a
                                        signatory to, or which becomes a
                                        signatory to, the Senior Credit
                                        Agreement.

                    10.11*              Second Amendment to Indenture dated as
                                        of February 17, 2000 among Brigham
                                        Exploration Company and Chase Bank of
                                        Texas, National Association.

                    10.12*              Conveyance of Adjustable Term Overriding
                                        Royalty Interest dated as of February
                                        17, 2000 by and between Brigham Oil &
                                        Gas, L.P., and ECT Merchant Investments
                                        Corp. and Joint Energy Development
                                        Investments II Limited Partnership.

                    10.13*              Warrant Certificate dated as of February
                                        17, 2000 by and between Brigham
                                        Exploration Company and Joint Energy
                                        Development Investments II Limited
                                        Partnership.



<PAGE>   6


                    10.14*              Warrant Certificate dated as of February
                                        17, 2000 by and between Brigham
                                        Exploration Company and ECT Merchant
                                        Investments Corp.

                    10.15*              Securities Purchase and Registration
                                        Rights Agreement dated as of February
                                        22, 2000 by and among Brigham
                                        Exploration Company and GAP Coinvestment
                                        Partners II, L.P., Special Situations
                                        Private Equity Fund, L.P., and Aspect
                                        Resources, L.L.C.

                    99.1*               Press Release dated February 22, 2000.

- -------
*  filed herewith.



<PAGE>   7


                                    SIGNATURE


         Pursuant to the requirements of the Securities Exchange Act of 1934,
the Registrant has duly caused this report to be signed on its behalf by the
undersigned thereunto duly authorized.


                                                 BRIGHAM EXPLORATION COMPANY



Date:      February 29, 2000                     By: /s/ Curtis F. Harrell
                                                     ---------------------------
                                                     Curtis F. Harrell
                                                     Chief Financial Officer



<PAGE>   8


                                INDEX TO EXHIBITS

<TABLE>
<CAPTION>

                    EXHIBIT NUMBER                 DESCRIPTION
                    --------------                 -----------

<S>                                     <C>
                    10.1*               Amended and Restated Credit Agreement
                                        dated as of February 17, 2000 among
                                        Brigham Oil & Gas, L.P., as Borrower,
                                        Bank of Montreal, as Agent, and the
                                        Lenders signatory hereto.

                    10.2*               Amended and Restated Guaranty Agreement
                                        dated as of February 17, 2000 by Brigham
                                        Exploration Company in favor of Bank of
                                        Montreal, as Agent, and each of the
                                        Lenders party to the Amended and
                                        Restated Credit Agreement.

                    10.3*               Partial Assignment of Notes dated as of
                                        February 17, 2000 by and among (i) Bank
                                        of Montreal, (ii) Societe Generale,
                                        Southwest Agency, (iii) Shell Capital
                                        Inc,, and (iv) Brigham Oil & Gas, L.P.

                    10.4*               First Amendment to Warrant Agreement
                                        dated as of February 17, 2000 between
                                        Brigham Exploration Company and Bank of
                                        Montreal.

                    10.5*               First Amendment to Warrant Agreement
                                        dated as of February 17, 2000 between
                                        Brigham Exploration Company and Societe
                                        Generale, Southwest Agency.

                    10.6*               Equity Conversion Agreement dated as of
                                        February 17, 2000 by and among Brigham
                                        Oil & Gas, L.P., Brigham Exploration
                                        Company and Shell Capital Inc. and its
                                        successors and assigns.

                    10.7*               Warrant Agreement dated as of February
                                        17, 2000 by and between Brigham
                                        Exploration Company and Shell Capital
                                        Inc.
</TABLE>

<PAGE>   9

<TABLE>
<S>                                     <C>

                    10.8*               Registration Rights Agreement dated as
                                        of February 17, 2000 by and between
                                        Brigham Exploration Company and Shell
                                        Capital Inc.

                    10.9*               Letter dated as of February 17, 2000
                                        regarding certain fees pursuant to
                                        Credit Agreement dated as of February
                                        17, 2000, among Brigham Oil & Gas, L.P.,
                                        Bank of Montreal, as Agent, Shell
                                        Capital Inc. and the lenders signatory
                                        thereto.

                    10.10*              Second Amendment to Intercreditor and
                                        Subordination Agreement dated as of
                                        February 17, 2000 by and among ECT
                                        Merchant Investments Corp., Joint Energy
                                        Development Investments II Limited
                                        Partnership and Bank of Montreal, as
                                        agent for each of the lenders that is a
                                        signatory to, or which becomes a
                                        signatory to, the Senior Credit
                                        Agreement.

                    10.11*              Second Amendment to Indenture dated as
                                        of February 17, 2000 among Brigham
                                        Exploration Company and Chase Bank of
                                        Texas, National Association.

                    10.12*              Conveyance of Adjustable Term Overriding
                                        Royalty Interest dated as of February
                                        17, 2000 by and between Brigham Oil &
                                        Gas, L.P., and ECT Merchant Investments
                                        Corp. and Joint Energy Development
                                        Investments II Limited Partnership.

                    10.13*              Warrant Certificate dated as of February
                                        17, 2000 by and between Brigham
                                        Exploration Company and Joint Energy
                                        Development Investments II Limited
                                        Partnership.
</TABLE>



<PAGE>   10
<TABLE>
<S>                                     <C>
                    10.14*              Warrant Certificate dated as of February
                                        17, 2000 by and between Brigham
                                        Exploration Company and ECT Merchant
                                        Investments Corp.

                    10.15*              Securities Purchase and Registration
                                        Rights Agreement dated as of February
                                        22, 2000 by and among Brigham
                                        Exploration Company and GAP Coinvestment
                                        Partners II, L.P., Special Situations
                                        Private Equity Fund, L.P., and Aspect
                                        Resources, L.L.C.

                    99.1*               Press Release dated February 22, 2000.
</TABLE>





<PAGE>   1
                                                                    EXHIBIT 10.1

                                                                  EXECUTION COPY




                      AMENDED AND RESTATED CREDIT AGREEMENT



                          Dated as of February 17, 2000



                                      Among

                             BRIGHAM OIL & GAS, L.P.
                                  as Borrower,


                                BANK OF MONTREAL,
                                    as Agent,

                                       and

                          THE LENDERS SIGNATORY HERETO


<PAGE>   2


                                TABLE OF CONTENTS

<TABLE>
<CAPTION>
                                                                                                               PAGE
<S>                                                                                                            <C>
Article 1         Definitions and Accounting Matters.............................................................2

         Section 1.01        Terms Defined Above.................................................................2

         Section 1.02        Certain Defined Terms...............................................................2

         Section 1.03        Accounting Terms and Determinations................................................19

Article 2         Commitments...................................................................................19

         Section 2.01        Loans..............................................................................19

         Section 2.02        Borrowings, Continuations and Conversions..........................................20

         Section 2.03        Changes of Commitments.............................................................21

         Section 2.04        Fees...............................................................................22

         Section 2.05        Several Obligations................................................................22

         Section 2.06        Notes..............................................................................22

         Section 2.07        Prepayments........................................................................23

         Section 2.08        Borrowing Base.....................................................................24

         Section 2.09        Lending Offices....................................................................25

Article 3         Payments of Principal and Interest............................................................26

         Section 3.01        Repayment of Loans.................................................................26

         Section 3.02        Interest...........................................................................26

Article 4         Payments; Pro Rata Treatment; Computations; Etc...............................................27

         Section 4.01        Payments...........................................................................27

         Section 4.02        Pro Rata Treatment.................................................................27

         Section 4.03        Computations.......................................................................27

         Section 4.04        Non-receipt of Funds by the Agent..................................................28

         Section 4.05        Set-off, Sharing of Payments, Etc..................................................28

         Section 4.06        Taxes..............................................................................29

Article 5         Capital Adequacy..............................................................................32

         Section 5.01        Additional Costs...................................................................32

         Section 5.02        Limitation on Eurodollar Loans.....................................................34

         Section 5.03        Illegality.........................................................................34

         Section 5.04        Base Rate Loans Pursuant to Sections 5.01, 5.02 and 5.03...........................35

         Section 5.05        Compensation.......................................................................35

         Section 5.06        Replacement Lenders................................................................36

Article 6         Conditions Precedent..........................................................................37
</TABLE>


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<PAGE>   3


                                TABLE OF CONTENTS
                                   (CONTINUED)
<TABLE>
<CAPTION>
                                                                                                               PAGE
<S>                                                                                                            <C>
         Section 6.01        Initial Funding....................................................................37

         Section 6.02        Initial, Subsequent Loans..........................................................39

         Section 6.03        Conditions Precedent for the Benefit of Lenders....................................39

         Section 6.04        No Waiver..........................................................................39

Article 7         Representations and Warranties................................................................39

         Section 7.01        Corporate Existence................................................................39

         Section 7.02        Financial Condition................................................................40

         Section 7.03        Litigation.........................................................................40

         Section 7.04        No Breach..........................................................................40

         Section 7.05        Authority..........................................................................40

         Section 7.06        Approvals..........................................................................41

         Section 7.07        Use of Loans.......................................................................41

         Section 7.08        ERISA..............................................................................41

         Section 7.09        Taxes..............................................................................42

         Section 7.10        Titles, etc........................................................................42

         Section 7.11        No Material Misstatements..........................................................43

         Section 7.12        Investment Company Act.............................................................44

         Section 7.13        Public Utility Holding Company Act.................................................44

         Section 7.14        Subsidiaries.......................................................................44

         Section 7.15        Location of Business and Offices...................................................44

         Section 7.16        Defaults...........................................................................44

         Section 7.17        Environmental Matters..............................................................44

         Section 7.18        Compliance with the Law............................................................45

         Section 7.19        Insurance..........................................................................46

         Section 7.20        Hedging Agreements.................................................................46

         Section 7.21        Restriction on Liens...............................................................47

         Section 7.22        Material Agreements................................................................47

         Section 7.23        Gas Imbalances.....................................................................47

         Section 7.24        Partnership Agreement..............................................................47

         Section 7.25        Prior Notes and Related Documents..................................................47

Article 8         Affirmative Covenants.........................................................................48

         Section 8.01        Financial Statements and Other Reports.............................................48
</TABLE>


                                       ii
<PAGE>   4


                                TABLE OF CONTENTS
                                   (CONTINUED)
<TABLE>
<CAPTION>
                                                                                                               PAGE
<S>                                                                                                            <C>
         Section 8.02        Litigation.........................................................................51

         Section 8.03        Maintenance, Etc...................................................................51

         Section 8.04        Environmental Matters..............................................................52

         Section 8.05        Further Assurances.................................................................53

         Section 8.06        Performance of Obligations.........................................................53

         Section 8.07        Engineering Reports................................................................53

         Section 8.08        Reserved...........................................................................55

         Section 8.09        Additional Collateral..............................................................55

         Section 8.10        ERISA Information and Compliance...................................................56

         Section 8.11        Subsidiary Security................................................................56

         Section 8.12        Payment of Trade Payables..........................................................57

         Section 8.13        Target Asset Value.................................................................57

Article 9         Negative Covenants............................................................................57

         Section 9.01        Debt...............................................................................58

         Section 9.02        Liens..............................................................................59

         Section 9.03        Investments, Loans and Advances....................................................59

         Section 9.04        Dividends, Distributions and Redemptions...........................................60

         Section 9.05        Sales and Leasebacks...............................................................60

         Section 9.06        Nature of Business.................................................................61

         Section 9.07        Limitation on Leases...............................................................61

         Section 9.08        Mergers, Etc.......................................................................61

         Section 9.09        Proceeds of Notes..................................................................61

         Section 9.10        ERISA Compliance...................................................................61

         Section 9.11        Sale or Discount of Receivables....................................................63

         Section 9.12        [Intentionally Omitted]............................................................63

         Section 9.13        Sale of Oil and Gas Properties.....................................................63

         Section 9.14        Environmental Matters..............................................................63

         Section 9.15        Transactions with Affiliates.......................................................63

         Section 9.16        Subsidiaries.......................................................................63

         Section 9.17        Negative Pledge Agreements.........................................................63

         Section 9.18        Gas Imbalances, Take-or-Pay or Other Prepayments...................................64

         Section 9.19        Borrower as Operator...............................................................64
</TABLE>


                                      iii
<PAGE>   5


                                TABLE OF CONTENTS
                                   (CONTINUED)
<TABLE>
<CAPTION>
                                                                                                               PAGE
<S>                                                                                                            <C>
         Section 9.20        Quest Resources LLC................................................................64

         Section 9.21        Subordinated Debt..................................................................64

         Section 9.22        Restrictions While Outstanding Indebtedness Exceeds the Borrowing Base.............64

Article 10        Events of Default; Remedies...................................................................65

         Section 10.01       Events of Default..................................................................65

         Section 10.02       Remedies...........................................................................67

         Section 10.03       Production and Proceeds............................................................68

Article 11        The Agent.....................................................................................68

         Section 11.01       Appointment, Powers and Immunities.................................................68

         Section 11.02       Reliance by Agent..................................................................69

         Section 11.03       Defaults...........................................................................69

         Section 11.04       Rights as a Lender.................................................................69

         Section 11.05       INDEMNIFICATION....................................................................69

         Section 11.06       Non-Reliance on Agent and other Lenders............................................70

         Section 11.07       Action by Agent....................................................................70

         Section 11.08       Resignation or Removal of Agent....................................................71

Article 12        Miscellaneous.................................................................................71

         Section 12.01       Waiver.............................................................................71

         Section 12.02       Notices............................................................................71

         Section 12.03       Payment of Expenses, Indemnities, etc..............................................72

         Section 12.04       Amendments, Etc....................................................................74

         Section 12.05       Successors and Assigns.............................................................75

         Section 12.06       Assignments and Participations.....................................................75

         Section 12.07       Invalidity.........................................................................77

         Section 12.08       Counterparts.......................................................................77

         Section 12.09       References.........................................................................77

         Section 12.10       Survival...........................................................................77

         Section 12.11       Captions...........................................................................77

         Section 12.12       NO ORAL AGREEMENTS.................................................................77

         Section 12.13       GOVERNING LAW; SUBMISSION TO JURISDICTION..........................................77

         Section 12.14       Interest...........................................................................79
</TABLE>


                                       iv
<PAGE>   6


                                TABLE OF CONTENTS
                                   (CONTINUED)
<TABLE>
<CAPTION>
                                                                                                               PAGE
<S>                                                                                                            <C>
         Section 12.15       Confidentiality....................................................................79

         Section 12.16       Prior Credit Agreement.............................................................80

         Section 12.17       Release Regarding the Prior Notes and Related Documents............................80

         Section 12.18       Effectiveness......................................................................80

         Section 12.19       EXCULPATION PROVISIONS.............................................................81

         Section 12.20       RELEASE............................................................................81
</TABLE>


                                        v
<PAGE>   7



       THIS AMENDED AND RESTATED CREDIT AGREEMENT dated as of February 17, 2000
is among: BRIGHAM OIL & GAS, L.P., a limited partnership formed under the laws
of the State of Delaware (the "Borrower"); BANK OF MONTREAL, a Canadian bank, in
its individual capacity (in its individual capacity, "BMO"), SHELL CAPITAL INC.
("SCI"), Societe Generale, Southwest Agency ("Soc-Gen") and any other lender
which becomes a signatory hereto as provided in Section 12.06 (individually,
together with its successors and assigns, a "Lender" and, collectively, the
"Lenders"); and BMO, in its capacity as agent for the Lenders (in such capacity,
together with its successors in such capacity, the "Agent").

                                 R E C I T A L S

       A. Pursuant to that certain Credit Agreement (the "Original Credit
Agreement") dated as of January 26, 1998 among the Borrower and BMO, as amended
by that certain First Amendment to Credit Agreement dated as of August 20, 1998
among the Borrower, BMO and Soc-Gen (the "First Amendment"), that certain Second
Amendment to Credit Agreement dated as of March 26, 1999 among the Borrower, BMO
and Soc-Gen (the "Second Amendment"), that certain Third Amendment to Credit
Agreement dated as of July 19, 1999 among the Borrower, BMO and Soc-Gen (the
"Third Amendment") and that certain Fourth Amendment to Credit Agreement dated
as of October 7, 1999 among the Borrower, BMO and Soc-Gen (the "Fourth
Amendment") (the Original Credit Agreement as amended by the First Amendment,
the Second Amendment, the Third Amendment and the Fourth Amendment being
hereafter called the "Prior Credit Agreement"),BMO and Soc-Gen provided to the
Borrower loans and extensions of credit, which loans and extensions of credit
are evidenced by those certain promissory notes from the Borrower in the
aggregate principal amount of $75,000,000 (the "Prior Notes").

       B. By Partial Assignment of Notes of even date herewith (the "SCI
Assignment") SCI has acquired a 53.3% interest in the Prior Notes and a like
interest in all security for the payment of the Prior Notes and the performance
of the Borrower's obligations under the Prior Credit Agreement.

       C. The Lenders have agreed to provide senior secured debt in the amount
of up to $75,000,000 consisting of a rearrangement of the Prior Notes and
advances to the Borrower for general corporate purposes, and the Borrower, the
Agent and the Lenders now desire to set forth their agreements with respect to
such credit facility and to amend and restate in their entirety the Prior Credit
Agreement, by means of this Agreement, and the Prior Notes, by means of the
Notes.

       D. Pursuant to that certain Intercreditor and Subordination Agreement
dated as of August 20, 1998, as from time to time amended (including that
certain Second Amendment to Intercreditor and Subordination Agreement dated as
of the date hereof), among Enron North America Corp., fka Enron Capital & Trade
Resources Corp., a Delaware corporation, Joint Energy Development Investments II
Limited Partnership, a Delaware limited partnership and Agent, for the benefit
of the Lenders, the Subordinated Debt (as hereinafter defined) is expressly
subordinated to the Indebtedness (as hereinafter defined).





                                       1
<PAGE>   8
              E. In consideration of the mutual covenants and agreements herein
contained and of the loans, extensions of credit and commitments hereinafter
referred to, the parties hereto agree as follows:

                                   ARTICLE 1

                       Definitions and Accounting Matters

              Section 1.01 Terms Defined Above. As used in this Agreement, the
terms "Agent," "BMO," "Borrower," "Lender," "Lenders," "Prior Credit Agreement,"
"Prior Notes", "SCI", "SCI Assignment" and "Soc-Gen" shall have the meanings
indicated above.

              Section 1.02 Certain Defined Terms. As used herein, the following
terms shall have the following meanings (all terms defined in this Article I or
in other provisions of this Agreement in the singular to have the same meanings
when used in the plural and vice versa):

              "Additional Costs" shall have the meaning assigned such term in
Section 5.01(a).

              "Affected Loans" shall have the meaning assigned such term in
Section 5.04.

              "Affiliate" of any Person shall mean (i) any Person directly or
indirectly controlled by, controlling or under common control with such first
Person, (ii) any director or officer of such first Person or of any Person
referred to in clause (i) above and (iii) if any Person in clause (i) above is
an individual, any member of the immediate family (including parents, spouse and
children) of such individual and any trust whose principal beneficiary is such
individual or one or more members of such immediate family and any Person who is
controlled by any such member or trust. For purposes of this definition, any
Person which owns directly or indirectly 20% or more of the securities having
ordinary voting power for the election of directors or other governing body of a
corporation or 20% or more of the partnership or other ownership interests of
any other Person (other than as a limited partner of such other Person) will be
deemed to "control" (including, with its correlative meanings, "controlled by"
and "under common control with") such corporation or other Person.

              "Agent's Fee Letter" shall mean that certain letter agreement from
the Agent to the Borrower dated of even date with this Agreement concerning
certain fees in connection with this Agreement and any agreements or instruments
executed in connection therewith, as the same may be amended or replaced from
time to time.

              "Agreement" shall mean this Amended and Restated Credit Agreement,
as the same may from time to time be amended or supplemented.

              "Aggregate Commitments" at any time shall equal the amount
calculated in accordance with Section 2.03 hereof.

              "Aggregate Maximum Credit Amounts" shall mean the amount of
$70,000,000 (minus any portion of the outstanding Loans converted pursuant to an
Equity Conversion), as the same may be reduced pursuant to Section 2.03(b) and
Section 2.07(d); provided, however, that at such time as there has occurred an
Increase Event, the Aggregate Maximum Credit Amounts






                                       2
<PAGE>   9

shall be $75,000,000, less any prior or contemporaneous reductions pursuant to
Section 2.03(b) and Section 2.07(d) and the portion of any outstanding Loans
converted pursuant to an Equity Conversion.

              "Applicable Lending Office" shall mean, for each Lender and for
each Type of Loan, the lending office of such Lender (or an Affiliate of such
Lender) designated for such Type of Loan on the signature pages hereof or such
other offices of such Lender (or of an Affiliate of such Lender) as such Lender
may from time to time specify to the Agent and the Borrower as the office by
which its Loans of such Type are to be made and maintained.

              "Applicable Margin" shall mean 2% per annum with respect to Base
Rate Loans and 3% per annum with respect to Eurodollar Loans.

              "Assignment" shall have the meaning assigned such term in Section
12.06(b).

              "Base Rate" shall mean, with respect to any Base Rate Loan, for
any day, the higher of (i) the Federal Funds Rate for any such day plus 1/2 of
1% or (ii) the Prime Rate for such day. Each change in any interest rate
provided for herein based upon the Base Rate resulting from a change in the Base
Rate shall take effect at the time of such change in the Base Rate.

              "Base Rate Loans" shall mean Loans that bear interest at rates
based upon the Base Rate.

              "BMO/Soc-Gen Lenders" means BMO and Soc-Gen and their respective
successors and assigns.

              "BMO/Soc-Gen Majority Lenders" shall mean, at any time while no
Loans are outstanding, BMO/Soc-Gen Lenders having at least sixty-six and
two-thirds percent (66-2/3%) of the Aggregate Commitments of the BMO/Soc-Gen
Lenders and, at any time while Loans are outstanding, BMO/Soc-Gen Lenders
holding at least sixty-six and two-thirds percent (66-2/3%) of the outstanding
aggregate principal amount of the portion of the Loans allocable to the
BMO/Soc-Gen Lenders (without regard to any sale by a BMO/Soc-Gen Lender of a
participation in any Loan under Section 12.06(c)).

              "Borrowing Base" shall mean at any time in amount equal to the
amount determined in accordance with Section 2.08.

              "Borrowing Base Redetermination Date" shall have the meaning
assigned such term in Section 2.08(a).

              "Brigham Exploration" shall mean Brigham Exploration Company, a
Delaware corporation and owner of 100% of the capital stock of the General
Partner.

              "Business Day" shall mean any day other than a day on which
commercial banks are authorized or required to close in Houston, Texas and,
where such term is used in the definition of "Quarterly Date" or if such day
relates to a borrowing or continuation of, a payment or prepayment of principal
of or interest on, or a conversion of or into, or the Interest Period for,




                                       3
<PAGE>   10

a Eurodollar Loan or a notice by the Borrower with respect to any such borrowing
or continuation, payment, prepayment, conversion or Interest Period, any day
which is also a day on which dealings in Dollar deposits are carried out in the
London interbank market.

              "CAPEX Plan" shall mean each Capital Expenditures Plan detailing
the projected capital expenditures of the Borrower for the twelve month period
from and after the month in which such plan is delivered, the first of which is
to be submitted on the Closing Date with similar plans for each succeeding
twelve month period to be submitted in accordance with Section 8.01(l).

              "Closing Date" shall mean February 17, 2000.

              "Code" shall mean the Internal Revenue Code of 1986, as amended
from time to time and any successor statute.

              "Commitment" shall mean, for any Lender, its obligation to make
Loans up to the lesser of such Lender's Maximum Credit Amount or, when the
Borrowing Base becomes effective, the Lender's Percentage Share of the amount
equal to the then effective Borrowing Base.

              "Consolidated Net Income" shall mean with respect to Brigham
Exploration and its Consolidated Subsidiaries, for any period, the aggregate of
the net income (or loss) of Brigham Exploration and its Consolidated
Subsidiaries after allowances for taxes for such period, determined on a
consolidated basis in accordance with GAAP; provided that there shall be
excluded from the calculation of such net income (to the extent otherwise
included therein) the following: (i) the net income of any Person in which
Brigham Exploration or any Consolidated Subsidiary has an interest (which
interest does not cause the net income of such other Person to be consolidated
with the net income of Brigham Exploration and its Consolidated Subsidiaries in
accordance with GAAP), except to the extent of the amount of dividends or
distributions actually paid in such period by such other Person to Brigham
Exploration or to a Consolidated Subsidiary, as the case may be; (ii) the net
income (but not loss) of any Consolidated Subsidiary to the extent that the
declaration or payment of dividends or similar distributions or transfers or
loans by that Consolidated Subsidiary is not at the time permitted by operation
of the terms of its charter or any agreement, instrument or Governmental
Requirement applicable to such Consolidated Subsidiary, or is otherwise
restricted or prohibited in each case determined in accordance with GAAP; (iii)
the net income (or loss) of any Person acquired in a pooling-of-interests
transaction for any period prior to the date of such transaction; (iv) any
extraordinary gains or losses, including gains or losses attributable to
Property sales not in the ordinary course of business; and (v) the cumulative
effect of a change in accounting principles and any gains or losses attributable
to writeups or writedowns of assets. Consolidated Net Income shall include all
amounts paid on account of the Term ORRI, regardless of the accounting treatment
given such Term ORRI.

              "Consolidated Subsidiaries" shall mean each Subsidiary of Brigham
Exploration (whether now existing or hereafter created or acquired) the
financial statements of which shall be (or should have been) consolidated with
the financial statements of Brigham Exploration in accordance with GAAP,
including, without limitation, the Borrower.




                                       4
<PAGE>   11

              "Covenant Release Date" means the first Borrowing Base
Redetermination Date on which the outstanding Indebtedness is less than or equal
to the Borrowing Base.

              "Debt" shall mean, for any Person the sum of the following
(without duplication): (i) all obligations of such Person for borrowed money or
evidenced by bonds, debentures, notes or other similar instruments (including
principal, interest, fees and charges); (ii) all obligations of such Person
(whether contingent or otherwise) in respect of bankers' acceptances, letters of
credit, surety or other bonds and similar instruments; (iii) all obligations of
such Person to pay the deferred purchase price of Property or services (other
than for borrowed money) excluding Trade Payables; (iv) all obligations under
leases which shall have been, or should have been, in accordance with GAAP,
recorded as capital leases in respect of which such Person is liable (whether
contingent or otherwise); (v) all obligations under leases (other than capital
leases and oil and gas leases) which require such Person or its Affiliate to
make payments exceeding $100,000 over the term of such lease, including payments
at termination, which are substantially equal to at least eighty percent (80%)
of the purchase price of the Property subject to such lease plus interest at an
imputed market rate of interest; (vi) all Debt (as described in the other
clauses of this definition) of others secured by a Lien on any asset of such
Person, whether or not such Debt is assumed by such Person; (vii) all Debt (as
described in the other clauses of this definition) of others guaranteed by such
Person or in which such Person otherwise assures a creditor against loss of the
Debt of others; (viii) all obligations or undertakings of such Person to
maintain or cause to be maintained the financial position or covenants of others
including without limitation agreements expressed as an agreement to purchase
the Debt or Property of others or otherwise; (ix) obligations to deliver
Hydrocarbons in consideration of advance payments; (x) obligations to pay for
goods or services whether or not such goods or services are actually received or
utilized by such Person; (xi) any capital stock of such Person in which such
Person has a mandatory obligation to redeem such stock; (xii) any Debt of a
Special Entity for which such Person is liable either by agreement or because of
a Governmental Requirement; (xiii) the undischarged balance of any production
payment created by such Person or for the creation of which such Person directly
or indirectly received payment; and (xiv) all obligations of such Person under
Hedging Agreements.

              "Default" shall mean an Event of Default or an event which with
notice or lapse of time or both would become an Event of Default.

              "Dollars" and "$" shall mean lawful money of the United States of
America. "EBITDA" shall mean, for any period, the sum of Consolidated Net Income
for such period PLUS the following expenses or charges to the extent deducted
from Consolidated Net Income in such period: interest, taxes, depreciation,
depletion and amortization, and other noncash charges, MINUS (i) all non cash
income added to Consolidated Net Income in such period and (ii) capitalized
general and administrative charges for such period.

              "ECT Merchant" shall mean ECT Merchant Investments Corp., a
Delaware corporation.

              "Effective Date" shall have the meaning assigned such term in
Section 12.16.




                                       5
<PAGE>   12

              "Engineering Reports" shall have the meaning assigned such term in
Section 2.08.

              "Environmental Laws" shall mean any and all Governmental
Requirements pertaining to the environment in effect in any and all
jurisdictions in which the Borrower or any Subsidiary is conducting or at any
time has conducted business, or where any Property of the Borrower or any
Subsidiary is located, including without limitation, the Oil Pollution Act of
1990 ("OPA"), the Clean Air Act, as amended, the Comprehensive Environmental,
Response, Compensation, and Liability Act of 1980 ("CERCLA"), as amended, the
Federal Water Pollution Control Act, as amended, the Occupational Safety and
Health Act of 1970, as amended, the Resource Conservation and Recovery Act of
1976 ("RCRA"), as amended, the Safe Drinking Water Act, as amended, the Toxic
Substances Control Act, as amended, the Superfund Amendments and Reauthorization
Act of 1986, as amended, the Hazardous Materials Transportation Act, as amended,
and other environmental conservation or protection laws. As used in the
provisions hereof relating to Environmental Laws, the term "oil" shall have the
meaning specified in OPA, the terms "hazardous substance" and "release" (or
"threatened release") have the meanings specified in CERCLA, and the terms
"solid waste" and "disposal" (or "disposed") have the meanings specified in
RCRA; provided, however, that (i) in the event either OPA, CERCLA or RCRA is
amended so as to broaden the meaning of any term defined thereby, such broader
meaning shall apply subsequent to the effective date of such amendment and (ii)
to the extent the laws of the state in which any Property of the Borrower or any
Subsidiary is located establish a meaning for "oil," "hazardous substance,"
"release," "solid waste" or "disposal" which is broader than that specified in
either OPA, CERCLA or RCRA, such broader meaning shall apply.

              "Equity Conversion" shall mean the conversion of a portion of the
Loans of the SCI Lenders into capital stock of Brigham Exploration pursuant to
the terms of the Equity Conversion Agreement.

              "Equity Conversion Agreement" shall mean that certain Equity
Conversion Agreement of even date herewith among the Borrower, Brigham
Exploration and Shell Capital, which sets forth the terms for one or more of the
Equity Conversions.

              "ERISA" shall mean the Employee Retirement Income Security Act of
1974, as amended from time to time and any successor statute.

              "ERISA Affiliate" shall mean each trade or business (whether or
not incorporated) which together with the Borrower or any Subsidiary of the
Borrower would be deemed to be a "single employer" within the meaning of section
4001(b)(1) of ERISA or subsections (b), (c), (m) or (o) of section 414 of the
Code.

              "ERISA Event" shall mean (i) a "Reportable Event" described in
Section 4043 of ERISA and the regulations issued thereunder (other than such an
event with respect to which the requirement to give notice has been waived),
(ii) the withdrawal of the Borrower or any ERISA Affiliate from a Plan during a
plan year in which it was a "substantial employer" as defined in Section
4001(a)(2) of ERISA, (iii) the filing of a notice of intent to terminate a Plan
(other than a defined contribution Plan) or the treatment of an amendment to
such a Plan as a termination under Section 4041 of ERISA, (iv) the institution
of proceedings to terminate a Plan by the




                                       6
<PAGE>   13

PBGC or (v) any other event or condition which might constitute grounds under
Section 4042 of ERISA for the termination of, or the appointment of a trustee to
administer, any Plan.

              "Eurodollar Loans" shall mean Loans the interest rates on which
are determined on the basis of rates referred to in the definition of
"Eurodollar Rate".

              "Eurodollar Rate" shall mean, with respect to any Eurodollar Loan,
the rate per annum (rounded upwards, if necessary, to the nearest 1/100 of 1%)
reported, on the date two Business Days prior to the first day of the Interest
Period for such Loan, on Telerate Access Service Page 3750 (British Bankers
Association Settlement Rate) as the London Interbank Offered Rate for U.S.
dollar deposits having a term comparable to such Interest Period and in an
amount of $1,000,000 or more (provided that, if such Page shall cease to be
publicly available or if the information contained on such Page shall cease to
be publicly available or if the information contained on such Page, in the
Agent's reasonable judgment, shall cease to accurately reflect such London
Interbank Offered Rate or if such page does not report information for the term
of the Interest Period selected by Borrower, such rate shall be that reported by
any publicly available source of similar market data selected by the Agent, or
that interpolated by Agent from such market data, which, in the Agent's
reasonable judgment, accurately reflects such London Interbank Offered Rate).

              "Event of Default" shall have the meaning assigned such term in
Section 10.01.

              "Excepted Liens" shall mean: (i) Liens for taxes, assessments or
other governmental charges or levies not yet due or which are being contested in
good faith by appropriate action and for which adequate reserves have been
maintained in accordance with GAAP; (ii) Liens in connection with workmen's
compensation, unemployment insurance or other social security, old age pension
or public liability obligations not yet due or which are being contested in good
faith by appropriate action and for which adequate reserves have been maintained
in accordance with GAAP; (iii) operators', vendors', carriers', warehousemen's,
repairmen's, mechanics', workmen's, materialmen's, construction or other like
Liens arising by operation of law in the ordinary course of business or incident
to the exploration, development, operation and maintenance of Oil and Gas
Properties or customary landlord's liens, each of which is in respect of
obligations that have not been outstanding more than 90 days or which are being
contested in good faith by appropriate proceedings and for which adequate
reserves have been maintained in accordance with GAAP; (iv) any Liens reserved
in leases or farmout agreements for rent or royalties and for compliance with
the terms of the farmout agreements or leases in the case of leasehold estates,
to the extent that any such Lien referred to in this clause does not materially
impair the use of the Property covered by such Lien for the purposes for which
such Property is held or materially impair the value of such Property subject
thereto; (v) encumbrances (other than to secure the payment of borrowed money or
the deferred purchase price of Property or services), easements, restrictions,
servitudes, permits, conditions, covenants, exceptions or reservations in any
rights of way or other Property for the purpose of roads, pipelines,
transmission lines, transportation lines, distribution lines for the removal of
gas, oil, coal or other minerals or timber, and other like purposes, or for the
joint or common use of real estate, rights of way, facilities and equipment, and
defects, irregularities, zoning restrictions and deficiencies in title of any
rights of way or other Property which in the aggregate do not materially impair
the use of such rights of way or other Property for the purposes of which such




                                       7
<PAGE>   14

rights of way and other Property are held or materially impair the value of such
Property subject thereto; (vi) deposits of cash or securities to secure the
performance of bids, trade contracts, leases, statutory obligations and other
obligations of a like nature incurred in the ordinary course of business; (vii)
Liens permitted by the Loan Documents; and (viii) liens securing any Debt
described in Section 9.01(f) hereof that is owing to a Lender or an Affiliate of
a Lender at the time such Debt is incurred.

              "Federal Funds Rate" shall mean, for any day, the rate per annum
(rounded upwards, if necessary, to the nearest 1/100 of 1%) equal to the
weighted average of the rates on overnight federal funds transactions with a
member of the Federal Reserve System arranged by federal funds brokers on such
day, as published by the Federal Reserve Bank of New York on the Business Day
next succeeding such day, provided that (i) if the date for which such rate is
to be determined is not a Business Day, the Federal Funds Rate for such day
shall be such rate on such transactions on the next preceding Business Day as so
published on the next succeeding Business Day, and (ii) if such rate is not so
published for any day, the Federal Funds Rate for such day shall be the average
rate charged to the Agent on such day on such transactions as determined by the
Agent.

              "Financial Statements" shall mean the financial statement or
statements described or referred to in Section 7.02.

              "First Asset Valuation Date" means September 30, 2000.

              "First Borrowing Base Determination Date" shall mean March 30,
2002, or such later date upon which the Borrower receives written notice of the
Borrowing Base from Agent; provided that the First Borrowing Base Determination
Date may occur prior to March 30, 2002, in the event Borrower calls for an
earlier determination of the Borrowing Base pursuant to Section 2.08(d).

              "GAAP" shall mean generally accepted accounting principles in the
United States of America in effect from time to time.

              "General Partner" shall mean Brigham, Inc., a Nevada corporation,
general partner of the Borrower.

              "Governmental Authority" shall include the country, the state,
county, city and political subdivisions in which any Person or such Person's
Property is located or which exercises valid jurisdiction over any such Person
or such Person's Property, and any court, agency, department, commission, board,
bureau or instrumentality of any of them including monetary authorities which
exercises valid jurisdiction over any such Person or such Person's Property.
Unless otherwise specified, all references to Governmental Authority herein
shall mean a Governmental Authority having jurisdiction over, where applicable,
the Borrower, the Subsidiaries or any of their Property or the Agent, any Lender
or any Applicable Lending Office.

              "Governmental Requirement" shall mean any law, statute, code,
ordinance, order, determination, rule, regulation, judgment, decree, injunction,
franchise, permit, certificate, license, authorization or other directive or
requirement (in the case of banking regulatory authorities whether or not having
the force of law), including, without limitation, Environmental




                                       8
<PAGE>   15

Laws, energy regulations and occupational, safety and health standards or
controls, of any Governmental Authority.

              "Guarantors" shall mean Brigham Exploration, the General Partner,
Brigham Holdings I, LLC and Brigham Holdings II, LLC and any other Person who
becomes party to a Guaranty Agreement pursuant to the terms of Section 8.11.

              "Guaranty Agreements" shall mean the agreements executed by the
Guarantors in form and substance satisfactory to the Agent guarantying,
unconditionally, payment of the Indebtedness, as the same may be amended,
modified or supplemented from time to time.

              "Hedging Agreements" shall mean any commodity, interest rate or
currency swap, cap, floor, collar, forward agreement or other exchange or
protection agreements or any option with respect to any such transaction.

              "Highest Lawful Rate" shall mean, with respect to each Lender, the
maximum nonusurious interest rate, if any, that at any time or from time to time
may be contracted for, taken, reserved, charged or received on the Notes or on
other Indebtedness under laws applicable to such Lender which are presently in
effect or, to the extent allowed by law, under such applicable laws which may
hereafter be in effect and which allow a higher maximum nonusurious interest
rate than applicable laws now allow.

              "Hydrocarbon Interests" shall mean all rights, titles, interests
and estates now or hereafter acquired in and to oil and gas leases, oil, gas and
mineral leases, or other liquid or gaseous hydrocarbon leases, mineral fee
interests, overriding royalty and royalty interests, net profit interests and
production payment interests, including any reserved or residual interests of
whatever nature.

              "Hydrocarbons" shall mean oil, gas, casinghead gas, drip gasoline,
natural gasoline, condensate, distillate, liquid hydrocarbons, gaseous
hydrocarbons and all products refined or separated therefrom.

              "Increase Event" means the satisfaction of any one of the
following conditions:

                     (a) if as of July 31, 2000, the RAPRV is $50,000,000 or
              greater and the Interest Coverage Ratio of Brigham Exploration is
              0.75 to 1.0 or greater, or

                     (b) if as of September 30, 2000, the RAPRV is $55,000,000
              or greater and the Interest Coverage Ratio of Brigham Exploration
              is 0.90 to 1.0 or greater, or

                     (c) if (i) Brigham Exploration sells common stock and/or
              preferred stock with cashless dividends of Brigham Exploration for
              at least $10,000,000 or (ii) Borrower and/or Brigham Exploration
              are able to acquire in exchange for Brigham Exploration common
              stock and/or preferred stock with cashless dividends, producing
              properties with PDP Reserves having a value (to be reasonably
              determined by the SCI Lenders and a discount rate of 10%) of at
              least $10,000,000, or (iii) Borrower and/or Brigham Exploration
              are able to effect some combination of (i) and (ii) above, that
              results in cash consideration received for




                                       9
<PAGE>   16

              the issuance of Brigham Exploration common stock and/or preferred
              stock with cashless dividends plus a value (to be reasonably
              determined by the SCI Lenders and a discount rate of 10%) of any
              PDP Reserves acquired in exchange for Brigham Exploration common
              stock and/or preferred stock with cashless dividends, that
              collectively equals or exceeds $10,000,000.

              "Indebtedness" shall mean any and all amounts owing or to be owing
by the Borrower to the Agent and/or Lenders in connection with the Loan
Documents and any Hedging Agreements now or hereafter existing between (i)
Borrower and BMO and its successors or assigns (a "BMO Hedge Party") and Soc-Gen
and its successors or assigns (a "Soc-Gen Hedge Party") entered into while such
BMO Hedge Party or such Soc-Gen Hedge Party is a Lender; and (ii) Borrower and
SCI and its successors or assigns (with Loans or Commitments of $20 million or
more) or any Affiliate of SCI (SCI and any Affiliate of SCI a "SCI Hedge Party")
entered into while such SCI Hedge Party or Fathom Energy Capital I, L.L.C, is a
Lender and permitted by the terms of this Agreement and all renewals, extensions
and/or rearrangements of any of the above.

              "Indemnified Parties" shall have the meaning assigned such term in
Section 12.03(b).

              "Indemnity Matters" shall mean any and all actions, suits,
proceedings (including any investigations, litigation or inquiries), claims,
demands and causes of action made or threatened against a Person and, in
connection therewith, all losses, liabilities, damages (including, without
limitation, consequential damages) or reasonable costs and expenses of any kind
or nature whatsoever incurred by such Person whether caused by the sole or
concurrent negligence of such Person seeking indemnification.

              "Indenture" shall mean that certain Indenture dated as of August
20, 1998 between Brigham Exploration, as the issuer of the Subordinated Debt,
and Chase Bank of Texas, National Association, as the trustee as amended by that
First Amendment to Indenture dated March 26, 1999 and that Second Amendment to
Indenture of even date herewith.

              "Initial Funding" shall mean the funding of the initial Loans
pursuant to Section 6.01 hereof.

              "Initial Reserve Report" shall mean the report of Cawley,
Gillespie & Associates with respect to the Oil and Gas Properties of the
Borrower as of December 31, 1999, a copy of which has been delivered to the
Agent.

              "Interest Coverage Ratio" shall have the meaning assigned such
term in the Amended and Restated Guaranty Agreement dated as of the date hereof,
as from time to time amended, executed by Brigham Exploration.

              "Interest Period" shall mean, with respect to (i) any Eurodollar
Loan made prior to the First Borrowing Base Determination Date, the period
commencing on the date such Eurodollar Loan is made and ending on the
numerically corresponding day in the first month thereafter and (ii) any
Eurodollar Loan made after the First Borrowing Base Determination Date, the
period commencing on the date such Eurodollar Loan is made and ending on the
numerically corresponding day in the first or third calendar month thereafter,
as the Borrower may select as




                                       10
<PAGE>   17

provided in Section 2.02, except that each Interest Period which commences on
the last Business Day of a calendar month (or on any day for which there is no
numerically corresponding day in the appropriate subsequent calendar month)
shall end on the last Business Day of the appropriate subsequent calendar month.

              Notwithstanding the foregoing: (i) no Interest Period may end
after the Revolving Credit Termination Date; (ii) no Interest Period for any
Eurodollar Loan may end after the due date of any installment, if any, provided
for in Section 3.01 hereof to the extent that such Eurodollar Loan would need to
be prepaid prior to the end of such Interest Period in order for such
installment to be paid when due; (iii) each Interest Period which would
otherwise end on a day which is not a Business Day shall end on the next
succeeding Business Day (or, if such next succeeding Business Day falls in the
next succeeding calendar month, on the next preceding Business Day); and (iv) no
Interest Period shall have a duration of less than one month and, if the
Interest Period for any Eurodollar Loans would otherwise be for a shorter
period, such Loans shall not be available hereunder.

              "JEDI-II" shall mean Joint Energy Development Investments II
Limited Partnership, a Delaware limited partnership.

              "Lending Relationship" shall refer to this Agreement and the other
Loan Documents, together with any and all negotiations, discussions, acts,
omissions, renewals, extensions, and other agreements or events related to this
Agreement and such other Loan Documents, the parties' obligations thereunder and
the transactions contemplated thereby, including, without limitation, any such
negotiations, discussions, acts, omissions, renewals, extensions, other
agreements or events that may occur on the date hereof and the instruments and
documents executed and delivered in connection herewith or relating hereto.

              "Lien" shall mean any interest in Property securing an obligation
owed to, or a claim by, a Person other than the owner of the Property, whether
such interest is based on the common law, statute or contract, and whether such
obligation or claim is fixed or contingent, and including but not limited to (i)
the lien or security interest arising from a mortgage, encumbrance, pledge,
security agreement, conditional sale or trust receipt or a lease, consignment or
bailment for security purposes or (ii) production payments and the like payable
out of Oil and Gas Properties. The term "Lien" shall include reservations,
exceptions, encroachments, easements, rights of way, covenants, conditions,
restrictions, leases and other title exceptions and encumbrances affecting
Property. For the purposes of this Agreement, a Person shall be deemed to be the
owner of any Property which it has acquired or holds subject to a conditional
sale agreement, or leases under a financing lease or other arrangement pursuant
to which title to the Property has been retained by or vested in some other
Person in a transaction intended to create a financing.

              "Loan Documents" shall mean this Agreement, the Notes, the Agent's
Fee Letter, the SCI Fee Letter, the Soc-Gen Fee Letter, the Equity Conversion
Agreement (and any warrants issued pursuant thereto), the agreements or
instruments described or referred to in Exhibit D, and any and all other
agreements or instruments now or hereafter executed and delivered by the
Borrower or any Subsidiary or Affiliate of the Borrower including, without
limitation, Brigham Exploration (other than assignments, participation or
similar agreements between any Lender and




                                       11
<PAGE>   18

any other lender or creditor with respect to any Indebtedness pursuant to this
Agreement) in connection with, or as security for the payment or performance of
the Notes, or this Agreement, as such agreements may be amended, supplemented or
restated from time to time.

              "Loans" shall mean the loans as provided for by Section 2.01(a).

              "Majority Lenders" means the BMO/Soc-Gen Majority Lenders and the
SCI Majority Lenders, together.

              "Material Adverse Effect" shall mean any material and adverse
effect on (i) the assets, liabilities, financial condition, business, operations
or affairs of Brigham Exploration and its Subsidiaries taken as a whole or the
Borrower and its Subsidiaries taken as a whole, from those reflected in the
Financial Statements or from the facts represented or warranted in any Loan
Document, or (ii) the ability of Brigham Exploration or the Borrower or Brigham
Exploration or the Borrower and their respective Subsidiaries taken as a whole
to carry out their business as at the Closing Date or as proposed as of the
Closing Date to be conducted or meet their obligations under the Loan Documents
on a timely basis.

              "Maximum Credit Amount" shall mean, as to each Lender, the amount
set forth opposite such Lender's name on Annex I under the caption "Maximum
Credit Amounts" (as the same may be reduced pursuant to Section 2.03(b) hereof
as modified from time to time to reflect any assignments permitted by Sections
12.06(b) and (c) and any reallocation of the respective Maximum Credit Amounts
of the Lenders effected pursuant to Section 8.13.

              "Mortgage" shall mean, collectively, the mortgages referred to in
items [2, 12 and 13] of Exhibit D and any other Standard Mortgages executed
pursuant to Section 8.09(b) hereof and New Mortgages executed pursuant to
Section 8.09 (a) hereof.

              "Mortgaged Property" shall mean the Property owned by the Borrower
and which is subject to the Liens existing and to exist under the terms of the
Loan Documents.

              "Multiemployer Plan" shall mean a Plan defined as such in Section
3(37) or 4001(a)(3) of ERISA.

              "Net Seismic and Land Expenditures" shall mean those costs
incurred after the Closing Date for seismic services, seismic data, and
acquisition of undeveloped Hydrocarbon Interests, less the net proceeds, if any,
received after the Closing Date through the sale or licensing of interests in
undeveloped Hydrocarbon Interests and/or seismic data.

              "NSLE Limit" shall have the meaning set forth in Section 9.22(a).

              "New Mortgage" shall mean, collectively, the "New Mortgage"
referred to in item 13 of Exhibit D and any other mortgages and supplements
executed pursuant to Section 8.09 (a) hereof.

              "Notes" shall mean the Notes provided for by Section 2.06,
together with any and all renewals, extensions for any period, increases,
rearrangements, substitutions or modifications thereof.




                                       12
<PAGE>   19

              "Oil and Gas Properties" shall mean Hydrocarbon Interests; the
Properties now or hereafter pooled or unitized with Hydrocarbon Interests; all
presently existing or future unitization, pooling agreements and declarations of
pooled units and the units created thereby (including without limitation all
units created under orders, regulations and rules of any Governmental Authority)
which may affect all or any portion of the Hydrocarbon Interests; all operating
agreements, contracts and other agreements which relate to any of the
Hydrocarbon Interests or the production, sale, purchase, exchange or processing
of Hydrocarbons from or attributable to such Hydrocarbon Interests; all
Hydrocarbons in and under and which may be produced and saved or attributable to
the Hydrocarbon Interests, including all oil in tanks, the lands covered thereby
and all rents, issues, profits, proceeds, products, revenues and other incomes
from or attributable to the Hydrocarbon Interests; all tenements, hereditaments,
appurtenances and Properties in any manner appertaining, belonging, affixed or
incidental to the Hydrocarbon Interests; and all Properties, rights, titles,
interests and estates described or referred to above, including any and all
Property, real or personal, now owned or hereinafter acquired and situated upon,
used, held for use or useful in connection with the operating, working or
development of any of such Hydrocarbon Interests or Property (excluding drilling
rigs, automotive equipment or other personal property which may be on such
premises for the purpose of drilling a well or for other similar temporary uses)
and including any and all oil wells, gas wells, injection wells or other wells,
buildings, structures, fuel separators, liquid extraction plants, plant
compressors, pumps, pumping units, field gathering systems, tanks and tank
batteries, fixtures, valves, fittings, machinery and parts, engines, boilers,
meters, apparatus, appliances, tools, implements, cables, wires, towers, casing,
tubing and rods, similar equipment, surface leases, rights-of-way, easements and
servitudes together with all additions, substitutions, replacements, accessions
and attachments to any and all of the foregoing.

              "Other Taxes" shall have the meaning assigned such term in Section
4.06(b).

              "Partners" shall mean the General Partner, Brigham Holdings I, LLC
and Brigham Holdings II, LLC.

              "Partnership Agreement" shall mean the written partnership
agreement of the Borrower among the Partners dated December 30, 1997, as amended
from time to time.

              "PBGC" shall mean the Pension Benefit Guaranty Corporation or any
entity succeeding to any or all of its functions.

              "PDNP Reserves" shall mean proved, developed, non-producing
Hydrocarbon reserves, as determined in conformity with the guidelines in effect
from time to time as promulgated by the Society of Petroleum Engineers or its
successor association.

              "PDP Reserves" shall mean proved, developed, producing Hydrocarbon
reserves, as determined in conformity with the guidelines in effect from time to
time as promulgated by the Society of Petroleum Engineers or its successor
association.

              "Percentage Share" shall mean the percentage of the Aggregate
Commitments to be provided by a Lender under this Agreement as indicated on
Annex I hereto, as modified from




                                       13
<PAGE>   20

time to time to reflect any assignments permitted by Section 12.06(b) or (c) and
any reallocation effected pursuant to Section 8.13 hereof.

              "Person" shall mean any individual, corporation, company,
voluntary association, partnership, joint venture, trust, limited liability
company, unincorporated organization or government or any agency,
instrumentality or political subdivision thereof, or any other form of entity.

              "Plan" shall mean any employee pension benefit plan, as defined in
Section 3(2) of ERISA, which (i) is currently or hereafter sponsored, maintained
or contributed to by the Borrower, any Subsidiary or an ERISA Affiliate or (ii)
was at any time during the preceding six calendar years sponsored, maintained or
contributed to, by the Borrower, any Subsidiary or an ERISA Affiliate.

              "Post-Default Rate" shall mean, in respect of any principal of any
Loan or any other amount payable by the Borrower under this Agreement or any
Note, a rate per annum during the period commencing on the date of an Event of
Default until such amount is paid in full or all Events of Default are cured or
waived equal to 2% per annum above the Base Rate as in effect from time to time
plus the Applicable Margin (if any), but in no event to exceed the Highest
Lawful Rate provided that, for a Eurodollar Loan, the "Post-Default Rate" for
such principal shall be, for the period commencing on the date of an Event of
Default and ending on the earlier to occur of the last day of the Interest
Period therefor or the date all Events of Default are cured or waived, 2% per
annum above the interest rate for such Loan as provided in Section 3.02(ii), but
in no event to exceed the Highest Lawful Rate.

              "Prime Rate" shall mean the rate of interest from time to time
announced publicly by the Agent at the Principal Office as its prime commercial
lending rate. Such rate is set by the Agent as a general reference rate of
interest, taking into account such factors as the Agent may deem appropriate, it
being understood that many of the Agent's commercial or other loans are priced
in relation to such rate, that it is not necessarily the lowest or best rate
actually charged to any customer and that the Agent may make various commercial
or other loans at rates of interest having no relationship to such rate.

              "Principal Office" shall mean the principal office of the Agent,
presently located at 115 South LaSalle Street, Chicago, Illinois 60603.

              "Prior Mortgage" shall have the meaning assigned to such term in
the Mortgage.

              "Property" shall mean any interest in any kind of property or
asset, whether real, personal or mixed, or tangible or intangible.

              "Proved Reserves" means PDP, PDNP and PUD Reserves.

              "PUD Reserves" shall mean proved, undeveloped Hydrocarbon
reserves, as determined in conformity with the guidelines in effect from time to
time as promulgated by the Society of Petroleum Engineers or its successor
association.




                                       14
<PAGE>   21

              "PV7%" shall mean the present value, determined utilizing the SCI
Lenders' price forecast and applying the SCI Lenders reasonable adjustments
(positive or negative) to the engineering analysis prepared by Brigham
Exploration's independent reserve engineers or in-house reserve engineers,
whichever the case may be, of the forecasted future cash flow attributable to
the subject Hydrocarbon reserves, discounted at an annual rate of 7%.

              "Quarterly Dates" shall mean the last day of each March, June,
September, and December, in each year, the first of which shall be March 31,
2000; provided, however, that if any such day is not a Business Day, such
Quarterly Date shall be the next succeeding Business Day.

              "Regulation D" shall mean Regulation D of the Board of Governors
of the Federal Reserve System (or any successor), as the same may be amended or
supplemented from time to time.

              "Regulatory Change" shall mean, with respect to any Lender, any
change after the Closing Date in any Governmental Requirement (including
Regulation D) or the adoption or making after such date of any interpretations,
directives or requests applying to a class of lenders (including such Lender or
its Applicable Lending Office) of or under any Governmental Requirement (whether
or not having the force of law) by any Governmental Authority charged with the
interpretation or administration thereof.

              "Released Claims" shall mean any and all claims (including without
limitation any liabilities, damages, demands and causes of action arising
therefrom), whether (a) at law or in equity, (b) on the alleged commission of a
tort, (c) on the alleged breach (or anticipatory breach or repudiation) of any
contract, duty, or warranty (whether oral or written, express or implied), (d)
on the alleged violation of any statute, tariff, or regulation (whether
promulgated by the United States, any state thereof, any foreign state or
country, or any other governmental agency or entity, wherever located), or (e)
on any other factual, legal or equitable theory, including, without limitation,
any claim for damages of any type or nature, for injunctive or other relief, for
attorneys' fees, interest or any other liability whatsoever on any theory,
including without limitation any loss, cost or damage in connection with or
based upon "lender liability", unfair dealing, duress, coercion, control or
undue influence, extortion or commercial bribery, breach of an implied covenant
or duty of good faith and fair dealing, material misrepresentation or omission,
overreaching, unconscionability, conflict of interest, bad faith, malpractice,
disparate bargaining position, detrimental reliance, promissory estoppel,
estoppel by deed, waiver, laches, or any other equitable theory, equitable
subordination, breach of fiduciary duty or any other duty, or tortious
inducement to commit such breach, tortious interference with contract or
prospective business relations, negligent performance of contractual
obligations, or other theories of negligence, negligent or intentional
infliction of emotional distress, slander, libel, other defamation, fraudulent
transfer, conversion, trespass to (or clouding the title of) property, usury,
violations of the Racketeer Influenced and Corrupt Organizations Act, deceptive
trade practices, conspiracy, or any theory of liability as partners or joint
venturers, that any Releasing Party may have as of the date hereof against any
Released Party with respect to the Lending Relationship.




                                       15
<PAGE>   22

              "Released Party" shall mean each of the Agent, the Lenders and
their respective predecessors, successors, assigns, directors, officers,
partners, employees, agents, attorneys, principals and Affiliates and all other
Persons liable or who might be claimed to be liable on their behalf
(collectively, the "Released Parties").

              "Releasing Party" shall mean each of the Borrower and the
Guarantors and their respective predecessors, successors, assigns, directors,
officers, partners, employees, agents, attorneys, principals, Affiliates and all
other Persons who might have a claim against any Released Party (collectively,
the "Releasing Parties").

              "Required Payment" shall have the meaning assigned such term in
Section 4.04.

              "Reserve Report" shall mean a report, in form satisfactory to the
Agent, setting forth, as of the dates set forth in Section 8.07(a) and (b) (or
such other date in the event of an unscheduled redetermination); (i) the proved
oil and gas reserves attributable to the Borrower's and its Subsidiaries'
Hydrocarbon Interests together with a projection of the rate of production and
future net income, taxes, operating expenses and capital expenditures with
respect thereto as of such date, based upon the pricing assumptions consistent
with SEC reporting requirements at the time (or other pricing provided by the
Agent) and (ii) such other information as the Agent may reasonably request. The
term "Reserve Report" shall also include the Initial Reserve Report, the
supplemental Reserve Reports described in Section 8.07(a), and the information
to be provided by the Borrower of each year pursuant to Section 8.07(c).

              "Responsible Officer" shall mean, as to any Person, the Chief
Executive Officer, the President or any Vice President of such Person and the
Chief Financial Officer of such Person. Unless otherwise specified, all
references to a Responsible Officer herein shall mean a Responsible Officer of
the Borrower.

              "Revolving Credit Termination Date" shall mean, unless the
Commitments are sooner terminated pursuant to Sections 2.03(b) or 10.02 hereof,
December 31, 2002.

              "Risk Adjusted Proved Reserve Value" or "RAPRV" means the lesser
of (i) 100% of the PV7% of the Borrower's and any Guarantor's PDP Reserves, and
(ii) the sum of 65% of the PV7% of the Borrower's and any Guarantor's PDP
Reserves, plus 43% of the PV7% of the Borrower's and any Guarantor's PDNP
Reserves, plus 33% of the PV7% of the Borrower's and any Guarantor's PUD
Reserves. For purposes of this definition only Proved Reserves subject to a
Standard Mortgage shall be included.

              "Scheduled Asset Valuation Date" means each March 30th and
September 30th following the First Asset Valuation Date.

              "Scheduled Borrowing Base Redetermination Date" shall have the
meaning assigned such term in Section 2.08(d).

              "SCI Assignment" shall mean that certain Partial Assignment of
Notes between BMO, Soc-Gen and SCI of even date herewith.




                                       16
<PAGE>   23

              "SCI Fee Letter" shall mean that certain letter agreement from SCI
to the Borrower dated of even date with this Agreement concerning certain fees
in connection with this Agreement and any agreements or instruments executed in
connection therewith, as the same may be amended or replaced from time to time.

              "SCI Lenders" means SCI and its successors and assigns.

              "SCI Majority Lenders" shall mean, at any time while no Loans are
outstanding, SCI Lenders having at least sixty-six and two-thirds percent
(66-2/3%) of the Aggregate Commitments of the SCI Lenders and, at any time while
Loans are outstanding, SCI Lenders holding at least sixty-six and two-thirds
percent (66-2/3%) of the outstanding aggregate principal amount of the portion
of the Loans allocable to the SCI Lenders (without regard to any sale by a SCI
Lender of a participation in any Loan under Section 12.06(c)).

              "SEC" shall mean the Securities and Exchange Commission or any
successor Governmental Authority.

              "Securities Purchase Agreement" shall mean that certain Securities
Purchase Agreement dated August 20, 1998 among Brigham Exploration, ECT Merchant
and JEDI-II, as agent for such purchasers regarding the Subordinated Debt.

              "Soc-Gen Fee Letter" shall mean that certain letter agreement from
Soc-Gen to the Borrower dated of even date with this Agreement concerning
certain fees in connection with this Agreement and any agreements or instruments
executed in connection therewith, as the same may be amended or replaced from
time to time.

              "Special Entity" shall mean any joint venture, limited liability
company or partnership, general or limited partnership or any other type of
partnership or company other than a corporation in which a Person or one or more
of its other Subsidiaries is a member, owner, partner or joint venturer and
owns, directly or indirectly, at least a majority of the equity of such entity
or controls such entity, but excluding any tax partnerships that are not
classified as partnerships under state law. For purposes of this definition, any
Person which owns directly or indirectly an equity investment in another Person
which allows the first Person to manage or elect managers who manage the normal
activities of such second Person will be deemed to "control" such second Person
(e.g. a sole general partner controls a limited partnership).

              "Standard Mortgage" shall mean, collectively, the "Standard
Mortgage" referred to in item 12 of Exhibit D hereto and any other mortgages and
supplements executed pursuant to Section 8.09 (b) hereof.

              "Subordinated Debt" shall mean the Debt in the principal amount
not to exceed $40,000,000 (plus interest paid in kind through December 31, 2000
pursuant to Section 9.02 of the Indenture or otherwise satisfied through payment
of the Term ORRI) of Brigham Exploration incurred under the Indenture and
expressly subordinated to the Indebtedness pursuant to the Subordination
Agreement.




                                       17
<PAGE>   24

              "Subordination Agreement" shall mean that certain Intercreditor
and Subordination Agreement dated as of August 20, 1998, and from time to time
amended, among ENA, JEDI-II and Agent, for the benefit of the Lenders.

              "Subsidiary" shall mean (i) any corporation of which at least a
majority of the outstanding shares of stock having by the terms thereof ordinary
voting power to elect a majority of the board of directors of such corporation
(irrespective of whether or not at the time stock of any other class or classes
of such corporation shall have or might have voting power by reason of the
happening of any contingency) is at the time directly or indirectly owned or
controlled by a Person or one or more of its Subsidiaries or by a Person and one
or more of its Subsidiaries and (ii) any Special Entity. Unless otherwise
indicated herein, each reference to the term "Subsidiary" shall mean a
Subsidiary of the Borrower. Quest Resources L.L.C. and Venture Acquisitions L.P.
shall not be considered Subsidiaries of Borrower or Brigham Exploration.

              "Tangible Net Worth" shall mean, as at any date, the sum of the
following for Brigham Exploration and its Consolidated Subsidiaries determined
(without duplication) in accordance with GAAP (determined without regard to any
write up or write down resulting from any changes in GAAP subsequent to
September 30, 1999):

                     (i)    the amount of preferred stock and common stock at
                            par plus the amount of surplus of Brigham
                            Exploration, plus

                     (ii)   the retained earnings (or, in the case of retained
                            earnings deficit, minus the amount of such deficit),
                            minus

                     (iii)  the sum of the following: cost of treasury shares
                            and the book value of all assets of Brigham
                            Exploration and its Consolidated Subsidiaries which
                            should be classified as intangibles (without
                            duplication of deductions in respect of items
                            already deducted in arriving at surplus and retained
                            earnings) but in any event including as such
                            intangibles the following: goodwill, research and
                            development costs, trademarks, trade names,
                            copyrights, patents and franchises, unamortized debt
                            discount and expense, all reserves and any writeup
                            in the book value of assets resulting from a
                            revaluation thereof.

              "Target Asset Value" has the meaning assigned to it in Section
8.13.

              "Taxes" shall have the meaning assigned such term in Section
4.06(a).

              "Term ORRI" means the term overriding royalty interest created in
favor of the holders of the Subordinated Debt pursuant to a Conveyance of
Adjustable Term Overriding Royalty Interest between Borrower, ECT Merchant and
JEDI-II.

              "Trade Payables" shall mean customary trade payables incurred in
the ordinary course of business.




                                       18
<PAGE>   25

              "Type" shall mean, with respect to any Loan, a Base Rate Loan or a
Eurodollar Loan.

              "Wholly-Owned Subsidiary" shall mean, as to a Person, any
Subsidiary of which all of the outstanding shares of stock (or other ownership
interests) having by the terms thereof ordinary voting power to elect the board
of directors (or other managing persons) of such entity, other than directors'
qualifying shares, are owned or controlled by such Person or one or more of the
Wholly-Owned Subsidiaries or by such Person and one or more of the Wholly-Owned
Subsidiaries.

              Section 1.03 Accounting Terms and Determinations. Unless otherwise
specified herein, all accounting terms used herein shall be interpreted, all
determinations with respect to accounting matters hereunder shall be made, and
all financial statements and certificates and reports as to financial matters
required to be furnished to the Agent or the Lenders hereunder shall be
prepared, in accordance with GAAP, applied on a basis consistent with the
audited financial statements of the Borrower referred to in Section 7.02 (except
for changes concurred with by the Borrower's independent public accountants).

                                    ARTICLE 2

                                   COMMITMENTS

              Section 2.01 Loans.

                     (a) Loans. Subject to the SCI Assignment, each Lender
              severally agrees, on the terms of this Agreement, to make Loans to
              the Borrower during the period from and including (i) the Closing
              Date or (ii) such later date that such Lender becomes a party to
              this Agreement as provided in Section 12.06(b), to but excluding,
              the Revolving Credit Termination Date in an aggregate principal
              amount at any one time outstanding up to but not exceeding the
              amount of such Lender's Commitment as then in effect; provided,
              however, that the aggregate principal amount of all such Loans by
              all Lenders hereunder at any one time outstanding shall not exceed
              the Aggregate Commitments; and provided further, that the
              BMO/Soc-Gen Lenders shall not be obligated to make any such Loans
              other than the initial Loans. Subject to the terms of this
              Agreement, during the period from the Closing Date to (i) the
              later to occur of the First Borrowing Base Determination Date and
              the date on which the outstanding Loans are less than or equal to
              the Borrowing Base, no principal amount of the Loans which are
              paid by Borrower may be reborrowed, and (ii) at any time
              thereafter to but excluding, the Revolving Credit Termination
              Date, the Borrower may borrow, repay and reborrow the amount
              described in this Section 2.01(a). The initial Loans hereunder
              shall be a rearrangement of the principal balance outstanding on
              the Prior Notes (as adjusted pursuant to the SCI Assignment) which
              shall be concurrently therewith rearranged as an advance under the
              Notes. Each of the SCI Lenders and Brigham Exploration may, at its
              option, call for an Equity Conversion, pursuant and subject to the
              terms and provisions set forth in the Equity Conversion Agreement
              without the consent of the BMO/Soc-Gen Lenders.




                                       19
<PAGE>   26

                     (b) Intentionally Left Blank

                     (c) Limitation on Types of Loans. Subject to the other
              terms and provisions of this Agreement, at the option of the
              Borrower, the Loans may be Base Rate Loans or Eurodollar Loans;
              provided that, without the prior written consent of the Majority
              Lenders, no more than six (6) Eurodollar Loans may be outstanding
              at any time from any Lender.

              Section 2.02 Borrowings, Continuations and Conversions.

                     (a) Borrowings. The Borrower shall give the Agent (which
              shall promptly notify the Lenders) advance notice as hereinafter
              provided of each borrowing hereunder, which shall specify the
              aggregate amount of such borrowing, the Type and the date (which
              shall be a Business Day) of the Loans to be borrowed and (in the
              case of Eurodollar Loans) the duration of the Interest Period
              therefor.

                     (b) Minimum Amounts. If the initial borrowing consists in
              whole or in part of Eurodollar Loans, such Eurodollar Loans shall
              be in amounts of at least $1,000,000 or any whole multiple of
              $1,000,000 in excess thereof. Eurodollar Loans, at Borrower's
              election, shall have a maturity date of 30, 60 or 90 days.

                     (c) Notices. All borrowings, continuations and conversions
              shall require advance written notice to the Agent (which shall
              promptly notify the Lenders) in the form of Exhibit B hereto (or
              telephonic notice promptly confirmed by such a written notice),
              which in each case shall be irrevocable, from the Borrower to be
              received by the Agent not later than 11:00 a.m. Houston, Texas
              time at least one Business Day prior to the date of each Base Rate
              Loan borrowing and three Business Days prior to the date of each
              Eurodollar Loan borrowing, continuation or conversion; provided,
              however, for Base Rate Loans, Borrower may request a same day
              advance of up to $5,000,000 if the request is received by the
              Agent not later than 11:00 a.m. on such day. Without in any way
              limiting the Borrower's obligation to confirm in writing any
              telephonic notice, the Agent may act without liability upon the
              basis of telephonic notice believed by the Agent in good faith to
              be from the Borrower prior to receipt of written confirmation. In
              each such case, the Borrower hereby waives the right to dispute
              the Agent's record of the terms of such telephonic notice except
              in the case of gross negligence or willful misconduct by the
              Agent.

                     (d) Continuation Options. Subject to the provisions made in
              this Section 2.02(d), the Borrower may elect to continue all or
              any part of any Eurodollar Loan beyond the expiration of the then
              current Interest Period relating thereto by giving advance notice
              as provided in Section 2.02(c) to the Agent (which shall promptly
              notify the Lenders) of such election, specifying the amount of
              such Loan to be continued and the Interest Period therefor. In the
              absence of such a timely and proper election, the Borrower shall
              be deemed to have elected to convert such Eurodollar Loan to a
              Base Rate Loan pursuant to Section 2.02(e). Unless the Borrowing
              Base is not equal to or greater than the outstanding




                                       20
<PAGE>   27

              principal amount of the Loans, all or any part of any Eurodollar
              Loan may be continued as provided herein, provided that (i) any
              continuation of any such Loan shall be (as to each Loan as
              continued for an applicable Interest Period) in amounts of at
              least $1,000,000 or any whole multiple of $1,000,000 in excess
              thereof and (ii) no Default shall have occurred and be continuing.
              If a Default shall have occurred and be continuing, each
              Eurodollar Loan shall be converted to a Base Rate Loan on the last
              day of the Interest Period applicable thereto.

                     (e) Conversion Options. The Borrower may elect to convert
              all or any part of any Eurodollar Loan on the last day of the then
              current Interest Period relating thereto to a Base Rate Loan by
              giving advance notice to the Agent (which shall promptly notify
              the Lenders) of such election. Subject to the provisions made in
              this Section 2.02(e), the Borrower may elect to convert all or any
              part of any Base Rate Loan at any time and from time to time to a
              Eurodollar Loan by giving advance notice as provided in Section
              2.02(c) to the Agent (which shall promptly notify the Lenders) of
              such election. Unless the Borrowing Base is not equal to or
              greater than the outstanding principal amount of the Loans, all or
              any part of any outstanding Loan may be converted as provided
              herein, provided that (i) any conversion of any Base Rate Loan
              into a Eurodollar Loan shall be (as to each such Loan into which
              there is a conversion for an applicable Interest Period) in
              amounts of at least $1,000,000 or any whole multiple of $1,000,000
              in excess thereof and (ii) no Default shall have occurred and be
              continuing. If a Default shall have occurred and be continuing, no
              Base Rate Loan may be converted into a Eurodollar Loan.

                     (f) Advances. Not later than 11:00 a.m. Houston, Texas time
              on the date specified for each borrowing hereunder, each Lender
              shall make available the amount of the Loan to be made by it on
              such date to the Agent, to an account which the Agent shall
              specify, in immediately available funds for the account of the
              Borrower. The amounts so received by the Agent shall, subject to
              the terms and conditions of this Agreement, be made available to
              the Borrower by depositing the same, in immediately available
              funds, in an account of the Borrower, designated by the Borrower
              and maintained at the Principal Office.

              Section 2.03 Changes of Commitments.

                     (a) Prior to the Covenant Release Date, the Aggregate
              Commitments shall at all times be equal to the Aggregate Maximum
              Credit Amounts, after which date the Aggregate Commitments shall
              be equal to the lesser of (i) the Aggregate Maximum Credit Amounts
              or (ii) the Borrowing Base as determined from time to time.

                     (b) The Borrower shall have the right to terminate or to
              reduce the amount of the Aggregate Maximum Credit Amounts at any
              time or from time to time upon not less than three (3) Business
              Days' prior notice to the Agent (which shall promptly notify the
              Lenders) of each such termination or reduction, which notice shall
              specify the effective date thereof and the amount of any such
              reduction




                                       21
<PAGE>   28

              (which shall not be less than $5,000,000 or any whole multiple of
              $1,000,000 in excess thereof) and shall be irrevocable and
              effective only upon receipt by the Agent. Any such reduction in
              the Aggregate Maximum Credit Amounts shall first reduce the
              Maximum Credit Amounts of the BMO/Soc-Gen Lenders pro rata until
              the Maximum Credit Amounts of the BMO/Soc-Gen Lenders have been
              reduced to zero, and then to reduce the Maximum Credit Amounts of
              the SCI Lenders.

                     (c) The Aggregate Maximum Credit Amounts once terminated or
              reduced may not be reinstated.

              Section 2.04 Fees.

                     (a) Commitment Fee. The Borrower shall pay to the Agent (to
              be allocated to the SCI Lenders) a commitment fee on the daily
              average unused amount of the Aggregate Commitments for the period
              from and including the Closing Date up to but excluding the
              earlier of the date the Aggregate Commitments are terminated or
              the Revolving Credit Termination Date at a rate per annum equal to
              5/8 of 1%. Accrued commitment fees shall be payable quarterly in
              arrears on each Quarterly Date and on the earlier of the date the
              Aggregate Commitments are terminated or the Revolving Credit
              Termination Date.

                     (b) The Borrower shall pay to the SCI Lenders for their
              account such other fees as are set forth in the SCI Fee Letter on
              the dates specified therein to the extent not paid prior to the
              Closing Date.

                     (c) The Borrower shall pay to the Agent for its account
              such other fees as are set forth in the Agent's Fee Letter on the
              dates specified therein to the extent not paid prior to the
              Closing Date.

              Section 2.05 Several Obligations. The failure of any Lender to
make any Loan to be made by it on the date specified therefor shall not relieve
any other Lender of its obligation to make its Loan or provide funds on such
date, but no Lender shall be responsible for the failure of any other Lender to
make a Loan to be made by such other Lender or to provide funds to be provided
by such other Lender.

              Section 2.06 Notes. The Loans made by each Lender shall be
evidenced by a single promissory note of the Borrower in substantially the form
of Exhibit A hereto, dated (i) the Closing Date or (ii) the effective date of an
Assignment pursuant to Sections 12.06(b) and (c), payable to the order of such
Lender in a principal amount equal to its Maximum Credit Amount as in effect and
otherwise duly completed and such substitute Notes as required by Section
12.06(d). The initial advance under the Notes shall be the amount of the
principal balance on each Lender's Prior Note (as adjusted pursuant to the SCI
Assignment) plus $2,000,000.00 advanced by SCI. The date, amount, Type, interest
rate and Interest Period of each Loan made by each Lender, and all payments made
on account of the principal thereof, shall be recorded by such Lender on its
books for its Note, and, prior to any transfer, may be




                                       22
<PAGE>   29

endorsed by such Lender on a schedule attached to such Note or any continuation
thereof or on any separate record maintained by such Lender. Failure to make any
such notation or to attach a schedule shall not affect any Lender's or the
Borrower's rights or obligations in respect of such Loans or affect the validity
of such transfer by any Lender of its Note.

              Section 2.07 Prepayments.

                     (a) The Borrower may prepay the Base Rate Loans upon not
              less than one (1) Business Day's prior notice to the Agent (which
              shall promptly notify the Lenders), which notice shall specify the
              prepayment date (which shall be a Business Day) and the amount of
              the prepayment (which shall be at least $1,000,000 or the
              remaining aggregate principal balance outstanding on the Notes)
              and shall be irrevocable and effective only upon receipt by the
              Agent, provided that interest on the principal prepaid, accrued to
              the prepayment date, shall be paid on the prepayment date. The
              Borrower may prepay Eurodollar Loans on the same condition as for
              Base Rate Loans and in addition such prepayments of Eurodollar
              Loans shall be subject to the terms of Section 5.05.

                     (b) If, after giving effect to any termination or reduction
              of the Aggregate Maximum Credit Amounts pursuant to Section
              2.03(a) or (b), the outstanding aggregate principal amount of the
              Loans exceeds the Aggregate Maximum Credit Amounts, the Borrower
              shall prepay the Loans on the date of such termination or
              reduction in an aggregate principal amount equal to the excess,
              together with interest on the principal amount paid accrued to the
              date of such prepayment.

                     (c) Upon any redetermination of the amount of the Borrowing
              Base in accordance with Section 2.08, if the redetermined
              Borrowing Base is less than the aggregate outstanding principal
              amount of the Loans, then within ninety (90) days (or such shorter
              period as hereinafter provided) of receipt of written notice of
              the redetermined Borrowing Base, the Borrower shall prepay the
              Loans in an aggregate principal amount equal to such excess,
              together with interest on the principal amount paid accrued to the
              date of such prepayment, provided however, that if the Borrowing
              Base is less than the outstanding principal amount of the Loans
              following the first Borrowing Base determination, such required
              prepayment shall be made on or before thirty 30 days after such
              first Borrowing Base determination, as applicable, if the amount
              of the required payment equals or exceeds an amount equal to 10%
              of the redetermined Borrowing Base.

                     (d) Prepayments permitted or required under this Section
              2.07 shall be without premium or penalty, except as required under
              Section 5.05 for prepayment of Eurodollar Loans. Prior to the
              First Borrowing Base Determination Date, all prepayments on the
              Loans shall reduce the Aggregate Maximum Credit Amounts. Any
              payments on the Loans made hereunder shall first be applied to
              reduce the outstanding Loans of the BMO/Soc-Gen Lenders until the
              outstanding Loans of the BMO/Soc-Gen Lenders have been reduced to
              zero, and then to reduce the outstanding Loans of the SCI Lenders.




                                       23
<PAGE>   30

                     (e) Except as otherwise provided in Section 2.01(a), any
              prepayments on the Loans may, subject to the Equity Conversion
              Agreement, be reborrowed subject to the then effective Aggregate
              Commitments.

                     (f) Convertible Amounts (as defined in the Equity
              Conversion Agreement) can only be prepaid or repaid in cash upon
              approval of the BMO/Soc-Gen Lenders.

                     (g) Unless otherwise specified in this Section 2.07, all
              prepayments under this Section 2.07 shall be allocated among the
              Lenders by the Agent in accordance with the SCI Assignment.

              Section 2.08 Borrowing Base.

                     (a) The Borrowing Base shall be determined in accordance
              with Section 2.08(b) by the Agent with the concurrence of all of
              the Lenders and is subject to redetermination in accordance with
              Section 2.08(d). The first determination of the Borrowing Base
              shall be made on the First Borrowing Base Determination Date. Upon
              any determination or redetermination of the Borrowing Base, such
              determination shall remain in effect until the next successive
              Borrowing Base Redetermination Date. "Borrowing Base
              Redetermination Date" shall mean the date that the Borrowing Base
              as determined or redetermined becomes effective subject to the
              notice requirements specified in Section 2.08(e) both for the
              scheduled determination, scheduled redeterminations and
              unscheduled redeterminations. After the First Borrowing Base
              Determination Date, so long as any of the Commitments are in
              effect or any Loans are outstanding hereunder, this facility shall
              be governed by the then effective Borrowing Base.

                     (b) Upon receipt of the reports required by Section 8.07
              and such other reports, data and supplemental information as may
              from time to time be reasonably requested by the Agent (the
              "Engineering Reports"), the Agent will determine or redetermine,
              as appropriate, the Borrowing Base and shall take into
              consideration, among other things, liquidity, market interest
              rates, other Debt, Trade Payables, general and administrative
              expenses and such other factors as the Lenders shall deem
              material. Such determination or redetermination will be in
              accordance with its normal and customary procedures for evaluating
              oil and gas reserves and other related assets as such exist at
              that particular time. The Agent, in its sole discretion, may make
              adjustments to the rates, volumes and prices and other assumptions
              set forth therein in accordance with its normal and customary
              procedures for evaluating oil and gas reserves and other related
              assets as such exist at that particular time. The Agent shall
              propose to the Lenders a Borrowing Base within ten (10) days
              following receipt by the Agent and the Lenders of the Engineering
              Reports in a timely and complete manner. After having received
              notice of such proposal by the Agent, the Lenders shall have five
              (5) days to agree or disagree with such proposal. If at the end of
              the 5 days, any Lender has not communicated its approval or
              disapproval, such silence shall be deemed to be an




                                       24
<PAGE>   31

              approval. If the Lenders have not approved within 5 days, the
              Lenders shall, within a reasonable period of time, agree on a new
              Borrowing Base and if no such agreement is reached, the new
              Borrowing Base shall be the lowest calculated by the BMO/Soc-Gen
              Majority Lenders or the SCI Majority Lenders. The Agent and all of
              the Lenders must approve the initial Borrowing Base and any
              increase in the Borrowing Base. The Majority Lenders (one of which
              must be the Agent) shall be required to approve a continuation or
              decrease in any Borrowing Base.

                     (c) The Agent may exclude any Oil and Gas Property or
              portion of production therefrom or any income from any other
              Property from the Borrowing Base, at any time, because title
              information is not reasonably satisfactory, such Property is not
              Mortgaged Property or such Property is not assignable. No Property
              of the Borrower subject to the New Mortgage nor any production or
              income therefrom shall be included in the Borrowing Base until
              such time as an amendment or supplement to the New Mortgage in
              form satisfactory to the Agent is filed of record, which shall
              contain with respect to such Property such representations,
              warranties and covenants as to title, defense of title, revenue
              and cost bearing interest, rentals paid and leases in effect, and
              such other provisions as are contained in the Standard Mortgage,
              as the Agent may request.

                     (d) So long as any of the Commitments are in effect and
              until payment in full of all Loans hereunder, on the First
              Borrowing Base Determination Date and on or around the 30th
              calendar day of each March and September, thereafter (each being a
              "Scheduled Borrowing Base Redetermination Date"), the Lenders
              shall determine or redetermine, as appropriate, the amount of the
              Borrowing Base in accordance with Section 2.08(b). In addition,
              each of the Majority Lenders and the Borrower may initiate a
              redetermination of the Borrowing Base during any consecutive
              twelve (12) month period after the First Borrowing Base
              Determination Date by specifying in writing the date on which such
              redetermination is to occur, and Borrower may initiate the initial
              determination of the Borrowing Base at any time prior to March 30,
              2002, by specifying in writing the date on which such
              determination is to occur.

                     (e) The Agent shall promptly notify in writing the Borrower
              and the Lenders of the Borrowing Base as determined or
              redetermined. Any determination of the Borrowing Base shall not be
              in effect until written notice is received by the Borrower.

              Section 2.09 Lending Offices. The Loans of each Type made by each
Lender shall be made and maintained at such Lender's Applicable Lending Office
for Loans of such Type.




                                       25
<PAGE>   32

                                   ARTICLE 3

                       PAYMENTS OF PRINCIPAL AND INTEREST

              Section 3.01 Repayment of Loans. On the Revolving Credit
Termination Date the Borrower shall repay the outstanding aggregate principal
and accrued and unpaid interest under the Notes.

              Section 3.02 Interest. The Borrower will pay to the Agent, for the
account of each Lender, interest on the unpaid principal amount of each Loan
made by such Lender for the period commencing on the date such Loan is made to
but excluding the date such Loan shall be paid in full, at the following rates
per annum:

                     (i)    if such a Loan is a Base Rate Loan, the Base Rate
                            (as in effect from time to time) plus the Applicable
                            Margin (as in effect from time to time), but in no
                            event to exceed the Highest Lawful Rate; and

                     (ii)   if such a Loan is a Eurodollar Loan, for each
                            Interest Period (or portion thereof) relating
                            thereto, the Eurodollar Rate for such Loan plus the
                            Applicable Margin (as in effect from time to time),
                            but in no event to exceed the Highest Lawful Rate.

Notwithstanding the foregoing, the Borrower will pay to the Agent, for the
account of each Lender interest at the applicable Post-Default Rate on any
principal of any Loan made by such Lender, and (to the fullest extent permitted
by law) on any other amount payable by the Borrower hereunder, under any Loan
Document or under any Note held by such Lender to or for account of such Lender,
for the period commencing on the date of an Event of Default until the same is
paid in full or all such Events of Default are cured or waived.

              Accrued interest on Base Rate Loans shall be payable on the last
day of each calendar month, and accrued interest on each Eurodollar Loan shall
be payable on the last day of the Interest Period therefor and, if such Interest
Period is longer than one month at one-month intervals following the first day
of each Interest Period, except that interest payable at the Post-Default Rate
shall be payable from time to time on demand and interest on any Eurodollar Loan
that is converted into a Base Rate Loan (pursuant to Section 5.04) shall be
payable on the date of conversion (but only to the extent so converted).

              Promptly after the determination of any interest rate provided for
herein or any change therein, the Agent shall notify the Lenders to which such
interest is payable and the Borrower thereof. Each determination by the Agent of
an interest rate or fee hereunder shall be prima facie evidence of the amount
thereof.




                                       26
<PAGE>   33

                                   ARTICLE 4

                PAYMENTS; PRO RATA TREATMENT; COMPUTATIONS; ETC.

              Section 4.01 Payments. Except to the extent otherwise provided
herein, all payments of principal, interest and other amounts to be made by the
Borrower under the Loan Documents shall be made in Dollars, in immediately
available funds, to the Agent at such account as the Agent shall specify by
notice to the Borrower from time to time, not later than noon Houston, Texas
time on the date on which such payments shall become due (each such payment made
after such time on such due date to be deemed to have been made on the next
succeeding Business Day). Such payments shall be made without (to the fullest
extent permitted by applicable law) defense, set-off or counterclaim. Each
payment received by the Agent under this Agreement or any Note for account of a
Lender shall be paid promptly to such Lender in immediately available funds.
Except as provided in clause (iii) of the definition of "Interest Period", if
the due date of any payment under this Agreement or any Note would otherwise
fall on a day which is not a Business Day such date shall be extended to the
next succeeding Business Day and interest shall be payable for any principal so
extended for the period of such extension. At the time of each payment to the
Agent of any principal of or interest on any borrowing, the Borrower shall
notify the Agent of the Loans to which such payment shall apply. In the absence
of such notice the Agent may specify the Loans to which such payment shall
apply, but to the extent possible such payment or prepayment will be applied
first to the Loans comprised of Base Rate Loans.

              Section 4.02 Pro Rata Treatment. Except to the extent as provided
in the SCI Assignment or as otherwise provided herein each Lender agrees that:
(i) each borrowing from the Lenders under Section 2.01 and each continuation and
conversion under Section 2.02 shall be made from the Lenders pro rata in
accordance with their Percentage Share, each payment of commitment fee or other
fees under Sections 2.04(a) and (b) shall be made for account of the Lenders pro
rata in accordance with their Percentage Share, and each termination or
reduction of the amount of the Aggregate Maximum Credit Amounts under Section
2.03(b) shall be applied to the Commitment of each Lender, pro rata according to
the amounts of its respective Commitment; (ii) each payment of principal of
Loans by the Borrower shall be made for account of the Lenders pro rata in
accordance with the respective unpaid principal amount of the Loans held by the
Lenders; and (iii) each payment of interest on Loans by the Borrower shall be
made for account of the Lenders pro rata in accordance with the amounts of
interest due and payable to the respective Lenders.

              Section 4.03 Computations. Interest on Eurodollar Loans and fees
shall be computed on the basis of a year of 360 days and actual days elapsed
(including the first day but excluding the last day) occurring in the period for
which such interest is payable, unless such calculation would exceed the Highest
Lawful Rate, in which case interest shall be calculated on the per annum basis
of a year of 365 or 366 days, as the case may be. Interest on Base Rate Loans
shall be computed on the basis of a year of 365 or 366 days, as the case may be,
and actual days elapsed (including the first day but excluding the last day)
occurring in the period for which such interest is payable.




                                       27
<PAGE>   34

              Section 4.04 Non-receipt of Funds by the Agent. Unless the Agent
shall have been notified by a Lender or the Borrower prior to the date on which
such notifying party is scheduled to make payment to the Agent (in the case of a
Lender) of the proceeds of a Loan or (in the case of the Borrower) a payment to
the Agent for account of one or more of the Lenders hereunder (such payment
being herein called the "Required Payment"), which notice shall be effective
upon receipt, that it does not intend to make the Required Payment to the Agent,
the Agent may assume that the Required Payment has been made and may, in
reliance upon such assumption (but shall not be required to), make the amount
thereof available to the intended recipient(s) on such date and, if such Lender
or the Borrower (as the case may be) has not in fact made the Required Payment
to the Agent, the recipient(s) of such payment shall, on demand, repay to the
Agent the amount so made available together with interest thereon in respect of
each day during the period commencing on the date such amount was so made
available by the Agent until but excluding the date the Agent recovers such
amount at a rate per annum which, for any Lender as recipient, will be equal to
the Federal Funds Rate, and for the Borrower as recipient, will be equal to the
Base Rate plus the Applicable Margin.

              Section 4.05 Set-off, Sharing of Payments, Etc.

                     (a) The Borrower agrees that, in addition to (and without
              limitation of) any right of set-off, bankers' lien or counterclaim
              a Lender may otherwise have, each Lender shall have the right and
              be entitled (after consultation with the Agent), at its option, to
              offset balances held by it or by any of its Affiliates for account
              of the Borrower at any of its offices, in Dollars or in any other
              currency, against any principal of or interest on any of such
              Lender's Loans, or any other amount payable to such Lender
              hereunder, which is not paid when due (regardless of whether such
              balances are then due to the Borrower), in which case it shall
              promptly notify the Borrower and the Agent thereof, provided that
              such Lender's failure to give such notice shall not affect the
              validity thereof.

                     (b) If any Lender shall obtain payment of any principal of
              or interest on any Loan made by it to the Borrower under this
              Agreement through the exercise of any right of set-off, banker's
              lien or counterclaim or similar right or otherwise, and, as a
              result of such payment, such Lender shall have received a greater
              percentage of the principal or interest then due hereunder by the
              Borrower to such Lender than the percentage received by any other
              Lenders, it shall promptly (i) notify the Agent and each other
              Lender thereof and (ii) purchase from such other Lenders
              participations in (or, if and to the extent specified by such
              Lender, direct interests in) the Loans made by such other Lenders
              (or in interest due thereon, as the case may be) in such amounts,
              and make such other adjustments from time to time as shall be
              equitable, to the end that all the Lenders shall share the benefit
              of such excess payment (net of any expenses which may be incurred
              by such Lender in obtaining or preserving such excess payment) pro
              rata in accordance with the unpaid principal and/or interest on
              the Loans held by each of the Lenders. To such end all the Lenders
              shall make appropriate adjustments among themselves (by the resale
              of participations sold or otherwise) if such payment is rescinded
              or must otherwise be restored. The Borrower agrees that any Lender
              so purchasing a participation (or direct interest) in the Loans
              made by




                                       28
<PAGE>   35

              other Lenders (or in interest due thereon, as the case may be) may
              exercise all rights of set-off, banker's lien, counterclaim or
              similar rights with respect to such participation as fully as if
              such Lender were a direct holder of Loans in the amount of such
              participation. Nothing contained herein shall require any Lender
              to exercise any such right or shall affect the right of any Lender
              to exercise, and retain the benefits of exercising, any such right
              with respect to any other indebtedness or obligation of the
              Borrower. If under any applicable bankruptcy, insolvency or other
              similar law, any Lender receives a secured claim in lieu of a
              set-off to which this Section 4.05 applies, such Lender shall, to
              the extent practicable, exercise its rights in respect of such
              secured claim in a manner consistent with the rights of the
              Lenders entitled under this Section 4.05 to share the benefits of
              any recovery on such secured claim.

              Section 4.06 Taxes.

                     (a) Payments Free and Clear. Any and all payments by the
              Borrower hereunder shall be made, in accordance with Section 4
              .01, free and clear of and without deduction for any and all
              present or future taxes, levies, imposts, deductions, charges or
              withholdings, and all liabilities with respect thereto, excluding,
              in the case of each Lender and the Agent, taxes imposed on its
              income, and franchise or similar taxes imposed on it, by (i) any
              jurisdiction (or political subdivision thereof) of which the Agent
              or such Lender, as the case may be, is a citizen or resident or in
              which such Lender has an Applicable Lending Office, (ii) the
              jurisdiction (or any political subdivision thereof) in which the
              Agent or such Lender is organized, or (iii) any jurisdiction (or
              political subdivision thereof) in which such Lender or the Agent
              is presently doing business in which taxes are imposed solely as a
              result of doing business in such jurisdiction (all such
              non-excluded taxes, levies, imposts, deductions, charges,
              withholdings and liabilities being hereinafter referred to as
              "Taxes"). If the Borrower shall be required by law to deduct any
              Taxes from or in respect of any sum payable hereunder to the
              Lenders or the Agent (i) the sum payable shall be increased by the
              amount necessary so that after making all required deductions
              (including deductions applicable to additional sums payable under
              this Section 4.06) such Lender or the Agent (as the case may be)
              shall receive an amount equal to the sum it would have received
              had no such deductions been made, (ii) the Borrower shall make
              such deductions and (iii) the Borrower shall pay the full amount
              deducted to the relevant taxing authority or other Governmental
              Authority in accordance with applicable law.

                     (b) Other Taxes. In addition, to the fullest extent
              permitted by applicable law, the Borrower agrees to pay any
              present or future stamp or documentary taxes or any other excise
              or property taxes, charges or similar levies that arise from any
              payment made hereunder or from the execution, delivery or
              registration of, or otherwise with respect to, this Agreement, any
              Assignment or any other Loan Document (hereinafter referred to as
              "Other Taxes").




                                       29
<PAGE>   36

                     (c) INDEMNIFICATION. TO THE FULLEST EXTENT PERMITTED BY
              APPLICABLE LAW, THE BORROWER WILL INDEMNIFY EACH LENDER AND THE
              AGENT FOR THE FULL AMOUNT OF TAXES AND OTHER TAXES (INCLUDING, BUT
              NOT LIMITED TO, ANY TAXES OR OTHER TAXES IMPOSED BY ANY
              GOVERNMENTAL AUTHORITY ON AMOUNTS PAYABLE UNDER THIS SECTION 4.06)
              PAID BY SUCH LENDER OR THE AGENT (ON THEIR BEHALF OR ON BEHALF OF
              ANY LENDER), AS THE CASE MAY BE, AND ANY LIABILITY (INCLUDING
              PENALTIES, INTEREST AND EXPENSES) ARISING THEREFROM OR WITH
              RESPECT THERETO, WHETHER OR NOT SUCH TAXES OR OTHER TAXES WERE
              CORRECTLY OR LEGALLY ASSERTED UNLESS THE PAYMENT OF SUCH TAXES WAS
              NOT CORRECTLY OR LEGALLY ASSERTED AND SUCH LENDER'S PAYMENT OF
              SUCH TAXES OR OTHER TAXES WAS THE RESULT OF ITS GROSS NEGLIGENCE
              OR WILLFUL MISCONDUCT. ANY PAYMENT PURSUANT TO SUCH
              INDEMNIFICATION SHALL BE MADE WITHIN THIRTY (30) DAYS AFTER THE
              DATE ANY LENDER OR THE AGENT, AS THE CASE MAY BE, MAKES WRITTEN
              DEMAND THEREFOR. IF ANY LENDER OR THE AGENT RECEIVES A REFUND OR
              CREDIT IN RESPECT OF ANY TAXES OR OTHER TAXES FOR WHICH SUCH
              LENDER OR THE AGENT HAS RECEIVED PAYMENT FROM THE BORROWER IT
              SHALL PROMPTLY NOTIFY THE BORROWER OF SUCH REFUND OR CREDIT AND
              SHALL, IF NO DEFAULT HAS OCCURRED AND IS CONTINUING, WITHIN THIRTY
              (30) DAYS AFTER RECEIPT OF A REQUEST BY THE BORROWER (OR PROMPTLY
              UPON RECEIPT, IF THE BORROWER HAS REQUESTED APPLICATION FOR SUCH
              REFUND OR CREDIT PURSUANT HERETO), PAY AN AMOUNT EQUAL TO SUCH
              REFUND OR CREDIT TO THE BORROWER WITHOUT INTEREST (BUT WITH ANY
              INTEREST SO REFUNDED OR CREDITED), PROVIDED THAT THE BORROWER,
              UPON THE REQUEST OF SUCH LENDER OR THE AGENT, AGREES TO RETURN
              SUCH REFUND OR CREDIT (PLUS PENALTIES, INTEREST OR OTHER CHARGES)
              TO SUCH LENDER OR THE AGENT IN THE EVENT SUCH LENDER OR THE AGENT
              IS REQUIRED TO REPAY SUCH REFUND OR CREDIT.

                     (d) Lender Representations.

                     (i)    Each Lender represents that it is either (1) a
                            corporation or banking association organized under
                            the laws of the United States of America or any
                            state thereof or (2) it is entitled to complete
                            exemption from United States withholding tax imposed
                            on or with respect to any payments, including fees,
                            to be made to it pursuant to this Agreement (A)
                            under an applicable provision of a tax convention to
                            which the United States of America is a party or (B)
                            because it is acting through a branch, agency or
                            office in the




                                       30
<PAGE>   37

                            United States of America and any payment to be
                            received by it hereunder is effectively connected
                            with a trade or business in the United States of
                            America. Each Lender that is not a corporation or
                            banking association organized under the laws of the
                            United States of America or any state thereof agrees
                            to provide to the Borrower and the Agent on the
                            Closing Date, or on the date of its delivery of the
                            Assignment pursuant to which it becomes a Lender,
                            and at such other times as required by United States
                            law or as the Borrower or the Agent shall reasonably
                            request, two accurate and complete original signed
                            copies of either (A) Internal Revenue Service Form
                            4224 (or successor form) certifying that all
                            payments to be made to it hereunder will be
                            effectively connected to a United States trade or
                            business (the "Form 4224 Certification") or (B)
                            Internal Revenue Service Form 1001 (or successor
                            form) certifying that it is entitled to the benefit
                            of a provision of a tax convention to which the
                            United States of America is a party which completely
                            exempts from United States withholding tax all
                            payments to be made to it hereunder (the "Form 1001
                            Certification"). In addition, each Lender agrees
                            that if it previously filed a Form 4224
                            Certification, it will deliver to the Borrower and
                            the Agent a new Form 4224 Certification prior to the
                            first payment date occurring in each of its
                            subsequent taxable years; and if it previously filed
                            a Form 1001 Certification, it will deliver to the
                            Borrower and the Agent a new certification prior to
                            the first payment date falling in the third year
                            following the previous filing of such certification.
                            Each Lender also agrees to deliver to the Borrower
                            and the Agent such other or supplemental forms as
                            may at any time be required as a result of changes
                            in applicable law or regulation in order to confirm
                            or maintain in effect its entitlement to exemption
                            from United States withholding tax on any payments
                            hereunder, provided that the circumstances of such
                            Lender at the relevant time and applicable laws
                            permit it to do so. If a Lender determines, as a
                            result of any change in either (i) a Governmental
                            Requirement or (ii) its circumstances, that it is
                            unable to submit any form or certificate that it is
                            obligated to submit pursuant to this Section 4.06,
                            or that it is required to withdraw or cancel any
                            such form or certificate previously submitted, it
                            shall promptly notify the Borrower and the Agent of
                            such fact. If a Lender is organized under the laws
                            of a jurisdiction outside the United States of
                            America, unless the Borrower and the Agent have
                            received a Form 1001 Certification or Form 4224
                            Certification satisfactory to them indicating that
                            all payments to be made to such Lender hereunder are
                            not subject to United States withholding tax, the
                            Borrower shall withhold taxes from such payments at
                            the applicable statutory rate. Each Lender agrees to
                            indemnify and hold harmless the Borrower or Agent,
                            as applicable,




                                       31
<PAGE>   38

                            from any United States taxes, penalties, interest
                            and other expenses, costs and losses incurred or
                            payable by (i) the Agent as a result of such
                            Lender's failure to submit any form or certificate
                            that it is required to provide pursuant to this
                            Section 4.06 or (ii) the Borrower or the Agent as a
                            result of their reliance on any such form or
                            certificate which such Lender has provided to them
                            pursuant to this Section 4.06.

                     (ii)   For any period with respect to which a Lender has
                            failed to provide the Borrower with the form
                            required pursuant to this Section 4.06, if any,
                            (other than if such failure is due to a change in a
                            Governmental Requirement occurring subsequent to the
                            date on which a form originally was required to be
                            provided), such Lender shall not be entitled to
                            indemnification under Section 4.06 with respect to
                            taxes imposed by the United States which taxes would
                            not have been imposed but for such failure to
                            provide such forms; provided, however, that should a
                            Lender, which is otherwise exempt from or subject to
                            a reduced rate of withholding tax becomes subject to
                            taxes because of its failure to deliver a form
                            required hereunder, the Borrower shall take such
                            steps as such Lender shall reasonably request to
                            assist such Lender to recover such taxes.

                     (iii)  Any Lender claiming any additional amounts payable
                            pursuant to this Section 4.06 shall use reasonable
                            efforts (consistent with legal and regulatory
                            restrictions) to file any certificate or document
                            requested by the Borrower or the Agent or to change
                            the jurisdiction of its Applicable Lending Office or
                            to contest any tax imposed if the making of such a
                            filing or change or contesting such tax would avoid
                            the need for or reduce the amount of any such
                            additional amounts that may thereafter accrue and
                            would not, in the sole determination of such Lender,
                            be otherwise disadvantageous to such Lender.

                                   ARTICLE 5

                                CAPITAL ADEQUACY

              Section 5.01 Additional Costs.

                     (a) Eurodollar Regulations, etc. The Borrower shall pay
              directly to each Lender from time to time such amounts as such
              Lender may determine to be necessary to compensate such Lender for
              any costs which it determines are attributable to its making or
              maintaining of any Eurodollar Loans hereunder or its obligation to
              make any Eurodollar Loans hereunder, or any reduction in any
              amount receivable by such Lender hereunder in respect of any of
              such Eurodollar Loans or such obligation (such increases in costs
              and reductions in amounts




                                       32
<PAGE>   39

              receivable being herein called "Additional Costs"), resulting from
              any Regulatory Change which: (i) changes the basis of taxation of
              any amounts payable to such Lender under this Agreement or any
              Note in respect of any of such Eurodollar Loans (other than taxes
              described as excluded under Section 4.06(a)); or (ii) imposes or
              modifies any reserve, special deposit, minimum capital, capital
              ratio or similar requirements relating to any extensions of credit
              or other assets of, or any deposits with or other liabilities of
              such Lender, or the Commitment or Loans of such Lender or the
              Eurodollar interbank market; or (iii) imposes any other condition
              affecting this Agreement or any Note (or any of such extensions of
              credit or liabilities) or such Lender's Commitment or Loans. Each
              Lender will notify the Agent and the Borrower of any event
              occurring after the Closing Date which will entitle such Lender to
              compensation pursuant to this Section 5.01(a) as promptly as
              practicable after it obtains knowledge thereof and determines to
              request such compensation, and will designate a different
              Applicable Lending Office for the Loans of such Lender affected by
              such event if such designation will avoid the need for, or reduce
              the amount of, such compensation and will not, in the reasonable
              opinion of such Lender, be disadvantageous to such Lender,
              provided that such Lender shall have no obligation to so designate
              an Applicable Lending Office located in the United States. If any
              Lender requests compensation from the Borrower under this Section
              5.01(a), the Borrower may, by notice to such Lender, suspend the
              obligation of such Lender to make additional Loans of the Type
              with respect to which such compensation is requested until the
              Regulatory Change giving rise to such request cease to be in
              effect (in which case the provisions of Section 5.04 shall be
              applicable).

                     (b) Regulatory Change. Without limiting the effect of the
              provisions of Section 5.01(a), in the event that, by reason of any
              Regulatory Change or any other circumstances arising after the
              Closing Date affecting such Lender, the Eurodollar interbank
              market or such Lender's position in such market, any Lender either
              (i) incurs Additional Costs based on or measured by the excess
              above a specified level of the amount of a category of deposits or
              other liabilities of such Lender which includes deposits by
              reference to which the interest rate on Eurodollar Loans is
              determined as provided in this Agreement or a category of
              extensions of credit or other assets of such Lender which includes
              Eurodollar Loans or (ii) becomes subject to restrictions on the
              amount of such a category of liabilities or assets which it may
              hold, then, if such Lender so elects by notice to the Borrower,
              the obligation of such Lender to make additional Eurodollar Loans
              shall be suspended until such Regulatory Change or other
              circumstances cease to be in effect (in which case the provisions
              of Section 5.04 shall be applicable).

                     (c) Capital Adequacy. Without limiting the effect of the
              foregoing provisions of this Section 5.01 (but without
              duplication), the Borrower shall pay directly to any Lender from
              time to time on request such amounts as such Lender may reasonably
              determine to be necessary to compensate such Lender or its parent
              or holding company for any costs which it determines are
              attributable to the maintenance by such Lender or its parent or
              holding company (or any Applicable Lending Office), pursuant to
              any Governmental Requirement resulting




                                       33
<PAGE>   40

              from any Regulatory Change, of capital in respect of its
              Commitment, its Note or its Loans, such compensation to include,
              without limitation, an amount equal to any reduction of the rate
              of return on assets or equity of such Lender or its parent or
              holding company (or any Applicable Lending Office) to a level
              below that which such Lender or its parent or holding company (or
              any Applicable Lending Office) could have achieved but for such
              Regulatory Change. Such Lender will notify the Borrower that it is
              entitled to compensation pursuant to this Section 5.01(c) as
              promptly as practicable after it determines to request such
              compensation.

                     (d) Compensation Procedure. Any Lender notifying the
              Borrower of the incurrence of additional costs under this Section
              5.01 shall in such notice to the Borrower and the Agent set forth
              in reasonable detail the basis and amount of its request for
              compensation. Determinations and allocations by each Lender for
              purposes of this Section 5.01 of the effect of any Regulatory
              Change pursuant to Section 5.01(a) or (b), or of the effect of
              capital maintained pursuant to Section 5.01(c), on its costs or
              rate of return of maintaining Loans or its obligation to make
              Loans or on amounts receivable by it in respect of Loans, and of
              the amounts required to compensate such Lender under this Section
              5.01, shall be conclusive and binding for all purposes, provided
              that such determinations and allocations are made on a reasonable
              basis. Any request for additional compensation under this Section
              5.01 shall be paid by the Borrower within thirty (30) days of the
              receipt by the Borrower of the notice described in this Section
              5.01(d).

              Section 5.02 Limitation on Eurodollar Loans. Anything herein to
the contrary notwithstanding, if, on or prior to the determination of any
Eurodollar Rate for any Interest Period:

                     (a) the Agent determines (which determination shall be
              conclusive, absent manifest error) that quotations of interest
              rates for the relevant deposits referred to in the definition of
              "Eurodollar Rate" in Section 1.02 are not being provided in the
              relevant amounts or for the relevant maturities for purposes of
              determining rates of interest for Eurodollar Loans as provided
              herein; or

                     (b) the Agent determines (which determination shall be
              conclusive, absent manifest error) that the relevant rates of
              interest referred to in the definition of "Eurodollar Rate" in
              Section 1.02 upon the basis of which the rate of interest for
              Eurodollar Loans for such Interest Period is to be determined are
              not sufficient to adequately cover the cost to the Lenders of
              making or maintaining Eurodollar Loans;

then the Agent shall give the Borrower prompt notice thereof, and so long as
such condition remains in effect, the Lenders shall be under no obligation to
make additional Eurodollar Loans.

              Section 5.03 Illegality. Notwithstanding any other provision of
this Agreement, in the event that it becomes unlawful for any Lender or its
Applicable Lending Office to honor




                                       34
<PAGE>   41

its obligation to make or maintain Eurodollar Loans hereunder, then such Lender
shall promptly notify the Borrower thereof and such Lender's obligation to make
Eurodollar Loans shall be suspended until such time as such Lender may again
make and maintain Eurodollar Loans (in which case the provisions of Section 5.04
shall be applicable).

              Section 5.04 Base Rate Loans Pursuant to Sections 5.01, 5.02 and
5.03. If the obligation of any Lender to make Eurodollar Loans shall be
suspended pursuant to Sections 5.01, 5.02 or 5.03 ("Affected Loans"), all
Affected Loans which would otherwise be made by such Lender shall be made
instead as Base Rate Loans (and, if an event referred to in Section 5.01(b) or
Section 5.03 has occurred and such Lender so requests by notice to the Borrower,
all Affected Loans of such Lender then outstanding shall be automatically
converted into Base Rate Loans on the date specified by such Lender in such
notice) and, to the extent that Affected Loans are so made as (or converted
into) Base Rate Loans, all payments of principal which would otherwise be
applied to such Lender's Affected Loans shall be applied instead to its Base
Rate Loans.

              Section 5.05 Compensation. The Borrower shall pay to each Lender
within thirty (30) days of receipt of written request of such Lender (which
request shall set forth, in reasonable detail, the basis for requesting such
amounts and which shall be conclusive and binding for all purposes provided that
such determinations are made on a reasonable basis), such amount or amounts as
shall compensate it for any loss, cost, expense or liability which such Lender
determines are attributable to:

                     (a) any payment, prepayment or conversion of a Eurodollar
              Loan properly made in accordance herewith by such Lender or the
              Borrower for any reason (including, without limitation, the
              acceleration of the Loans pursuant to Section 10.02) on a date
              other than the last day of the Interest Period for such Loan; or

                     (b) any failure by the Borrower for any reason (including
              but not limited to, the failure of any of the conditions precedent
              specified in Article VI to be satisfied) to borrow, continue or
              convert a Eurodollar Loan from such Lender on the date for such
              borrowing, continuation or conversion specified in the relevant
              notice given pursuant to Section 2.02(c).

Without limiting the effect of the preceding sentence, such compensation shall
include an amount equal to the excess, if any, of (i) the amount of interest
which would have accrued on the principal amount so paid, prepaid or converted
or not borrowed for the period from the date of such payment, prepayment or
conversion or failure to borrow to the last day of the Interest Period for such
Loan (or, in the case of a failure to borrow, the Interest Period for such Loan
which would have commenced on the date specified for such borrowing) at the
applicable rate of interest for such Loan provided for herein over (ii) the
interest component of the amount such Lender would have bid in the London
interbank market for Dollar deposits of leading banks in amounts comparable to
such principal amount and with maturities comparable to such period (as
reasonably determined by such Lender).




                                       35
<PAGE>   42

              Section 5.06 Replacement Lenders.

                     (a) If any Lender has notified the Borrower and the Agent
              of its incurring additional costs under Section 5.01 hereof or has
              required the Borrower to make payments for Taxes under Section
              4.06 hereof, then the Borrower may, unless such Lender has
              notified the Borrower and the Agent that the circumstances giving
              rise to such notice no longer apply, terminate, in whole but not
              in part, the Commitment of any Lender (other than the Agent) (the
              "Terminated Lender") at any time upon five (5) Business Days'
              prior written notice to the Terminated Lender and the Agent (such
              notice referred to herein as a "Notice of Termination").

                     (b) In order to effect the termination of the Commitment of
              the Terminated Lender, the Borrower shall: (i) obtain an agreement
              with one or more Lenders to increase their Commitment or
              Commitments and/or (ii) request any one or more other banking
              institutions to become parties to this Agreement in place and
              instead of such Terminated Lender and agree to accept a Commitment
              or Commitments; provided, however, that such one or more other
              banking institutions are reasonably acceptable to the Agent and
              become parties by executing an Assignment (the Lenders or other
              banking institutions that agree to accept in whole or in part the
              Commitment of the Terminated Lender being referred to herein as
              the "Replacement Lenders"), such that the aggregate increased
              and/or accepted Commitments of the Replacement Lenders under
              clauses (i) and (ii) above equal the Commitment of the Terminated
              Lender.

                     (c) The Notice of Termination shall include the name of the
              Terminated Lender, the date the termination will occur (the
              "Termination Date"), and the Replacement Lender or Replacement
              Lenders to which the Terminated Lender will assign its Commitment
              and, if there will be more than one Replacement Lender, the
              portion of the Terminated Lender's Commitment to be assigned to
              each Replacement Lender.

                     (d) On the Termination Date, (i) the Terminated Lender
              shall by execution and delivery of an Assignment assign its
              Commitment to the Replacement Lender or Replacement Lenders (pro
              rata, if there is more than one Replacement Lender, in proportion
              to the portion of the Terminated Lender's Commitment to be
              assigned to each Replacement Lender) indicated in the Notice of
              Termination and shall assign to the Replacement Lender or
              Replacement Lenders each of its Loans (if any) then outstanding,
              (ii) the Terminated Lender shall endorse its Note, payable without
              recourse, representation or warranty to the order of the
              Replacement Lender or Replacement Lenders (pro rata as aforesaid),
              (iii) the Replacement Lender or Replacement Lenders shall purchase
              the Note held by the Terminated Lender (pro rata as aforesaid) at
              a price equal to the unpaid principal amount thereof plus interest
              and facility and other fees accrued and unpaid to the Termination
              Date, and (iv) the Replacement Lender or Replacement Lenders will
              thereupon (pro rata as aforesaid) succeed to and be substituted in
              all respects for the Terminated Lender with like effect as if
              becoming a Lender pursuant to the




                                       36
<PAGE>   43

              terms of Section 12.06(b), and the Terminated Lender will have the
              rights and benefits of an assignor under Section 12.06(b). To the
              extent not in conflict, the terms of Section 12.06(b) shall
              supplement the provisions of this Section 5.06(d). For each
              assignment made under this Section 5.06, the Replacement Lender
              shall pay to the Agent the processing fee provided for in Section
              12.06(b). The Borrower will be responsible for the payment of any
              breakage costs associated with termination of the Terminated
              Lender, as set forth in Section 5.05.

                                   ARTICLE 6

                              CONDITIONS PRECEDENT

              Section 6.01 Initial Funding.

              The obligation of the Lenders to make the Initial Funding (which
shall include the rearrangement of the principal balance on the Prior Notes) is
subject to the receipt by the Agent and the Lenders of all fees payable pursuant
to Section 2.04 on or before the Closing Date and the receipt by the Agent of
the following documents and satisfaction of the other conditions provided in
this Section 6.01, each of which shall be satisfactory to the Agent in form and
substance:

                     (a) A certificate of the Secretary or an Assistant
              Secretary of each of Brigham Exploration, the General Partner and
              the manager of each other Guarantor setting forth (i) resolutions
              of its board of directors with respect to its authorization to
              execute and deliver the Loan Documents to which it is a party and
              to enter into the transactions contemplated in those documents,
              (ii) the officers (y) who are authorized to sign the Loan
              Documents to which it is a party and (z) who will, until replaced
              by another officer or officers duly authorized for that purpose,
              act as its representative for the purposes of signing documents
              and giving notices and other communications in connection with
              this Agreement and the transactions contemplated hereby, (iii)
              specimen signatures of its authorized officers, and (iv) its
              articles or certificate of incorporation and bylaws or operating
              agreement, certified as being true and complete. The Agent and the
              Lenders may conclusively rely on such certificate until the Agent
              receives notice in writing from the Borrower to the contrary.

                     (b) Certificates of the appropriate state agencies with
              respect to the existence, qualification and good standing of the
              Borrower and the Guarantors.

                     (c) A compliance certificate which shall be substantially
              in the form of Exhibit C-1, duly and properly executed by a
              Responsible Officer and dated as of the Closing Date.

                     (d) The Notes, duly completed and executed.

                     (e) The Loan Documents described on Exhibit D, duly
              completed and executed in sufficient number of counterparts for
              recording, if necessary, including the SCI Assignment, the New
              Mortgage and the Standard Mortgage.




                                       37
<PAGE>   44

                     (f) Execution and delivery of amendments to the
              Subordinated Debt documents and the Subordination Agreement,
              including the ratification of this transaction by the holders of
              the Subordinated Debt.

                     (g) An opinion of Thompson & Knight LLP, special counsel to
              the Borrower and the Guarantors in form reasonably satisfactory to
              the Agent.

                     (h) A certificate of insurance coverage of the Borrower
              evidencing that the Borrower is carrying insurance in accordance
              with Section 7.19 hereof.

                     (i) The Agent shall be reasonably satisfied with the
              environmental condition of the Mortgaged Properties.

                     (j) Appropriate UCC search certificates reflecting no prior
              liens or security interests.

                     (k) Borrower shall have submitted to the Lenders the
              projections of the Borrower reflecting projected Proved Reserves,
              based upon the Borrower's various categories of reserves and on
              the initial CAPEX Plan, which projections shall be satisfactory in
              form and substance to the SCI Lenders.

                     (l) Borrower shall have submitted to the Lenders the
              initial CAPEX Plan, which CAPEX Plan shall be satisfactory in form
              and substance to the SCI Lenders.

                     (m) Borrower shall have submitted to the Lenders the
              Hedging Agreements described on Schedule 7.20, which Hedging
              Agreements shall be satisfactory in form and substance to the
              Majority Lenders.

                     (n) Execution and delivery of the Agent's Fee Letter, the
              SCI Fee Letter and the Soc-Gen Fee Letter.

                     (o) Such other documents as the Agent or any Lender or
              special counsel to the Agent may reasonably request.

Notwithstanding the foregoing, the Borrower will deliver within thirty (30) days
after the Closing Date (i) the supplementary opinion to the opinion described in
6.01(g) above, (ii) this Agreement executed by Brigham Holdings I, LLC, (iii)
the First Amendment to Guaranty Agreement executed by Brigham Holdings I, LLC,
(iv) the Second Amendment to Security Agreement executed by Brigham Holdings I,
LLC, (v) this Agreement executed by Brigham Holdings II, LLC, (vi) the First
Amendment to Guaranty Agreement executed by Brigham Holdings II, LLC, (vii) the
Second Amendment to Security Agreement executed by Brigham Holdings II, LLC and
(viii) evidence that all other actions necessary, or in the opinion of Agent,
desirable to perfect and protect the security interests and liens granted
thereby have been taken. Failure to deliver the documents described above shall
constitute an "Event of Default" under this Agreement.




                                       38
<PAGE>   45

              Section 6.02 Initial, Subsequent Loans. The obligation of the
Lenders to purchase the Prior Notes and make Loans to the Borrower upon the
occasion of each borrowing hereunder (including the Initial Funding) is subject
to the further conditions precedent that, as of the date of such Loans and after
giving effect thereto:

                     (a) no Default shall have occurred and be continuing;

                     (b) no Material Adverse Effect shall have occurred and be
              continuing; and

                     (c) the representations and warranties made by the Borrower
              in Article VII and in the Loan Documents or by any Guarantor in
              any other Loan Document shall be true in all material respects on
              and as of the date of the making of such Loans with the same force
              and effect as if made on and as of such date and following such
              new borrowing, except to the extent such representations and
              warranties are expressly limited to an earlier date or the
              Majority Lenders may expressly consent in writing to the contrary.

              Each request for a borrowing by the Borrower hereunder shall
constitute a certification by the Borrower to the effect set forth in Section
6.02(c) (as of the date of such notice and, unless the Borrower otherwise
notifies the Agent prior to the date of and immediately following such
borrowing).

              Section 6.03 Conditions Precedent for the Benefit of Lenders. All
conditions precedent to the obligations of the Lenders to make any Loan are
imposed hereby solely for the benefit of the Lenders, and no other Person may
require satisfaction of any such condition precedent or be entitled to assume
that the Lenders will refuse to make any Loan in the absence of strict
compliance with such conditions precedent.

              Section 6.04 No Waiver. No waiver of any condition precedent shall
preclude the Agent or the Lenders from requiring such condition to be met prior
to making any subsequent Loan or preclude the Lenders from thereafter declaring
that a subsequent failure of the Borrower to satisfy such condition precedent
constitutes a Default.

                                   ARTICLE 7

                         REPRESENTATIONS AND WARRANTIES

              The Borrower represents and warrants to the Agent and the Lenders
that (each representation and warranty herein is given as of the Closing Date
and shall be deemed repeated and reaffirmed on the dates of each borrowing as
provided in Section 6.02):

              Section 7.01 Corporate Existence. The Borrower: (i) is a limited
partnership duly organized, legally existing and in good standing under the laws
of the jurisdiction of its formation; (ii) has all requisite power, and has all
material governmental licenses, authorizations, consents and approvals necessary
to own its assets and carry on its business as now being or as proposed to be
conducted; and (iii) is qualified to do business in all jurisdictions in which
the nature of the business conducted by it makes such qualification necessary
and where failure so to qualify would have a Material Adverse Effect.




                                       39
<PAGE>   46

              Section 7.02 Financial Condition. The audited consolidated balance
sheet of Brigham Exploration and its Consolidated Subsidiaries as at December
31, 1998 and the related consolidated statement of income, stockholders' equity
and cash flow of Brigham Exploration and its Consolidated Subsidiaries for the
fiscal year ended on said date, with the opinion thereon of Price Waterhouse
heretofore furnished to each of the Lenders and the unaudited consolidated
balance sheet of Brigham Exploration and its Consolidated Subsidiaries as at
September 30, 1999, and their related consolidated statements of income,
stockholders' equity and cash flow of Brigham Exploration and its Consolidated
Subsidiaries for the nine-month period ended on such date heretofore furnished
to the Agent, are complete and correct and fairly present the consolidated
financial condition of Brigham Exploration and its Consolidated Subsidiaries as
at said dates and the results of its operations for the fiscal year and the
nine-month period on said dates, all in accordance with GAAP, as applied on a
consistent basis (subject, in the case of the interim financial statements, to
normal year-end adjustments). Neither Brigham Exploration nor any Consolidated
Subsidiary has on the Closing Date any material Debt, Trade Payables, contingent
liabilities, liabilities for taxes, unusual forward or long-term commitments or
unrealized or anticipated losses from any unfavorable commitments, except as
referred to or reflected or provided for in the Financial Statements or in
Schedule 7.02. Since December 31, 1998, there has been no change or event having
a Material Adverse Effect, except as disclosed to the Lenders in writing. Since
the date of the Financial Statements, neither the business nor the Properties of
Brigham Exploration Consolidated Subsidiaries, taken as a whole, have been
materially and adversely affected as a result of any fire, explosion,
earthquake, flood, drought, windstorm, accident, strike or other labor
disturbance, embargo, requisition or taking of Property or cancellation of
contracts, permits or concessions by any Governmental Authority, riot,
activities of armed forces or acts of God or of any public enemy.

              Section 7.03 Litigation. Except as disclosed to the Lenders in
Schedule 7.03 hereto, at the Closing Date there is no litigation, legal,
administrative or arbitral proceeding, investigation or other action of any
nature pending or, to the knowledge of the Borrower threatened against or
affecting the Borrower or any Subsidiary which both (a) involves the possibility
of any judgment or liability against the Borrower or any Subsidiary not fully
covered by insurance (except for normal deductibles), and (b) would be more
likely than not to have a Material Adverse Effect.

              Section 7.04 No Breach. Neither the execution and delivery of the
Loan Documents, nor compliance with the terms and provisions hereof will
conflict with or result in a breach of, or require any consent which has not
been obtained as of the Closing Date under, the Partnership Agreement, the
respective charter or by-laws of any Subsidiary or any Governmental Requirement
or any material agreement or instrument to which the Borrower or any Subsidiary
is a party or by which it is bound or to which it or its Properties are subject,
or constitute a default under any such agreement or instrument, or result in the
creation or imposition of any Lien upon any of the material revenues or assets
of the Borrower or any Subsidiary pursuant to the terms of any such agreement or
instrument other than the Liens created by the Loan Documents.

              Section 7.05 Authority. The Borrower and each Subsidiary has all
necessary power and authority to execute, deliver and perform its obligations
under the Loan Documents to which it is a party; and the execution, delivery and
performance by the Borrower and each Subsidiary of the Loan Documents to which
it is a party, have been duly authorized by all




                                       40
<PAGE>   47

necessary action on its part; and the Loan Documents constitute the legal, valid
and binding obligations of the Borrower and each Subsidiary, enforceable in
accordance with their terms, except as such enforceability may be limited by
bankruptcy, insolvency, fraudulent transfer and similar laws affecting
creditors' rights generally or by general principles of equity.

              Section 7.06 Approvals. No authorizations, approvals or consents
of, and no filings or registrations with, any Governmental Authority are
necessary for the execution, delivery or performance by the Borrower or any
Subsidiary of the Loan Documents or for the validity or enforceability thereof.

              Section 7.07 Use of Loans. Subject to the terms and conditions
elsewhere herein, the proceeds of the Loans (other than those representing the
purchase price for the outstanding indebtedness under the Prior Credit
Agreement), shall be used to pay payables, provide additional drilling capital
and for general working capital purposes. In no event shall the proceeds of the
Loans be used to finance in whole or in part any hostile acquisition. The
Borrower is not engaged principally, or as one of its important activities, in
the business of extending credit for the purpose, whether immediate, incidental
or ultimate, of buying or carrying margin stock (within the meaning of
Regulation G, U or X of the Board of Governors of the Federal Reserve System)
and no part of the proceeds of any Loan hereunder will be used to buy or carry
any margin stock.

              Section 7.08 ERISA.

                     (a) The Borrower and each ERISA Affiliate have complied in
              all material respects with ERISA and, where applicable, the Code
              regarding each Plan.

                     (b) Each Plan is, and has been, maintained in substantial
              compliance with ERISA and, where applicable, the Code.

                     (c) No act, omission or transaction has occurred which
              could result in imposition on the Borrower or any ERISA Affiliate
              (whether directly or indirectly) of an amount of $100,000 or more
              as (i) either a civil penalty assessed pursuant to section 502(c),
              (i) or (1) of ERISA or a tax imposed pursuant to Chapter 43 of
              Subtitle D of the Code or (ii) breach of fiduciary duty liability
              damages under section 409 of ERISA.

                     (d) No Plan (other than a defined contribution plan) or any
              trust created under any such Plan has been terminated since
              September 2, 1974. No liability to the PBGC in excess of $100,000
              (other than for the payment of current premiums which are not past
              due) by the Borrower or any ERISA Affiliate has been or is
              expected by the Borrower or any ERISA Affiliate to be incurred
              with respect to any Plan. No ERISA Event with respect to any Plan
              has occurred which could reasonably be expected to result in
              liabilities of $100,000 or more.

                     (e) Full payment when due has been made of all amounts
              which the Borrower or any ERISA Affiliate is required under the
              terms of each Plan or applicable law to have paid as contributions
              to such Plan, and no accumulated funding deficiency in an amount
              of $100,000 or more (as defined in section 302




                                       41
<PAGE>   48

              of ERISA and section 412 of the Code), whether or not waived,
              exists with respect to any Plan.

                     (f) The actuarial present value of the benefit liabilities
              under each Plan which is subject to Title IV of ERISA does not, as
              of the end of the Borrower's most recently ended fiscal year,
              exceed the current value of the assets (computed on a plan
              termination basis in accordance with Title IV of ERISA) of such
              Plan allocable to such benefit liabilities by $100,000 or more.
              The term "actuarial present value of the benefit liabilities"
              shall have the meaning specified in section 4041 of ERISA.

                     (g) None of the Borrower or any ERISA Affiliate sponsors,
              maintains, or contributes to an employee welfare benefit plan, as
              defined in section 3(1) of ERISA, including, without limitation,
              any such plan maintained to provide benefits to former employees
              of such entities, that may not be terminated by the Borrower or
              any ERISA Affiliate in its sole discretion at any time without any
              material liability.

                     (h) None of the Borrower or any ERISA Affiliate sponsors,
              maintains or contributes to, or has at any time in the preceding
              six calendar years, sponsored, maintained or contributed to, any
              Multiemployer Plan.

                     (i) None of the Borrower or any ERISA Affiliate is required
              to provide security under section 401(a)(29) of the Code due to a
              Plan amendment that results in an increase in current liability
              for the Plan.

              Section 7.09 Taxes. Except as set out in Schedule 7.09, the
Borrower has filed all United States Federal income tax returns and all other
tax returns which are required to be filed by it and has paid all material taxes
due pursuant to such returns or pursuant to any assessment received by the
Borrower, except for any taxes which are being contested in good faith and by
proper proceedings and against which adequate reserves are being maintained. The
charges, accruals and reserves on the books of the Borrower in respect of taxes
and other governmental charges are, in the opinion of the Borrower, adequate. No
tax lien has been filed and, to the knowledge of the Borrower, no claim is being
asserted with respect to any such tax, fee or other charge, except for any
taxes, fees or other charges which are being contested in good faith and by
proper proceedings and against which adequate reserves are being maintained.

              Section 7.10 Titles, etc.

                     (a) Subject to the matters set out in Schedule 7.10, each
              of the Borrower and the Subsidiaries has good and defensible title
              to (i) the Oil and Gas Properties that are both evaluated (A) in
              the most recently delivered Reserve Report and (B) described in a
              Standard Mortgage, free and clear of all Liens except Liens
              permitted by Section 9.02, and (ii) to the best of Borrower's
              knowledge, the balance of Borrower's material (individually or in
              the aggregate) Oil and Gas Properties (and/or those of the
              Subsidiaries) that are described in any other Mortgage or that are
              otherwise evaluated in the most recently delivered Reserve




                                       42
<PAGE>   49

              Report, free and clear (to the best of Borrower's knowledge) of
              all Liens except Liens permitted by Section 9.02. Except for
              immaterial divergences, after giving full effect to the Excepted
              Liens and the matters set forth in Schedule 7.10, the Borrower
              owns the net interests in production attributable to the
              Hydrocarbon Interests that are both (A) evaluated in the most
              recently delivered Reserve Report and (b) reflected in a Standard
              Mortgage, and the ownership of such Hydrocarbon Interests shall
              not in any material respect obligate the Borrower to bear the
              costs and expenses relating to the maintenance, development and
              operations of each such Hydrocarbon Interest in an amount in
              excess of the working interest of such Hydrocarbon Interest set
              forth in a Standard Mortgage (without a corresponding increase in
              net revenue interest). The Borrower does not believe, based upon
              information in its possession, that its most recently delivered
              Reserve Report materially overstates its oil and gas reserves,
              bearing in mind that reserves are evaluated based upon estimates
              and assumptions with respect to which reasonable minds of
              competent reserve engineers may differ.

                     (b) All leases and agreements necessary for the conduct of
              the business of the Borrower and the Subsidiaries are valid and
              subsisting, in full force and effect and there exists no default
              or event or circumstance which with the giving of notice or the
              passage of time or both would give rise to a default under any
              such lease or leases, which would affect in any material respect
              the conduct of the business of the Borrower and the Subsidiaries.

                     (c) The Properties presently owned, leased or licensed by
              the Borrower and the Subsidiaries, including, without limitation,
              all easements and rights of way, include all Properties necessary
              to permit the Borrower and the Subsidiaries to conduct their
              business in all material respects in the same manner as its
              business has been conducted prior to the Closing Date.

                     (d) All of the Properties of the Borrower and the
              Subsidiaries which are reasonably necessary for the operation of
              their business are in good working condition in all material
              respects and are maintained in accordance with prudent business
              standards.

              Section 7.11 No Material Misstatements. Taken as a whole, the
written information, statements, exhibits, certificates, documents and reports
furnished to the Agent and the Lenders (or any of them) by the Borrower or any
Guarantor in connection with the negotiation of this Agreement do not contain
any material misstatement of fact or omit to state a material fact or any fact
necessary to make the statements contained therein not materially misleading in
the light of the circumstances in which made and with respect to the Borrower or
any Guarantor. As of the Closing Date, there is no fact peculiar to the Borrower
or Guarantor which has a Material Adverse Effect or in the future is reasonably
likely to have (so far as the Borrower can now foresee) a Material Adverse
Effect and which has not been set forth in this Agreement or the other
documents, certificates and statements furnished to the Agent by or on behalf of
the Borrower or any Guarantor prior to, or on, the Closing Date in connection
with the transactions contemplated hereby.




                                       43
<PAGE>   50

              Section 7.12 Investment Company Act. Neither the Borrower nor any
Subsidiary is an "investment company" or a company "controlled" by an
"investment company," within the meaning of the Investment Company Act of 1940,
as amended.

              Section 7.13 Public Utility Holding Company Act. Neither the
Borrower nor any Subsidiary is a "holding company," or a "subsidiary company" of
a "holding company," or an "affiliate" of a "holding company" or of a
"subsidiary company" of a "holding company," or a "public utility" within the
meaning of the Public Utility Holding Company Act of 1935, as amended.

              Section 7.14 Subsidiaries. Except as set forth on Schedule 7.14 or
as allowed by Section 9.16, the Borrower has no Subsidiaries.

              Section 7.15 Location of Business and Offices. As of the Closing
Date, the Borrower's principal place of business and chief executive offices are
located at the address stated on the signature page of this Agreement. The
principal place of business and chief executive office of each Subsidiary are
located at the addresses stated on Schedule 7.14.

              Section 7.16 Defaults. The Borrower is not in default nor has any
event or circumstance occurred which, but for the expiration of any applicable
grace period or the giving of notice, or both, would constitute a default under
any material agreement or instrument to which the Borrower is a party or by
which the Borrower is bound which default would have a Material Adverse Effect.
Brigham Exploration is not in default nor has any event or circumstance occurred
which, but for the expiration of any applicable grace period or the giving of
notice, or both, would constitute a default under any material agreement or
instrument related to the Subordinated Debt. No Default hereunder or under the
Subordinated Debt has occurred and is continuing or will result from the
execution, delivery and performance of this Agreement and the other Loan
Documents.

              Section 7.17 Environmental Matters. Except as provided in Schedule
7.17 or for matters which are more likely than not to not to have a Material
Adverse Effect (or with respect to (c), (d) and (e) below, where the failure to
take such actions is more likely than not to not have a Material Adverse
Effect):

                     (a) Neither any Property of Brigham Exploration or any of
              its Subsidiaries nor the operations conducted thereon violate any
              order or requirement of any court or Governmental Authority or any
              Environmental Laws;

                     (b) Without limitation of clause (a) above, no Property of
              Brigham Exploration or any of its Subsidiaries nor the operations
              currently conducted thereon or, to the best knowledge of the
              Borrower, by any prior owner or operator of such Property or
              operation, are in violation of or subject to any existing, pending
              or threatened action, suit, investigation, inquiry or proceeding
              by or before any court or Governmental Authority or to any
              remedial obligations under Environmental Laws;

                     (c) All notices, permits, licenses or similar
              authorizations, if any, required to be obtained or filed by the
              Borrower or any of its Subsidiaries in connection




                                       44
<PAGE>   51

              with the operation or use of any and all Property of Brigham
              Exploration and each of its Subsidiaries, including without
              limitation present, or to the best of Borrower's knowledge, past
              treatment, storage, disposal or release of a hazardous substance
              or solid waste into the environment, have been duly obtained or
              filed, and Brigham Exploration and each Subsidiary thereof are in
              compliance with the terms and conditions of all such notices,
              permits, licenses and similar authorizations;

                     (d) All hazardous substances, solid waste, and oil and gas
              exploration and production wastes, if any, generated at any and
              all Property of Brigham Exploration and each of its Subsidiaries
              have in the past, during Borrower's tenure of ownership and to the
              best of Borrower's knowledge, prior thereto, been transported,
              treated and disposed of in accordance with Environmental Laws and
              so as not to pose an imminent and substantial endangerment to
              public health or welfare or the environment, and, to the best
              knowledge of the Borrower, all such transport carriers and
              treatment and disposal facilities have been and are operating in
              compliance with Environmental Laws and so as not to pose an
              imminent and substantial endangerment to public health or welfare
              or the environment, and are not the subject of any existing,
              pending or threatened action, investigation or inquiry by any
              Governmental Authority in connection with any Environmental Laws;

                     (e) The Borrower has taken all steps reasonably necessary
              to determine and has determined that no hazardous substances,
              solid waste, or oil and gas exploration and production wastes,
              have been disposed of or otherwise released and there has been no
              threatened release of any hazardous substances on or to any
              Property of Brigham Exploration or any of its Subsidiaries except
              in compliance with Environmental Laws and so as not to pose an
              imminent and substantial endangerment to public health or welfare
              or the environment;

                     (f) To the extent applicable, all Property of Brigham
              Exploration and each of its Subsidiaries currently satisfies all
              design, operation, and equipment requirements imposed by the OPA
              or scheduled as of the Closing Date to be imposed by OPA during
              the term of this Agreement, and the Borrower does not have any
              reason to believe that such Property, to the extent subject to
              OPA, will not be able to maintain compliance with the OPA
              requirements during the term of this Agreement; and

                     (g) Neither Brigham Exploration nor any of its Subsidiaries
              has any known contingent liability in connection with any release
              or threatened release of any oil, hazardous substance or solid
              waste into the environment.

              Section 7.18 Compliance with the Law. Neither the Borrower nor any
Subsidiary has violated any Governmental Requirement or failed to obtain any
license, permit, franchise or other governmental authorization necessary for the
ownership of any of its Properties or the conduct of its business, which
violation or failure would have (in the event such violation or failure were
asserted by any Person through appropriate action) a Material Adverse




                                       45
<PAGE>   52

Effect. Except for such acts or failures to act as would not have a Material
Adverse Effect, the Oil and Gas Properties (and properties unitized therewith)
have been maintained, operated and developed in a good and workmanlike manner
and in conformity with all applicable laws and all rules, regulations and orders
of all duly constituted authorities having jurisdiction and in conformity with
the provisions of all leases, subleases or other contracts comprising a part of
the Hydrocarbon Interests and other contracts and agreements forming a part of
the Oil and Gas Properties; specifically in this connection, but subject to the
Material Adverse Effect qualification set forth above, (i) after the Closing
Date, no Oil and Gas Property is subject to having allowable production reduced
below the full and regular allowable (including the maximum permissible
tolerance) because of any overproduction (whether or not the same was
permissible at the time) prior to the Closing Date and (ii) none of the wells
comprising a part of the Oil and Gas Properties (or properties unitized
therewith) are deviated from the vertical more than the maximum permitted by
applicable laws, regulations, rules and orders, and such wells are, in fact,
bottomed under and are producing from, and the well bores are wholly within, the
Oil and Gas Properties (or in the case of wells located on properties unitized
therewith, such unitized properties).

              Section 7.19 Insurance. Schedule 7.19 attached hereto contains an
accurate and complete description of all material policies of fire, liability,
workmen's compensation and other forms of insurance owned or held by the
Borrower and each Subsidiary as of the Closing Date. Schedule 7.19 shall be
updated by the Borrower as appropriate from time to time and the representations
in this Section 7.19 shall apply to such updated Schedules. All such policies
are in full force and effect, all premiums with respect thereto covering all
periods up to and including the Closing Date have been paid, and no notice of
cancellation or termination has been received with respect to any such policy.
Such policies are sufficient for compliance with all requirements of law and of
all agreements to which the Borrower or any Subsidiary is a party; are valid,
outstanding and enforceable policies; provide adequate insurance coverage in at
least such amounts and against at least such risks (but including in any event
public liability) as are usually insured against in the same general area by
companies engaged in the same or a similar business for the assets and
operations of the Borrower and each Subsidiary; will remain in full force and
effect through the respective dates set forth in Schedule 7.19 without the
payment of additional premiums; and will not in any way be affected by, or
terminate or lapse by reason of, the transactions contemplated by this
Agreement. Schedule 7.19 identifies all material risks, if any, which the
General Partner of the Borrower, the Subsidiaries and their respective Board of
Directors or officers have designated as being self insured. Neither the
Borrower nor any Subsidiary has been refused any insurance with respect to its
assets or operations, nor has its coverage been limited below usual and
customary policy limits, by an insurance carrier to which it has applied for any
such insurance or with which it has carried insurance during the last three
years.

              Section 7.20 Hedging Agreements. Schedule 7.20 sets forth, as of
the Closing Date, a true and complete list of all Hedging Agreements (including
commodity price swap agreements, forward agreements or contracts of sale which
provide for prepayment for deferred shipment or delivery of oil, gas or other
commodities) of the Borrower and each Subsidiary, the material terms thereof
(including the type, term, effective date, termination date and notional amounts
or volumes), the net mark to market value thereof, all credit support agreements
relating




                                       46
<PAGE>   53

thereto (including any margin required or supplied), and the counterparty to
each such agreement.

              Section 7.21 Restriction on Liens. Neither the Borrower nor any
Subsidiary is a party to or subject to any agreement or arrangement (other than
the Loan Documents, the documents described in Section 4.01(a) through (d) of
the Indenture, the Indenture, and any other documents permitted under Section
9.02(f)), or subject to any order, judgment, writ or decree, which either
restricts or purports to restrict its ability to grant Liens to other Persons on
or in respect of their respective assets or Properties.

              Section 7.22 Material Agreements. Set forth on Schedule 7.22
hereto is a complete and correct list of all material agreements, leases,
indentures, purchase agreements, obligations in respect of letters of credit,
guarantees, joint venture agreements, and other instruments in effect or to be
in effect as of the Closing Date (other than Hedging Agreements) providing for,
evidencing, securing or otherwise relating to any material Debt of the Borrower
or any Subsidiary, and all obligations of the Borrower or any Subsidiary to
issuers of surety or appeal bonds (excluding operator's bonds, plugging and
abandonment bonds, and similar surety obligations obtained in the ordinary
course of business) issued for account of the Borrower or any such Subsidiary,
and such list correctly sets forth the names of the debtor or lessee and
creditor or lessor with respect to the Debt or lease obligations outstanding or
to be outstanding and the property subject to any Lien securing such Debt or
lease obligation.

              Section 7.23 Gas Imbalances. As of the Closing Date, except as set
forth in the most recent Reserve Report furnished to Agent or on Schedule 7.23
or on the most recent certificate delivered pursuant to Section 8.07(b), on a
net basis there are no gas imbalances, take or pay or other prepayments with
respect to the Borrower's or any Subsidiary's Hydrocarbon Interests which would
require the Borrower or such Subsidiary to deliver five percent (5%) or more of
the monthly production from the Borrower's and its Subsidiaries' Hydrocarbons
produced on a monthly basis from the Hydrocarbon Interests, at some future time
without then or thereafter receiving full payment therefor.

              Section 7.24 Partnership Agreement. The Partnership Agreement has
not been terminated, is in full force and effect as of the date hereof and no
default has occurred and is in continuance thereunder which would have a
Material Adverse Effect.

              Section 7.25 Prior Notes and Related Documents.

                     (a) The aggregate principal balance outstanding on the
              Prior Notes as of the Closing Date plus all accrued interest on
              the Prior Notes as of the Closing Date is $56,391,703.13.

                     (b) The Borrower has not assigned its rights or obligations
              under the Prior Notes or the Prior Credit Agreement.




                                       47
<PAGE>   54
                                   ARTICLE 8

                              AFFIRMATIVE COVENANTS

         The Borrower covenants and agrees that, so long as any of the
Commitments are in effect and until payment in full of all Indebtedness
hereunder, all interest thereon and all other amounts payable by the Borrower
hereunder:

         Section 8.01 Financial Statements and Other Reports. The Borrower shall
deliver, or shall cause to be delivered, to the Agent with sufficient copies of
each for the Lenders:

              (a) Annual Financial Statements. As soon as available and in any
         event within 90 days after the end of each fiscal year of Brigham
         Exploration, the audited consolidated statements of income,
         stockholders' equity, changes in financial position and cash flow of
         Brigham Exploration and its Consolidated Subsidiaries for such fiscal
         year, and the related consolidated and unaudited consolidating balance
         sheets of Brigham Exploration and its Consolidated Subsidiaries as at
         the end of such fiscal year, and setting forth in each case in
         comparative form the corresponding figures for the preceding fiscal
         year, and accompanied by the related opinion of independent public
         accountants of recognized national standing acceptable to the Agent
         which opinion shall state that said financial statements fairly present
         the consolidated financial condition and results of operations of
         Brigham Exploration and its Consolidated Subsidiaries as at the end of,
         and for, such fiscal year and that such financial statements have been
         prepared in accordance with GAAP except for such changes in such
         principles with which the independent public accountants shall have
         concurred and such opinion shall not contain a "going concern" or like
         qualification or exception.

              (b) Quarterly Financial Statements. As soon as available and in
         any event within 45 days after the end of each of the first three
         fiscal quarterly periods of each fiscal year of Brigham Exploration,
         consolidated statements of income, stockholders' equity, changes in
         financial position and cash flow of Brigham Exploration and its
         Consolidated Subsidiaries for such period and for the period from the
         beginning of the respective fiscal year to the end of such period, and
         the related consolidated and consolidating balance sheets as at the end
         of such period, and setting forth in each case in comparative form the
         corresponding figures for the corresponding period in the preceding
         fiscal year, accompanied by the certificate of a Responsible Officer,
         which certificate shall state that said financial statements fairly
         present the consolidated financial condition and results of operations
         of Brigham Exploration and its Consolidated Subsidiaries in accordance
         with GAAP, as at the end of, and for, such period (subject to normal
         year-end audit adjustments).

              (c) Monthly Financial Statements. As soon as available and in any
         event within thirty (30) days after the end of each calendar month that
         is not also the




                                       48
<PAGE>   55

          end of one of Brigham Exploration's first three fiscal quarterly
          periods or of Brigham Exploration's fiscal year, consolidated
          statements of income and changes in financial position of Brigham
          Exploration and its Consolidated Subsidiaries for such period and for
          the period from the beginning of the respective fiscal year to the end
          of such period, and the related consolidated balance sheets as at the
          end of such period and, beginning March 31, 2000, statements setting
          forth in each case in comparative form the corresponding figures for
          the corresponding period in the preceding fiscal year, accompanied by
          the certificate of a Responsible Officer, which certificate shall
          state that such financial statements fairly present the consolidated
          financial condition and results of operations of Brigham Exploration
          and its Consolidated Subsidiaries in accordance with GAAP, as at the
          end of, and for, such period (subject to normal year-end audit
          adjustments).

              (d) Notice of Default. Promptly after the Borrower knows that any
         Default or any Material Adverse Effect has occurred, a notice of such
         Default or Material Adverse Effect, describing the same in reasonable
         detail and the action the Borrower proposes to take with respect
         thereto.

              (e) Other Accounting Reports. Promptly upon receipt thereof, a
         copy of each other report or letter (excluding routine correspondence)
         submitted to the Borrower or Brigham Exploration by independent
         accountants in connection with any annual, interim or special audit
         made by them of the books of the Borrower or Brigham Exploration, and a
         copy of any response by the Borrower or Brigham Exploration to such
         letter or report.

              (f) SEC Filings, Etc. Promptly, upon its becoming available, each
         financial statement, report, notice or proxy statement sent by Brigham
         Exploration to stockholders generally and each regular or periodic
         report and any registration statement, prospectus or written
         communication (other than transmittal letters) in respect thereof filed
         by Brigham Exploration with or received by Brigham Exploration in
         connection therewith from any securities exchange or the SEC or any
         successor agency.

              (g) Notices Under Other Loan Agreements. Promptly after the
         furnishing thereof, copies of any statement, report or notice furnished
         to any Person pursuant to the terms of any indenture, loan or credit or
         other similar agreement including, but not limited to, any statement,
         report or notice furnished to any Person pursuant to the Subordinated
         Debt, other than this Agreement and not otherwise required to be
         furnished to the Lenders pursuant to any other provision of this
         Section 8.01.

              (h) Other Matters. Subject to any applicable restrictions on
         disclosure, from time to time such other information regarding the
         business, affairs or financial condition of the Borrower or Brigham
         Exploration (including, without limitation, any Plan or Multiemployer
         Plan and any reports or other information



                                       49
<PAGE>   56

          required to be filed under ERISA) as any Lender or the Agent may
          reasonably request.

              (i) Annual Budgets. On or before January 31 of each year, a
         one-year financial projection for Brigham Exploration and its
         Subsidiaries in form acceptable to the Agent, which projection shall
         include revenues, expenses and capital expenditures.

              (j) Monthly Operating Statements. As soon as available and in any
         event within 30 days after the end of each month, monthly operating
         statements of the Borrower including, without limitation, production
         reports and general and administrative cost summaries by lease for its
         Oil and Gas Properties, which reports shall include quantities or
         volume of production, revenue, realized product prices, taxes, capital
         expenditures by category and lease operating costs which have accrued
         to the Borrower's accounts in such period, and such other information
         with respect thereto as the Agent may require.

              (k) Weekly Cash Budgets. During the period from the Closing Date
         through the Covenant Release Date, the Borrower will cause Brigham
         Exploration to deliver weekly cash budgets reasonably satisfactory to
         the Agent and each Lender and weekly cash flow statements reasonably
         satisfactory to the Agent and each Lender based on such form, with
         variance analysis to budget (including accounts receivables and
         accounts payables reporting) not later than the Friday following the
         week to which such budgets and statements relate.

              (l) CAPEX Plans. A CAPEX Plan, delivered simultaneously with each
         of the Reserve Reports to be delivered in March and September of each
         year; the first such CAPEX Plan, to be submitted on the Closing Date,
         shall be for the twelve month period beginning January 1, 2000, and
         ending December 31, 2000, and each subsequent CAPEX Plan shall cover
         the next succeeding twelve-month period. No such CAPEX Plan shall
         include a blended risk profile that deviates materially from the risk
         profile of the CAPEX Plan submitted on the Closing Date without the
         consent of the SCI Lenders.

The Borrower will furnish to the Agent, at the time it furnishes each set of
financial statements pursuant to paragraph (a) or (b) above, a certificate
substantially in the form of Exhibit C-2 hereto executed by a Responsible
Officer (i) certifying as to the matters set forth therein and stating that no
Default has occurred and is continuing (or, if any Default has occurred and is
continuing, describing the same in reasonable detail), (ii) setting forth in
reasonable detail the computations necessary to determine whether Brigham
Exploration is in compliance with Sections 5.2(q), (r) and (s) of its Guaranty
Agreement as of the end of the respective fiscal quarter or fiscal year, and
(iii) certifying that said financial statements fairly present the consolidated
and consolidating financial condition and consolidated results of operations in
accordance with GAAP, as at the end of, and for, such period (subject to normal
year-end audit adjustments).





                                       50
<PAGE>   57

         Section 8.02 Litigation. The Borrower shall promptly give to the Agent
notice of: (i) all legal or arbitral proceedings, and of all proceedings before
any Governmental Authority involving the Borrower or any Guarantor, except
proceedings which, if adversely determined within any reasonable range of loss,
would not have a Material Adverse Effect, and (ii) of any material litigation or
material proceeding against the Borrower or any Guarantor in which the amount
involved is not covered in full by insurance (subject to normal and customary
deductibles), or in which injunctive or similar relief is sought. The Borrower
will, and will cause each of the Guarantors to, promptly notify the Agent and
each of the Lenders of any claim, judgment, Lien or other encumbrance affecting
any Property of the Borrower or any Guarantor if the value of the claim,
judgment, Lien, or other encumbrance affecting such Property shall exceed
$1,000,000.

         Section 8.03 Maintenance, Etc.

              (a) The Borrower shall and shall cause each Subsidiary to:
         preserve and maintain its corporate existence and all of its material
         rights, privileges and franchises; keep books of record and account in
         which full, true and correct entries will be made of all dealings or
         transactions in relation to its business and activities; comply with
         all Governmental Requirements if failure to comply with such
         requirements will have a Material Adverse Effect; pay and discharge all
         taxes, assessments and governmental charges or levies imposed on it or
         on its income or profits or on any of its Property prior to the date on
         which penalties attach thereto, except for any such tax, assessment,
         charge or levy the payment of which is being contested in good faith
         and by proper proceedings and against which adequate reserves are being
         maintained; upon reasonable notice, permit representatives of the Agent
         or any Lender (accompanied by the Agent), during normal business hours,
         to examine, copy and make extracts from its financial books and
         records, to inspect its Properties, and to discuss its business and
         affairs with its officers, all to the extent reasonably requested by
         such Lender or the Agent (as the case may be); and keep, or cause to be
         kept, insured by financially sound and reputable insurers all Property
         of a character usually insured by Persons engaged in the same or
         similar business similarly situated against loss or damage of the kinds
         and in the amounts customarily insured against by such Persons and
         carry such other insurance as is usually carried by such Persons
         including, without limitation, environmental risk insurance to the
         extent reasonably available.

              (b) Contemporaneously with the delivery of the financial
         statements required by Section 8.01(a) to be delivered for each year,
         the Borrower will furnish or cause to be furnished to the Agent and the
         Lenders a certificate of insurance coverage from the insurer in form
         and substance satisfactory to the Agent and, if requested by the Agent,
         will furnish the Agent and the Lenders copies of the applicable
         policies.

              (c) The Borrower will and will cause each Subsidiary to operate
         its Oil and Gas Properties or cause such Oil and Gas Properties to be
         operated in a good and workmanlike manner in accordance with the
         practices of the industry and in



                                       51
<PAGE>   58

         compliance in all material respects with all applicable contracts and
         agreements and in compliance in all material respects with all
         Governmental Requirements.

              (d) The Borrower will and will cause each Subsidiary to, at its
         own expense, do or cause to be done (to the extent it has the power to
         do so) all things reasonably necessary to preserve and keep in good
         repair, working order and efficiency all of its Oil and Gas Properties
         and other material Properties including, without limitation, all
         equipment, machinery and facilities, and from time to time will make
         all the reasonably necessary repairs, renewals and replacements so that
         at all times the state and condition of its Oil and Gas Properties and
         other material Properties will be fully preserved and maintained,
         except to the extent a portion of such Properties is not capable of
         producing Hydrocarbons in economically reasonable amounts. The Borrower
         will and will cause each Subsidiary to promptly: (i) pay and discharge,
         or make reasonable and customary efforts to cause to be paid and
         discharged, all delay rentals, royalties, expenses and indebtedness
         accruing under the leases or other agreements affecting or pertaining
         to its Oil and Gas Properties, (ii) perform or make reasonable and
         customary efforts to cause to be performed, in accordance with industry
         standards, the obligations required by each and all of the assignments,
         deeds, leases, sub-leases, contracts and agreements affecting its
         interests in its Oil and Gas Properties and other material Properties,
         (iii) will and will cause each Subsidiary to do all other things
         necessary to keep unimpaired, except for Liens described in Section
         9.02, its rights with respect to its Oil and Gas Properties and other
         material Properties and prevent any forfeiture thereof or a default
         thereunder, except to the extent a portion of such Properties is no
         longer capable of producing Hydrocarbons in economically reasonable
         amounts. The Borrower will and will cause each Subsidiary to operate
         its Oil and Gas Properties and other material Properties or cause or
         make reasonable and customary efforts to cause such Oil and Gas
         Properties and other material Properties to be operated in a good and
         workmanlike manner in accordance with the practices of the industry and
         in compliance with all applicable contracts and agreements and in
         compliance in all material respects with all Governmental Requirements.
         The covenants contained in this Section 8.03(d) shall not apply to
         insignificant Properties unless a failure of such covenant could have a
         Material Adverse Effect.

              (e) The Borrower will provide to the Agent from time to time upon
         request by the Agent the certificate of a Responsible Officer of the
         Borrower stating that, except as disclosed in a schedule thereto, the
         Borrower has not received written notice that any mechanics' liens have
         been filed or will be filed on the Mortgaged Properties; provided that
         mere receipt of an invoice for services rendered shall not constitute
         written notice that a mechanics' lien will be filed.

         Section 8.04 Environmental Matters.


              (a) To the extent that a reasonably prudent owner or operator
         would do so under the same or similar circumstances, the Borrower will
         and will cause each Subsidiary to establish and implement such
         procedures as may be reasonably




                                       52
<PAGE>   59

         necessary to periodically determine and assure that any failure of the
         following does not have a Material Adverse Effect: (i) all Property of
         the Borrower and the Subsidiaries and the operations conducted thereon
         and other activities of the Borrower and the Subsidiaries are in
         compliance with and do not violate the requirements of any
         Environmental Laws, (ii) no oil, hazardous substances or solid wastes
         are disposed of or otherwise released on o r to any Property owned by
         any such party except in compliance with Environmental Laws, (iii) no
         hazardous substance will be released on or to any such Property in a
         quantity equal to or exceeding that quantity which requires reporting
         pursuant to Section 103 of CERCLA, and (iv) no oil, oil and gas
         exploration and production wastes or hazardous substance is released on
         or to any such Property so as to pose an imminent and substantial
         endangerment to public health or welfare or the environment.

              (b) The Borrower will promptly notify the Agent and the Lenders in
         writing of any threatened action, investigation or inquiry by any
         Governmental Authority of which the Borrower has knowledge in
         connection with any Environmental Laws with respect to the Property of
         the Borrower or any Subsidiary, excluding routine testing, compliance
         and corrective action.

         Section 8.05 Further Assurances. The Borrower will and will cause each
Guarantor to cure promptly any defects in the creation and issuance of the Notes
and the execution and delivery of the Loan Documents. The Borrower at its
expense will and will cause each Guarantor to promptly execute and deliver to
the Agent upon request all such other documents, agreements and instruments to
comply with or accomplish the covenants and agreements of the Borrower or any
Guarantor, as the case may be, in the Loan Documents, or to further evidence and
more fully describe the collateral intended as security for the Notes, or to
correct any omissions in the Loan Documents, or to state more fully the security
obligations set out herein or in any of the Loan Documents, or to perfect,
protect or preserve any Liens created pursuant to any of the Loan Documents, or
to make any recordings, to file any notices or obtain any consents, all as may
be necessary or appropriate in connection therewith.

         Section 8.06 Performance of Obligations. The Borrower will pay the
Notes according to the reading, tenor and effect thereof; and the Borrower will
and will cause each Guarantor to do and perform every act and discharge all of
the obligations to be performed and discharged by them under the Loan Documents,
at the time or times and in the manner specified.

         Section 8.07 Engineering Reports.


              (a) Not less than 15 days prior to each of the First Borrowing
         Base Determination Date, the First Asset Valuation Date, each Scheduled
         Asset Valuation Date and any Scheduled Borrowing Base Redetermination
         Date, the Borrower shall furnish to the Agent and the Lenders a Reserve
         Report. The Reserve Report furnished for the First Asset Valuation Date
         shall be prepared as of July 31, 2000, and the Reserve Report furnished
         for the First Borrowing Base Determination Date shall be prepared as of
         December 31, 2001. The Reserve Report furnished for the Scheduled Asset
         Valuation Date or Borrowing Base






                                       53
<PAGE>   60



         Redetermination Date to occur in March of each year shall be prepared
         as of the preceding December 31, and the Reserve Report furnished for
         the Scheduled Asset Valuation Date or the Scheduled Borrowing Base
         Redetermination Date to occur in September of each year shall be
         prepared as of the preceding June 30. The Reserve Report to be
         furnished in March of each year shall be prepared by certified
         independent petroleum engineers or other independent petroleum
         consultant(s) acceptable to the Agent and the Reserve Reports to be
         furnished in September of each year shall be prepared by or under the
         supervision of the chief engineer or Vice President of Operations of
         the Borrower who shall certify such Reserve Report to have been
         prepared in accordance with the procedures used in the immediately
         preceding March Reserve Report. At Borrower's option, the Reserve
         Report to be furnished in September of each year may instead consist of
         a report from the independent petroleum engineers referred to above on
         any new wells and a roll-forward by Borrower on any wells previously
         reported in the Reserve Report described in the immediately preceding
         March.

              (b) In the event of an unscheduled Borrowing Base redetermination,
         the Borrower shall furnish to the Agent and the Lenders a Reserve
         Report prepared by or under the supervision of the chief engineer of
         the Borrower who shall certify such Reserve Report to be true and
         accurate and to have been prepared in accordance with the procedures
         used in the immediately preceding Reserve Report. For any unscheduled
         Borrowing Base redetermination requested by the Lenders or the Borrower
         pursuant to Section 2.08(d), the Borrower shall provide such Reserve
         Report with an "as of" date as required by the Majority Lenders as soon
         as possible, but in any event no later than 30 days following the
         receipt of the request by the Agent on behalf of the Lenders.

              (c) With the delivery of each Reserve Report, the Borrower shall
         provide to the Agent and the Lenders:

                  (A) a certificate from a Responsible Officer certifying that,
              to the best of his knowledge and in all material respects: (i) the
              most recently delivered Reserve Report does not in the belief of
              such officer and based upon information in the Borrower's
              possession, materially overstate the oil and gas reserves of the
              Borrower and the Subsidiaries as a whole bearing in mind that
              reserves are evaluated based upon estimates and assumptions with
              respect to which reasonable minds of competent engineers may
              differ, (ii) except as set forth in such Reserve Report or on an
              exhibit to the certificate, on a net basis there are no gas
              imbalances, take or pay or other prepayments with respect to its
              Oil and Gas Properties evaluated in such Reserve Report which
              would violate Section 9.18, (iii) none of its proved Hydrocarbon
              Interests have been sold since the date of the last Borrowing Base
              determination except as set forth on an exhibit to the
              certificate, which certificate shall list all of its proved
              Hydrocarbon Interests sold and in such detail as reasonably
              required by the Majority Lenders, (iv) attached to the certificate
              is a list of its proved Hydrocarbon Interests added to and deleted
              from the immediately prior Reserve Report




                                       54
<PAGE>   61
              and a list showing any change in working interest or net revenue
              interest in its Hydrocarbon Interests occurring, (v) at the
              Agent's request, attached to the certificate is a list of all
              Persons disbursing proceeds to the Borrower from its Oil and Gas
              Properties and (vi) except as set forth on a schedule attached to
              the certificate all of proved Hydrocarbon Interests evaluated by
              such Reserve Report are Mortgaged Property; and

                  (B) a certificate from a Responsible Officer certifying that,
              to the best of his knowledge and in all material respects (i) the
              representations of the Borrower in Section 7.10 are true and
              correct and apply to the Hydrocarbon Interests evaluated in the
              Reserve Report that are described in a Standard Mortgage and (ii)
              the Borrower has, with respect to those material Hydrocarbon
              Interests that are evaluated in the most recently delivered
              Reserve Report, but that are not covered by a Standard Mortgage,
              conducted overall title due diligence that, in all material
              respects, equals or exceeds industry standards given the
              applicable facts and circumstances.

         Section 8.08 Reserved.


         Section 8.09 Additional Collateral.


              (a) The Borrower will grant and will cause each of its
         Subsidiaries to grant to the Agent as security for the Indebtedness a
         perfected Lien on the Borrower's or such Subsidiary's interest in any
         Oil and Gas Properties that are (i) acquired after the date hereof at
         the cash acquisition cost to the Borrower or such Subsidiary equal to
         or exceeding $1,000,000, and (ii) do not constitute Proved Reserves,
         which Lien will be created and perfected by and in accordance with the
         provisions of deeds of trust, security agreements and financing
         statements, or other Loan Documents, all in form substantially the same
         as the New Mortgage (subject to such changes as are necessary as a
         result of, to reflect and/or to account for changes in applicable law)
         and in sufficient executed (and acknowledged where necessary or
         appropriate) counterparts for recording purposes.

              (b) The Borrower will grant and will cause each of its
         Subsidiaries to grant to the Agent as security for the Indebtedness a
         first-priority Lien interest (subject only to Excepted Liens and the
         matters set forth on Schedule 7.10 hereto) on the Borrower's or such
         Subsidiary's interest in any Oil and Gas Properties identified after
         the Closing Date as containing Proved Reserves, which Lien will be
         created and perfected by and in accordance with the provisions of deeds
         of trust, security agreements and financing statements, or other Loan
         Documents, all in form substantially the same as the Standard Mortgage
         (subject to such changes as are necessary as a result of, to reflect
         and/or to account for changes in applicable law) and in sufficient
         executed (and acknowledged where necessary or appropriate) counterparts
         for recording purposes.




                                       55
<PAGE>   62


              (c) Concurrently with the granting of the Lien or other action
         referred to in Section 8.09(b) above, the Borrower will provide to the
         Agent title information in form and substance satisfactory to the Agent
         in its sole discretion with respect to the Borrower's and its
         Subsidiaries' interests in such Oil and Gas Properties to the extent
         needed to cause the Agent to have received, together with title
         information previously delivered to the Agent, satisfactory title
         information on at least 90% of the value of the proved Hydrocarbon
         Interests evaluated by the most recent Reserve Report.

              (d) Also, promptly after the filing of any new Loan Document in
         any state, other than the New Mortgage and any other mortgage filed
         pursuant to subsection (a) of this Section 8.09 or any other mortgage
         substantially in the form of the New Mortgage, upon the reasonable
         request of the Agent, the Borrower will provide to the Agent an opinion
         addressed to the Agent for the benefit of the Lenders in form and
         substance reasonably satisfactory to the Agent in its sole discretion
         from counsel acceptable to Agent, stating that such Loan Document is
         valid, binding and enforceable in accordance with its terms and in
         legally sufficient form for such jurisdiction.

         Section 8.10 ERISA Information and Compliance. The Borrower will
promptly furnish and will cause any ERISA Affiliate to promptly furnish to the
Agent with sufficient copies to the Lenders (i) if requested by the Agent
promptly after the filing thereof with the United States Secretary of Labor, the
Internal Revenue Service or the PBGC, copies of each annual and other report
with respect to each Plan or any trust created thereunder, (ii) immediately upon
becoming aware of the occurrence of any ERISA Event or of any "prohibited
transaction," as described in section 406 of ERISA or in section 4975 of the
Code, in connection with any Plan or any trust created thereunder, a written
notice signed by a Responsible Officer specifying the nature thereof, what
action the Borrower or the ERISA Affiliate is taking or proposes to take with
respect thereto, and, when known, any action taken or proposed by the Internal
Revenue Service, the Department of Labor or the PBGC with respect thereto, and
(iii) immediately upon receipt thereof, copies of any notice of the PBGC's
intention to terminate or to have a trustee appointed to administer any Plan.
With respect to each Plan (other than a Multiemployer Plan), the Borrower will,
and will cause each ERISA Affiliate to, (i) satisfy in full and in a timely
manner, without incurring any late payment or underpayment charge or penalty and
without giving rise to any lien, all of the contribution and funding
requirements of section 412 of the Code (determined without regard to
subsections (d), (e), (f) and (k) thereof) and of section 302 of ERISA
(determined without regard to sections 303, 304 and 306 of ERISA), and (ii) pay,
or cause to be paid, to the PBGC in a timely manner, without incurring any late
payment or underpayment charge or penalty, all premiums required pursuant to
sections 4006 and 4007 of ERISA.

         Section 8.11 Subsidiary Security. Should the Borrower create or acquire
any Subsidiary pursuant to Section 9.16 hereof it will promptly grant to the
Agent for the benefit of the Lenders a security interest and pledge of all the
capital stock of such Subsidiary in form and substance satisfactory to the Agent
and the Borrower will cause such Subsidiary to enter into a guaranty of the
Indebtedness in form and substance satisfactory to the Agent. The delivery of



                                       56
<PAGE>   63


such security and guaranty shall be accompanied by such back up corporate
authority and opinions of counsel as the Agent may reasonably request.

         Section 8.12 Payment of Trade Payables. The Borrower will pay and cause
all of its Subsidiaries to pay all of their Trade Payables now or hereafter
incurred within 60 days of the date the invoice is received by Borrower, unless
subject to legal offset or unless being contested in good faith by appropriate
proceedings and reserves adequate under GAAP shall have been established
therefor.

         Section 8.13 Target Asset Value. On the First Asset Valuation Date and
on each Scheduled Asset Valuation Date thereafter, the Borrower and its
Subsidiaries shall have Proved Reserves with a value (the "Target Asset Value")
that would, if a Borrowing Base were set in accordance with the parameters and
procedures set out in Section 2.08 hereof, support borrowings of at least the
Maximum Credit Amounts of the BMO/Soc-Gen Lenders at the time the valuation is
made; such a valuation shall be made by the BMO/Soc-Gen Lenders only. In the
event the Target Asset Value is less at the First Target Asset Valuation Date or
at any Scheduled Asset Valuation Date than the Maximum Credit Amounts of the
BMO/Soc-Gen Lenders at that time, the SCI Lenders shall have the right, but not
the obligation, to purchase that portion of the Maximum Credit Amounts of the
BMO/Soc-Gen Lenders that exceeds the applicable Target Asset Value (the
"Deficiency Amount"); such right must be exercised within 30 days after receipt
by the SCI Lenders of notice from the BMO/Soc-Gen Lenders of the Deficiency
Amount, and if it is so exercised, it shall, except as otherwise provided in the
next succeeding sentence, be deemed that the Borrower is, until the next
succeeding Scheduled Asset Valuation Date, in compliance with this Section 8.13.
If the SCI Lenders fail to exercise such right, then the Borrower shall prepay
the Loans of the BMO/Soc-Gen Lenders within such same thirty day period in an
aggregate principal amount equal to the Deficiency Amount. Each of the
BMO/Soc-Gen Lenders and the Borrower may initiate a new calculation of the
Target Asset Value once during each consecutive twelve (12) month period by
specifying in writing the date on which such new calculation is to be made. In
the event of an unscheduled Target Asset Value calculation, the Borrower shall
furnish to the Agent and the Lenders a Reserve Report prepared by or under the
supervision of the chief engineer of the Borrower who shall certify such Reserve
Report to be true and accurate and to have been prepared in accordance with the
procedures used in the immediately preceding Reserve Report. For any unscheduled
Target Asset Value calculation, requested by the BMO/Soc-Gen Lenders or the
Borrower, the Borrower shall provide such Reserve Report with an "as of" date as
required by the BMO/Soc-Gen Lenders as soon as possible, but in any event no
later than 30 days following the receipt of the request by the Agent on behalf
of the BMO/Soc-Gen Lenders.

                                   ARTICLE 9

                               NEGATIVE COVENANTS

         The Borrower covenants and agrees that, so long as any of the
Commitments are in effect and until payment in full of the Indebtedness
hereunder, all interest thereon and all other amounts payable by the Borrower
hereunder, without the prior written consent of the Majority Lenders:



                                       57
<PAGE>   64


         Section 9.01 Debt. Neither the Borrower nor any Subsidiary will incur,
create, assume or suffer to exist any Debt, except:

              (a) the Notes or other Indebtedness arising under the Loan
         Documents or any guaranty of or suretyship arrangement for the Notes or
         other Indebtedness arising under the Loan Documents;

              (b) Debt of the Borrower existing on the Closing Date which is
         reflected in the Financial Statements or is disclosed in Schedule 9.01,
         and any renewals or extensions (but not increases) thereof;

              (c) accounts payable for the deferred purchase price of Property
         or services (other than Trade Payables) from time to time incurred in
         the ordinary course of business which, if greater than 60 days past the
         date the invoice is received by Borrower, are being contested in good
         faith by appropriate proceedings if reserves adequate under GAAP shall
         have been established therefor;

              (d) Debt owing to a Guarantor which is subordinated to the
         Indebtedness as provided in such Guarantor's Guaranty Agreement or
         owing to the Borrower.

              (e) Debt of the Borrower under capital leases (as required to be
         reported on the financial statements of the Borrower pursuant to GAAP)
         not to exceed $2,000,000;

              (f) Debt of the Borrower under Hedging Agreements made with a
         Person that is made (i) with a Person that is, at the time such Hedging
         Agreement is made, either a Lender or an Affiliate of a Lender, or (ii)
         with another investment grade counterparty, provided that the aggregate
         notional amounts under all such Hedging Agreements do not exceed 80% of
         Borrower's anticipated oil and/or gas production to be produced during
         the term of such Hedging Agreements and that such Hedging Agreements
         are entered into as a part of its normal business operations as a risk
         management strategy and/or hedge against changes resulting from market
         conditions related to the Borrower's and its Subsidiaries' operations;

              (g) Debt associated with bonds or surety obligations required by
         Governmental Requirements in connection with the operation of the Oil
         and Gas Properties; and

              (h) Debt of the Borrower described on Schedule 9.01(h) and such
         other Debt of the Borrower related to the acquisition of software and
         licensing rights related thereto that does not exceed $100,000 at any
         one time outstanding.

              (i) Guarantees of the Borrower and its Subsidiaries which have
         executed prior and senior guarantees of the Indebtedness in form and
         substance satisfactory to the Agent, of the Subordinated Debt, which
         Guarantees are subordinated to the Indebtedness and otherwise in form
         and substance satisfactory to the Agent consistent with the
         Subordination Agreement.



                                       58
<PAGE>   65


     Section 9.02 Liens. Neither the Borrower nor any Subsidiary will create,
incur, assume or permit to exist any Lien on any of its Properties (now owned or
hereafter acquired), except:

              (a) Liens securing the payment of any Indebtedness;

              (b) Excepted Liens;

              (c) Liens securing leases allowed under Section 9.01(e) but only
         on the Property under lease;

              (d) Liens disclosed on Schedule 9.02;

              (e) Any Permitted Encumbrances as described in the Prior Mortgages
         or the Mortgage;

              (f) Liens securing the Subordinated Debt or Guarantees permitted
         under Section 9.01(i) on Properties upon which prior Liens have been
         granted to secure the Indebtedness pursuant to documents in form and
         substance satisfactory to the Agent, provided such Liens (i) are
         subordinated to those in favor of the Lenders and are otherwise in form
         and substance satisfactory to the Agent consistent with the
         Subordination Agreement and (ii) do not directly or indirectly secure
         any Hedging Agreements; and

              (g) the Term ORRI.

         Section 9.03 Investments, Loans and Advances. Neither the Borrower nor
any Subsidiary will make or permit to remain outstanding any loans or advances
to or investments in any Person, except that the foregoing restriction shall not
apply to:

              (a) investments, loans or advances reflected in the Financial
         Statements or which are disclosed to the Lenders in Schedule 9.03;

              (b) accounts receivable arising in the ordinary course of
         business;

              (c) for the Borrower only, direct obligations of the United States
         or any agency thereof, or obligations guaranteed by the United States
         or any agency thereof, in each case maturing within one year from the
         date of creation thereof;

              (d) for the Borrower only, commercial paper maturing within one
         year from the date of creation thereof rated in the highest grade by
         Standard & Poors Corporation or Moody's Investors Service, Inc.;

              (e) for the Borrower only, deposits maturing within one year from
         the date of creation thereof with, including certificates of deposit
         issued by, any Lender or any office located in the United States,
         Canada, or England of any other bank or trust company which is
         organized under the laws of the United States, Canada or England or any
         state or province thereof, has capital, surplus and undivided



                                       59
<PAGE>   66


         profits aggregating at least $100,000,000.00 (as of the date of such
         Lender's or bank or trust company's most recent financial reports) and
         has a short term deposit rating of no lower than A2 or P2, as such
         rating is set forth from time to time, by Standard & Poors Corporation
         or Moody's Investors Service, Inc., respectively;

              (f) for the Borrower only, deposits in money market funds
         investing exclusively in investments described in Section 9.03(c),
         9.03(d) or 9.03(e);

              (g) investments of the Borrower up to $100,000 in the aggregate in
         Quest Resources L.L.C.;

              (h) investments by the Borrower in direct or indirect (through a
         Subsidiary to the extent permitted by Section 9.16 below) ownership
         interests in additional Oil and Gas Properties and gas gathering
         systems gas plants, and similar assets related thereto;

              (i) investments, distributions, loans and advances by a Subsidiary
         to the Borrower; and

              (j) investments, distributions, loans and advances by the
         Borrower:

                    (a) to Brigham Exploration, Brigham, Inc., Brigham Holdings
               I, LLC and/or Brigham Holdings II, LLC

                         (i) to pay Federal or State taxes owing by any of them,
                    payroll and payroll related taxes and other reasonable
                    general and administrative expenses, or consisting of
                    forgiveness of indebtedness, and

                         (ii) so long as no Borrowing Base deficiency exists or
                    will be created thereby, no Event of Default or, with
                    respect to Section 5.2(q), (r), (s) or (u) of the Guaranty
                    Agreement of Brigham Exploration, Default, is in existence
                    or will be created thereby, to enable Brigham Exploration to
                    pay accrued and unpaid interest owing on the "Notes" (as
                    defined in the Indenture).

                    (b) to Subsidiaries which are Guarantors.

         Section 9.04 Dividends, Distributions and Redemptions. The Borrower
will not declare or pay any dividend, purchase, redeem or otherwise acquire for
value any of its stock now or hereafter outstanding, return any capital to its
stockholders or make any distribution of its assets to its partners, except as
permitted under Section 9.03(j)(a) above.

         Section 9.05 Sales and Leasebacks. Neither the Borrower nor any
Subsidiary will enter into any arrangement, directly or indirectly, with any
Person whereby the Borrower or any Subsidiary shall sell or transfer any of its
Property, whether now owned or hereafter




                                       60
<PAGE>   67

acquired, and whereby the Borrower or any Subsidiary shall then or thereafter
rent or lease as lessee such Property or any part thereof or other Property
which the Borrower or any Subsidiary intends to use for substantially the same
purpose or purposes as the Property sold or transferred.

         Section 9.06 Nature of Business. Neither the Borrower nor any
Subsidiary will allow any material change to be made in the character of its
business as an independent oil and gas exploration and production company. Among
other things, a transfer of a substantial portion of Borrower's seismic data and
Hydrocarbon Interests which do not contain identified proved Hydrocarbon
reserves (other than transfers to participants of any participation interest
earned by them in the ordinary course of Borrower's business and abandonment of
prospects) shall be considered a material change in Borrower's business.

         Section 9.07 Limitation on Leases. Neither the Borrower nor any
Subsidiary will create, incur, assume or suffer to exist any obligation for the
payment of rent or hire of Property of any kind whatsoever (real or personal
including capital leases but excluding leases of Hydrocarbon Interests and the
equipment used thereon), under leases or lease agreements which would cause the
aggregate amount of all payments made by the Borrower and the Subsidiaries
pursuant to all such leases or lease agreements to exceed $2,000,000 in any
period of twelve consecutive calendar months during the life of such leases.

         Section 9.08 Mergers, Etc.. The Borrower will not and will not permit
any Subsidiary to merge into or with or consolidate with any other Person or
sell, lease or otherwise dispose of (whether in one transaction or in a series
of transactions) all or substantially all of its Property or assets to any other
Person unless the Borrower, Brigham Exploration or any Guarantor whose Guaranty
Agreement is in full force and effect is the surviving entity and no Default
exists or will be created thereby.

         Section 9.09 Proceeds of Notes. The Borrower will not permit the
proceeds of the Notes to be used for any purpose other than those permitted by
Section 7.07. Neither the Borrower nor any Person acting on behalf of the
Borrower has taken or will take any action which might cause any of the Loan
Documents to violate Regulation G, U or X or any other regulation of the Board
of Governors of the Federal Reserve System or to violate Section 7 of the
Securities Exchange Act of 1934 or any rule or regulation thereunder, in each
case as now in effect or as the same may hereinafter be in effect.

         Section 9.10 ERISA Compliance. The Borrower will not at any time:


              (a) Engage in, or permit any ERISA Affiliate to engage in, any
         transaction in connection with which the Borrower or any ERISA
         Affiliate could be subjected to either a civil penalty assessed
         pursuant to section 502(c), (i) or (1) of ERISA or a tax imposed by
         Chapter 43 of Subtitle D of the Code in excess of $100,000;

              (b) Terminate, or permit any ERISA Affiliate to terminate, any
         Plan in a manner, or take any other action with respect to any Plan,
         which could reasonably be expected to result in any liability of the
         Borrower or any ERISA Affiliate to the PBGC in excess of $100,000;





                                       61
<PAGE>   68


              (c) Fail to make, or permit any ERISA Affiliate to fail to make,
         full payment when due of all amounts under the provisions of any Plan,
         agreement relating thereto or applicable law, the Borrower or any ERISA
         Affiliate is required to pay as contributions thereto;

              (d) Permit to exist, or allow any ERISA Affiliate to permit to
         exist, any accumulated funding deficiency in excess of $100,000 within
         the meaning of Section 302 of ERISA or section 412 of the Code, whether
         or not waived, with respect to any Plan;

              (e) Permit, or allow any ERISA Affiliate to permit, the actuarial
         present value of the benefit liabilities under any Plan maintained by
         the Borrower or any ERISA Affiliate which is regulated under Title IV
         of ERISA to exceed the current value of the assets (computed on a plan
         termination basis in accordance with Title IV of ERISA) of such Plan
         allocable to such benefit liabilities by an amount in excess of
         $100,000. The term "actuarial present value of the benefit liabilities"
         shall have the meaning specified in section 4041 of ERISA;

              (f) Contribute to or assume an obligation to contribute to, or
         permit any ERISA Affiliate to contribute to or assume an obligation to
         contribute to, any Multiemployer Plan;

              (g) Acquire, or permit any ERISA Affiliate to acquire, an interest
         in any Person that causes such Person to become an ERISA Affiliate with
         respect to the Borrower or any ERISA Affiliate if such Person sponsors,
         maintains or contributes to, or at any time in the six-year period
         preceding such acquisition has sponsored, maintained, or contributed
         to, (1) any Multiemployer Plan, or (2) any other Plan that is subject
         to Title IV of ERISA under which the actuarial present value of the
         benefit liabilities under such Plan exceeds the current value of the
         assets (computed on a plan termination basis in accordance with Title
         IV of ERISA) of such Plan allocable to such benefit liabilities;

              (h) Incur, or permit any ERISA Affiliate to incur, a liability to
         or on account of a Plan under sections 515, 4062, 4063, 4064, 4201 or
         4204 of ERISA which the aggregate for all such liability exceeds
         $100,000;

              (i) Contribute to or assume an obligation to contribute to, or
         permit any ERISA Affiliate to contribute to or assume an obligation to
         contribute to, any employee welfare benefit plan, as defined in section
         3(1) of ERISA, including, without limitation, any such plan maintained
         to provide benefits to former employees of such entities, that may not
         be terminated by such entities in their sole discretion at any time
         without any material liability; or

              (j) Amend or permit any ERISA Affiliate to amend, a Plan resulting
         in an increase in current liability such that the Borrower or any ERISA
         Affiliate is required to provide security to such Plan under section
         401(a)(29) of the Code.




                                       62
<PAGE>   69

         Section 9.11 Sale or Discount of Receivables. Neither the Borrower nor
any Subsidiary will discount or sell (with or without recourse) any of its notes
receivable or accounts receivable.

         Section 9.12 [INTENTIONALLY OMITTED]

         Section 9.13 Sale of Oil and Gas Properties. The Borrower will not, and
will not permit any Subsidiary to, sell, assign, farm-out, convey or otherwise
transfer any Hydrocarbon Interests except for (i) the sale of Hydrocarbons in
the ordinary course of business; and (ii) the sale or transfer of equipment that
is no longer necessary for the business of the Borrower or such Subsidiary or is
replaced by equipment of at least comparable value and use.

         Section 9.14 Environmental Matters. Neither the Borrower nor any
Subsidiary will knowingly cause or permit any of its Property to be in violation
of, or knowingly do anything or permit anything to be done which will subject
any such Property to any remedial obligations under any Environmental Laws,
assuming disclosure to the applicable Governmental Authority of all relevant
facts, conditions and circumstances, if any, pertaining to such Property where
such violations or remedial obligations would have a Material Adverse Effect.

         Section 9.15 Transactions with Affiliates. Neither the Borrower nor any
Subsidiary will enter into any transaction, including, without limitation, any
purchase, sale, lease or exchange of Property or the rendering of any service,
with any Affiliate unless such transactions are otherwise not in violation of
this Agreement, are in the ordinary course of its business and are upon fair and
reasonable terms no less favorable to it than it would obtain in a comparable
arm's length transaction with a Person not an Affiliate.

         Section 9.16 Subsidiaries. The Borrower will not, and will not permit
any Subsidiary to, create any additional Subsidiaries or make any additional
investment in a Subsidiary. All Subsidiaries together at no time shall own or
hold Oil and Gas Properties having proved reserves with a net discounted present
value calculated in the same manner as in the most recent Reserve Report in
excess of 10% of the total net discounted present value of Proved Reserves of
the Borrower and its Subsidiaries as reflected in said Reserve Report (plus such
Subsidiaries' proved reserves not included in such Reserve Report). No
Subsidiary may enter into any agreement other than the Loan Documents which
limits upstream transfer of dividends to the Borrower (other than the Indenture,
the documents described in Section 4.01(a) through (d) of the Indenture, and any
other documents permitted under Section 9.02(f)). No assets may be transferred
to a Subsidiary which is not a Guarantor.

         Section 9.17 Negative Pledge Agreements. The Borrower will not and will
not permit any Subsidiary to create, incur, assume or suffer to exist any
contract, agreement or understanding (other than the Loan Documents) which in
any way prohibits or restricts (i) the granting, conveying, creation or
imposition of any Lien on any of its Property (other than the Indenture, the
documents described in Section 4.01(a) through (d) of the Indenture, and any
other documents permitted under Section 9.02 (f) or (g)) or (ii) any Subsidiary
from paying dividends or making any other distribution to the Borrower or which
requires the consent of or notice to other Persons in connection with any of the
foregoing.





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         Section 9.18 Gas Imbalances, Take-or-Pay or Other Prepayments. The
Borrower will not allow gas imbalances, take-or-pay or other prepayments with
respect to the Hydrocarbon Interests of the Borrower and its Subsidiaries which
would require the Borrower or its Subsidiaries to deliver five percent (5%) or
more of the Borrower's and its Subsidiaries' Hydrocarbons produced on a monthly
basis from the Hydrocarbon Interests at some future time without then or
thereafter receiving full payment therefor.

         Section 9.19 Borrower as Operator. The Borrower will not and will not
permit any of the Subsidiaries to voluntarily resign as operator of more than
twenty-five percent (25%) of their currently operated Oil and Gas Properties
unless the new operator is acceptable to the Majority Lenders.

         Section 9.20 Quest Resources LLC. The Borrower will not, and will not
permit any of its Subsidiaries to, (i) transfer any assets to Quest Resources
LLC or (ii) make any investments in or loans or advances to Quest Resources LLC.

         Section 9.21 Subordinated Debt. The Borrower shall not prepay any of
the Subordinated Debt except as authorized in the Amended and Restated Guaranty
Agreement as of the date hereof by Brigham Exploration in favor of Agent, for
the Lenders.

         Section 9.22 Restrictions While Outstanding Indebtedness Exceeds the
Borrowing Base. The Borrower covenants and agrees that until the Covenant
Release Date without prior written consent of the Majority Lenders:

              (a) The Borrower will not permit Net Seismic and Land Expenditures
         to exceed two million dollars (the NSLE Limit). Upon completion of the
         CAPEX Plan submitted on the Closing Date, the NSLE Limit will increase
         at the beginning of each succeeding quarter of a year by an amount
         equal to 10% of the total projected capital expenditures for such
         quarter. This limitation in this subsection (a)shall only be in place
         at any time that Indebtedness at the end of the quarter plus actual Net
         Seismic and Land Expenditures for such quarter divided by such
         quarter's EBITDA minus capitalized general and administrative expenses
         is greater than 16:1 (or 4:1 on an annualized basis). The two million
         dollar limitation and 10% of the total projected capital expenditures
         shall increase respectively to three million dollars and 15% at such
         time as Brigham Exploration has raised four million dollars in equity.

              (b) The Borrower will not permit its capital expenditures to
         deviate materially from the then current CAPEX Plan, with the
         materiality of any such deviation to be determined by the SCI Lenders
         in their sole but reasonable discretion.

              (c) The Borrower will not allow growth in general and
         administrative expenses to exceed the amount which is reasonable and
         necessary to retain key employees and to execute the Borrower's
         business plan to maximize growth in resources, net assets, cash flow
         and equity value.






                                       64
<PAGE>   71

              (d) The Borrower will not permit any new wells to be spudded for
         which the weekly cash budget indicates that there will be insufficient
         working capital to complete, after taking into account availability
         under this Agreement.

              (e) The Borrower will not permit RAPRV to fall below a value of
         (i) $50,000,000 as of July 31, 2000, (ii) $62,500,000 as of January 1,
         2001, and (iii) $67,500,000 as of July 31, 2001, if the Subordinated
         Debt does not exceed $25,000,000, or $72,500,000 as of July 31, 2001,
         if the Subordinated Debt does exceed $25,000,000.

                                   ARTICLE 10

                           EVENTS OF DEFAULT; REMEDIES

         Section 10.01 Events of Default. One or more of the following events
shall constitute an "Event of Default":


              (a) the Borrower shall default in the payment or prepayment when
         due of any principal of or interest on any Loan or any fees or other
         amount payable by it hereunder or under any other Loan Document and
         such default, other than a default of a payment or prepayment of
         principal (which shall have no cure period), shall continue unremedied
         for a period of three (3) Business Days; or

              (b) the Borrower or any Guarantor shall default in the payment
         when due of any principal of or interest on any of its other Debt
         aggregating $1,000,000 or more, or any event specified in any note,
         agreement, indenture or other document evidencing or relating to any
         such Debt shall occur if the effect of such event is to cause, or (with
         the giving of any notice or the lapse of time or both) to permit the
         holder or holders of such Debt (or a trustee or agent on behalf of such
         holder or holders) to cause, such Debt to become due prior to its
         stated maturity; or

              (c) any representation, warranty, or certification made or deemed
         made herein or in any other Loan Document by the Borrower or any
         Guarantor, or any certificate furnished by the Borrower or any
         Guarantor to any Lender or the Agent pursuant to the provisions hereof
         or any Loan Document, shall prove to have been false or misleading as
         of the time made or furnished in any material and adverse respect; or

              (d) the Borrower shall default in the performance of any of its
         obligations under Article IX or Section 8.01(c) of this Agreement; or
         the Borrower shall default in the performance of any of its obligations
         under any other Article of the Agreement or under or any other Loan
         Document to which it is a party (other than the payment of amounts due
         which shall be governed by Section 10.01(a)) and such default shall
         continue unremedied for a period of thirty (30) days after notice
         thereof to the Borrower by the Agent or any of the Lenders (through the
         Agent); or






                                       65
<PAGE>   72


              (e) any Guarantor shall default in the performance of its
         obligation to pay the Liabilities (as defined therein) at maturity or,
         with respect to Brigham Exploration, performance of any covenant under
         Section 5.1(i) or Section 5.2 of its Guaranty Agreement; or any
         Guarantor shall default in the performance of any of its other
         obligations under its Guaranty Agreement and such default shall
         continue unremedied for a period of thirty (30) days after notice
         thereof to the Guarantor by the Agent or the any of the Lenders
         (through the Agent); or

              (f) the Borrower shall admit in writing its inability to, or be
         generally unable to, pay its debts as such debts become due; or

              (g) the Borrower shall (i) apply for or consent to the appointment
         of, or the taking of possession by, a receiver, custodian, trustee or
         liquidator of itself or of all or a substantial part of its property,
         (ii) make a general assignment for the benefit of its creditors, (iii)
         commence a voluntary case under the Federal Bankruptcy Code (as now or
         hereafter in effect), (iv) tile a petition seeking to take advantage of
         any other law relating to bankruptcy, insolvency, reorganization,
         winding-up, liquidation or composition or readjustment of debts, (v)
         fail to controvert in a timely and appropriate manner, or acquiesce in
         writing to, any petition filed against it in an involuntary case under
         the Federal Bankruptcy Code, or (vi) take any corporate action for the
         purpose of effecting any of the foregoing; or

              (h) a proceeding or case shall be commenced, without the
         application or consent of the Borrower, in any court of competent
         jurisdiction, seeking (i) its liquidation, reorganization, dissolution
         or winding-up, or the composition or readjustment of its debts, (ii)
         the appointment of a trustee, receiver, custodian, liquidator or the
         like of the Borrower of all or any substantial part of its assets, or
         (iii) similar relief in respect of the Borrower under any law relating
         to bankruptcy, insolvency, reorganization, winding-up, or composition
         or adjustment of debts, and such proceeding or case shall continue
         undismissed, or an order, judgment or decree approving or ordering any
         of the foregoing shall be entered and continue unstayed and in effect,
         for a period of 60 days; or an order for relief against the Borrower
         shall be entered in an involuntary case under the Federal Bankruptcy
         Code; or

              (i) a judgment or judgments for the payment of money in excess of
         $1,000,000 in the aggregate shall be rendered by a court against the
         Borrower and the same shall not be discharged (or provision shall not
         be made for such discharge), or a stay of execution thereof shall not
         be procured, within thirty (30) days from the date of entry thereof and
         the Borrower shall not, within said period of 30 days, or such longer
         period during which execution of the same shall have been stayed,
         appeal therefrom and cause the execution thereof to be stayed during
         such appeal; or

              (j) the Loan Documents after delivery thereof shall for any
         reason, except to the extent permitted by the terms thereof, cease to
         be in full force and effect




                                       66
<PAGE>   73

         and valid, binding and enforceable in all material respects in
         accordance with their terms, or cease in any material respect to create
         a valid and perfected Lien of the priority required thereby on any of
         the collateral purported to be covered thereby, except to the extent
         permitted by the terms of this Agreement, or the Borrower or any
         Guarantor shall so state in writing; or

              (k) any Guarantor discontinues its usual business or suffers to
         exist any material change in its ownership, control or management; or

              (l) any Guarantor takes, suffers or permits to exist any of the
         events or conditions referred to in paragraphs (f), (g), (h) or (i)
         hereof or if any guaranty agreement related thereto shall for any
         reason cease to be valid and binding on such Guarantor in all material
         respects or if such Guarantor shall so state in writing; or

              (m) Brigham Exploration ceases to own (directly or indirectly)
         100% of the Borrower; or

              (n) the Borrower ceases to be the primary operating entity for
         Brigham Exploration and its Subsidiaries and the Borrower and its
         Subsidiaries cease to be the only Brigham Exploration entities owning
         Oil and Gas Properties.

         Section 10.02 Remedies.


              (a) At any time during the continuance of an Event of Default
         other than one referred to in clauses (f), (g) or (h) of Section 10.01
         or in clause (m) to the extent it relates to clauses (f), (g) or (h),
         the Agent, upon request of the Majority Lenders, shall, by notice to
         the Borrower, cancel the Commitments and/or declare the principal
         amount then outstanding of, and the accrued interest on, the Loans and
         all other amounts payable by the Borrower hereunder and under the Notes
         to be forthwith due and payable, whereupon such amounts shall be
         immediately due and payable without presentment, demand, protest,
         notice of intent to accelerate, notice of acceleration or other
         formalities of any kind, all of which are hereby expressly waived by
         the Borrower. Once an acceleration has been declared pursuant to the
         foregoing, no subsequent cure of the Event of Default shall negate such
         acceleration or the rights and remedies of the Agent and the Lenders
         with respect thereto without the express written consent of all of the
         Lenders.

              (b) In the case of the occurrence of an Event of Default referred
         to in clauses (f), (g) or (h) of Section 10.01 or in clause (m) to the
         extent it relates to clauses (f), (g) or (h), the Commitments shall be
         automatically canceled and the principal amount then outstanding of,
         and the accrued interest on, the Loans and all other amounts payable by
         the Borrower hereunder and under the Notes shall become automatically
         immediately due and payable without presentment, demand, protest,
         notice of intent to accelerate, notice of acceleration or other
         formalities of any kind, all of which are hereby expressly waived by
         the Borrower.






                                       67
<PAGE>   74

              (c) All proceeds received after maturity of the Notes, whether by
         acceleration or otherwise shall be applied first to reimbursement of
         expenses and indemnities provided for in the Loan Documents; second to
         accrued interest on the Notes of the BMO/Soc-Gen Lenders; third to fees
         of the BMO/Soc-Gen Lenders; fourth pro rata to principal outstanding on
         the Notes and other Indebtedness of the BMO/Soc-Gen Lenders; fifth to
         accrued interest on the Notes of the SCI Lenders; sixth to fees of the
         SCI Lenders; seventh, pro rata to principal outstanding on the Notes
         and other Indebtedness of the SCI Lenders and any excess shall be paid
         to the Borrower or as otherwise required by any Governmental
         Requirement.

         Section 10.03 Production and Proceeds. Notwithstanding that, by the
terms of the various Mortgages and other Loan Documents, the Borrower and any
other mortgagors are and will be assigning to Agent all of the Hydrocarbons
covered thereby and all of the products thereof and proceeds and revenues
attributable thereto and all payments in lieu of such Hydrocarbons (in this
section collectively called the "Production and Proceeds"), so long as no
Default has occurred and is continuing (a) the Borrower and such mortgagors may
continue to receive all such Production and Proceeds, subject, however, to the
Liens created under the Mortgages and other Loan Documents, and (b) upon the
Borrower's request the Agent will confirm to any purchasers of Hydrocarbons,
title examiners, or other Persons that the Borrower and such mortgagors continue
to have the right so to receive such Production and Proceeds until notification
by the Agent of the occurrence of a Default. During the continuance of a
Default, however, the Agent may exercise its rights and remedies granted under
the Mortgages and the other Loan Documents, including the rights and remedies
granted under the Mortgages and the other Loan Documents, including the right to
obtain possession of all Production and Proceeds then held by the Borrower and
such mortgagors and to receive directly from the purchasers of Hydrocarbons all
other Production Proceeds. In no case shall any failure by the Agent to collect
directly any such Production and Proceeds constitute in any way a release of any
of its rights under the Loan Documents.

                                   ARTICLE 11

                                    THE AGENT

         Section 11.01 Appointment, Powers and Immunities. Each Lender hereby
irrevocably appoints and authorizes the Agent to act as its agent hereunder and
under the other Loan Documents with such powers as are specifically delegated to
the Agent by the terms of this Agreement and the other Loan Documents, together
with such other powers as are reasonably incidental thereto. The Agent (which
term as used in this sentence and in Section 11.05 and the first sentence of
Section 11.06 shall include reference to its Affiliates and its and its
Affiliates' officers, directors, employees, attorneys, accountants, experts and
agents): (i) shall have no duties or responsibilities except those expressly set
forth in the Loan Documents, and shall not by reason of the Loan Documents be a
trustee or fiduciary for any Lender; (ii) makes no representation or warranty to
any Lender and shall not be responsible to the Lenders for any recitals,
statements, representations or warranties contained in this Agreement, or in any
certificate or other document referred to or provided for in, or received by any
of them under, this Agreement, or for the value, validity, effectiveness,
genuineness, execution, effectiveness,




                                       68
<PAGE>   75

legality, enforceability or sufficiency of this Agreement, any Note or any other
document referred to or provided for herein or for any failure by the Borrower
or any other Person (other than the Agent) to perform any of its obligations
hereunder or thereunder or for the existence, value, perfection or priority of
any collateral security or the financial or other condition of the Borrower, the
Subsidiaries or any other obligor or guarantor; (iii) except pursuant to Section
11.07 shall not be required to initiate or conduct any litigation or collection
proceedings hereunder; and (iv) SHALL NOT BE RESPONSIBLE FOR ANY ACTION TAKEN OR
OMITTED TO BE TAKEN BY IT HEREUNDER OR UNDER ANY OTHER DOCUMENT OR INSTRUMENT
REFERRED TO OR PROVIDED FOR HEREIN OR IN CONNECTION HEREWITH INCLUDING ITS OWN
ORDINARY NEGLIGENCE, EXCEPT FOR ITS OWN GROSS NEGLIGENCE OR WILLFUL MISCONDUCT.
The Agent may employ agents, accountants, attorneys and experts and shall not be
responsible for the negligence or misconduct of any such agents, accountants,
attorneys or experts selected by it in good faith or any action taken or omitted
to be taken in good faith by it in accordance with the advice of such agents,
accountants, attorneys or experts. The Agent may deem and treat the payee of any
Note as the holder thereof for all purposes hereof unless and until a written
notice of the assignment or transfer thereof permitted hereunder shall have been
filed with the Agent. The Agent is authorized to release any collateral that is
permitted to be sold or released pursuant to the terms of the Loan Documents.

         Section 11.02 Reliance by Agent. The Agent shall be entitled to rely
upon any certification, notice or other communication (including any thereof by
telephone, telex, telecopier, telegram or cable) believed by it to be genuine
and correct and to have been signed or sent by or on behalf of the proper Person
or Persons, and upon advice and statements of legal counsel, independent
accountants and other experts selected by the Agent.

         Section 11.03 Defaults. The Agent shall not be deemed to have knowledge
of the occurrence of a Default (other than the non-payment of principal of or
interest on Loans or of fees) unless the Agent has received notice from a Lender
or the Borrower specifying such Default and stating that such notice is a
"Notice of Default." In the event that the Agent receives such a notice of the
occurrence of a Default, the Agent shall give prompt notice thereof to the
Lenders. In the event of a payment Default, the Agent shall give each Lender
prompt notice of each such payment Default.

         Section 11.04 Rights as a Lender. With respect to its Commitments and
the Loans made by it, BMO (and any successor BMO/Soc-Gen Lender acting as Agent)
in its capacity as a BMO/Soc-Gen Lender hereunder shall have the same rights and
powers hereunder as any other BMO/Soc-Gen Lender and may exercise the same as
though it were not acting as the Agent, and the term "Lender" or "Lenders"
shall, unless the context otherwise indicates, include the Agent in its
individual capacity. BMO (and any successor acting as Agent) and its Affiliates
may (without having to account therefor to any Lender) accept deposits from,
lend money to and generally engage in any kind of banking, trust or other
business with the Borrower (and any of its Affiliates) as if it were not acting
as the Agent, and BMO and its Affiliates may accept fees and other consideration
from the Borrower for services in connection with this Agreement or otherwise
without having to account for the same to the Lenders.

         Section 11.05 INDEMNIFICATION. THE LENDERS AGREE TO INDEMNIFY THE AGENT
RATABLY IN ACCORDANCE WITH THEIR PERCENTAGE SHARES FOR THE INDEMNITY MATTERS AS
DESCRIBED IN






                                       69
<PAGE>   76


SECTION 12.03 TO THE EXTENT NOT INDEMNIFIED OR REIMBURSED BY THE BORROWER UNDER
SECTION 12.03, BUT WITHOUT LIMITING THE OBLIGATIONS OF THE BORROWER UNDER SAID
SECTION 12.03 AND FOR ANY AND ALL OTHER LIABILITIES, OBLIGATIONS, LOSSES,
DAMAGES, PENALTIES, ACTIONS, JUDGMENTS, SUITS, COSTS, EXPENSES OR DISBURSEMENTS
OF ANY KIND AND NATURE WHATSOEVER WHICH MAY BE IMPOSED ON, INCURRED BY OR
ASSERTED AGAINST THE AGENT IN ANY WAY RELATING TO OR ARISING OUT OF: (I) THIS
AGREEMENT, THE OTHER LOAN DOCUMENTS OR ANY OTHER DOCUMENTS CONTEMPLATED BY OR
REFERRED TO HEREIN OR THE TRANSACTIONS CONTEMPLATED HEREBY, BUT EXCLUDING,
UNLESS A DEFAULT HAS OCCURRED AND IS CONTINUING, NORMAL ADMINISTRATIVE COSTS AND
EXPENSES INCIDENT TO THE PERFORMANCE OF ITS AGENCY DUTIES HEREUNDER OR (II) THE
ENFORCEMENT OF ANY OF THE TERMS OF THIS AGREEMENT, ANY OTHER LOAN DOCUMENT OR OF
ANY SUCH OTHER DOCUMENTS; WHETHER OR NOT ANY OF THE FOREGOING SPECIFIED IN THIS
SECTION 11.05 ARISES FROM THE SOLE OR CONCURRENT NEGLIGENCE OF THE AGENT,
PROVIDED THAT NO LENDER SHALL BE LIABLE FOR ANY OF THE FOREGOING TO THE EXTENT
THEY ARISE FROM THE GROSS NEGLIGENCE OR WILLFUL MISCONDUCT OF THE AGENT.

         Section 11.06 Non-Reliance on Agent and other Lenders. Each Lender
acknowledges and agrees that it has, independently and without reliance on the
Agent or any other Lender, and based on such documents and information as it has
deemed appropriate, made its own credit analysis of the Borrower and its
decision to enter into this Agreement, and that it will, independently and
without reliance upon the Agent or any other Lender, and based on such documents
and information as it shall deem appropriate at the time, continue to make its
own analysis and decisions in taking or not taking action under this Agreement.
The Agent shall not be required to keep itself informed as to the performance or
observance by the Borrower of the Loan Documents or any other document referred
to or provided for herein or to inspect the properties or books of the Borrower.
Except for notices, reports and other documents and information expressly
required to be furnished to the Lenders by the Agent hereunder, the Agent shall
not have any duty or responsibility to provide any Lender with any credit or
other information concerning the affairs, financial condition or business of the
Borrower (or any of its Affiliates) which may come into the possession of the
Agent or any of its Affiliates. In this regard, each Lender acknowledges that
Weil, Gotshal & Manges LLP is acting in this transaction as special counsel to
the Agent only, except to the extent otherwise expressly stated in any legal
opinion or any Loan Document. Each Lender will consult with its own legal
counsel to the extent that it deems necessary in connection with the Loan
Documents and the matters contemplated therein.

         Section 11.07 Action by Agent. Except for action or other matters
expressly required of the Agent hereunder, the Agent shall in all cases be fully
justified in failing or refusing to act hereunder unless it shall (i) receive
written instructions from the Majority Lenders (or all of the Lenders as
expressly required by Section 12.04) specifying the action to be taken, and (ii)
be indemnified to its satisfaction by the Lenders against any and all liability
and expenses which may be incurred by it by reason of taking or continuing to
take any such action. The instructions of the Majority Lenders (or all of the
Lenders as expressly required by





                                       70
<PAGE>   77

Section 12.04) and any action taken or failure to act pursuant thereto by the
Agent shall be binding on all of the Lenders. If a Default has occurred and is
continuing, the Agent shall take such action with respect to such Default as
shall be directed by the Majority Lenders (or all of the Lenders as required by
Section 12.04) in the written instructions (with indemnities) described in this
Section 11.07, provided that, unless and until the Agent shall have received
such directions, the Agent may (but shall not be obligated to) take such action,
or refrain from taking such action, with respect to such Default as it shall
deem advisable in the best interests of the Lenders. In no event, however, shall
the Agent be required to take any action which exposes the Agent to personal
liability or which is contrary to this Agreement and the other Loan Documents or
applicable law.

         Section 11.08 Resignation or Removal of Agent. Subject to the
appointment and acceptance of a successor Agent as provided below, the Agent may
resign at any time by giving notice thereof to the Lenders and the Borrower, and
the Agent may be removed at any time with or without cause by the Majority
Lenders. Upon any such resignation or removal, the BMO/Soc-Gen Majority Lenders
shall have the right to appoint a successor Agent. If no successor Agent shall
have been so appointed by the BMO/Soc-Gen Majority Lenders and shall have
accepted such appointment within thirty (30) days after the retiring Agent's
giving of notice of resignation or the Majority Lenders' removal of the retiring
Agent, then the retiring Agent may, on behalf of the Lenders, appoint a
successor Agent from among the BMO/Soc-Gen Lenders. Upon the acceptance of such
appointment hereunder by a successor Agent, such successor Agent shall thereupon
succeed to and become vested with all the rights, powers, privileges and duties
of the retiring Agent, and the retiring Agent shall be discharged from its
duties and obligations hereunder. After any retiring Agent's resignation or
removal hereunder as Agent, the provisions of this Article XI and Section 12.03
shall continue in effect for its benefit in respect of any actions taken or
omitted to be taken by it while it was acting as the Agent.

                                   ARTICLE 12

                                  MISCELLANEOUS

         Section 12.01 Waiver. No failure on the part of the Agent or any Lender
to exercise and no delay in exercising, and no course of dealing with respect
to, any right, power or privilege under any of the Loan Documents shall operate
as a waiver thereof, nor shall any single or partial exercise of any right,
power or privilege under any of the Loan Documents preclude any other or further
exercise thereof or the exercise of any other right, power or privilege. The
remedies provided herein are cumulative and not exclusive of any remedies
provided by law.

         Section 12.02 Notices. All notices and other communications provided
for herein and in the other Loan Documents (including, without limitation, any
modifications of, or waivers or consents under, this Agreement or the other Loan
Documents) shall be given or made by telex, telecopy, courier or U.S. Mail or in
writing and telexed, telecopied, mailed or delivered to the intended recipient
at the "Address for Notices" specified below its name on the signature pages
hereof or in the Loan Documents or, as to any party, at such other address as
shall be designated by such party in a notice to each other party. Except as
otherwise provided in this Agreement or in the other Loan Documents, all such
communications shall be deemed to have been duly given when transmitted, if
transmitted before 1:00 p.m. Houston time on a Business Day (otherwise on




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the next succeeding Business Day) by telex or telecopier and evidence or
confirmation of receipt is obtained, or personally delivered or, in the case of
a mailed notice, three (3) Business Days after the date deposited in the mails,
postage prepaid, in each case given or addressed as aforesaid.

         Section 12.03 Payment of Expenses, Indemnities, etc. The Borrower
         agrees:


              (a) whether or not the transactions hereby contemplated are
         consummated, to pay all reasonable expenses of the Agent and one SCI
         Lender in the administration (both before and after the execution
         hereof and including advice of counsel as to the rights and duties of
         the Agent and the Lenders with respect thereto) of, and in connection
         with the negotiation, syndication, investigation, preparation,
         execution and delivery of, recording or filing of, preservation of
         rights under, enforcement of, and refinancing, renegotiation or
         restructuring of, the Loan Documents and any amendment, waiver or
         consent relating thereto (including, without limitation, the reasonable
         fees and disbursements of counsel and other outside consultants for the
         Agent and, in the case of enforcement, the reasonable fees and
         disbursements of counsel for the Agent and any of the Lenders); and
         promptly reimburse the Agent for all amounts expended, advanced or
         incurred by the Agent or the Lenders to satisfy any obligation of the
         Borrower under this Agreement or any other Loan Document, including
         without limitation, all costs and expenses of foreclosure;

              (b) TO INDEMNIFY THE AGENT AND EACH LENDER AND EACH OF THEIR
         AFFILIATES AND EACH OF THEIR OFFICERS, DIRECTORS, EMPLOYEES,
         REPRESENTATIVES, AGENTS, ATTORNEYS, ACCOUNTANTS AND EXPERTS
         ("INDEMNIFIED PARTIES") FROM, HOLD EACH OF THEM HARMLESS AGAINST AND
         PROMPTLY UPON DEMAND PAY OR REIMBURSE EACH OF THEM FOR, THE INDEMNITY
         MATTERS WHICH MAY BE INCURRED BY OR ASSERTED AGAINST OR INVOLVE ANY OF
         THEM (WHETHER OR NOT ANY OF THEM IS DESIGNATED A PARTY THERETO) AS A
         RESULT OF, ARISING OUT OF OR IN ANY WAY RELATED TO (I) ANY ACTUAL OR
         PROPOSED USE BY THE BORROWER OF THE PROCEEDS OF ANY OF THE LOANS, (II)
         THE EXECUTION, DELIVERY AND PERFORMANCE OF THE LOAN DOCUMENTS, (III)
         THE OPERATIONS OF THE BUSINESS OF THE BORROWER AND THE SUBSIDIARIES,
         (IV) THE FAILURE OF THE BORROWER OR ANY GUARANTOR TO COMPLY WITH THE
         TERMS OF ANY OTHER LOAN DOCUMENT OR THIS AGREEMENT, OR WITH ANY
         GOVERNMENTAL REQUIREMENT, (V) ANY INACCURACY OF ANY REPRESENTATION OR
         ANY BREACH OF ANY WARRANTY OF THE BORROWER OR ANY GUARANTOR SET FORTH
         IN ANY OF THE LOAN DOCUMENTS, (VI) ANY ASSERTION THAT THE LENDERS WERE
         NOT ENTITLED TO RECEIVE THE PROCEEDS RECEIVED PURSUANT TO THE LOAN
         DOCUMENTS OR (VII) ANY OTHER ASPECT OF THE LOAN DOCUMENTS,




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<PAGE>   79

         INCLUDING, WITHOUT LIMITATION, THE REASONABLE FEES AND DISBURSEMENTS OF
         COUNSEL AND ALL OTHER REASONABLE EXPENSES INCURRED IN CONNECTION WITH
         INVESTIGATING, DEFENDING OR PREPARING TO DEFEND ANY SUCH ACTION, SUIT,
         PROCEEDING (INCLUDING ANY INVESTIGATIONS, LITIGATION OR INQUIRIES) OR
         CLAIM AND INCLUDING ALL INDEMNITY MATTERS ARISING BY REASON OF THE
         ORDINARY NEGLIGENCE OF ANY INDEMNIFIED PARTY, BUT EXCLUDING ALL
         INDEMNITY MATTERS ARISING SOLELY BY REASON OF CLAIMS BETWEEN THE
         LENDERS OR ANY LENDER AND THE AGENT OR A LENDER'S SHAREHOLDERS AGAINST
         THE AGENT OR LENDER OR BY REASON OF THE GROSS NEGLIGENCE OR WILLFUL
         MISCONDUCT ON THE PART OF ANY INDEMNIFIED PARTY; AND

              (c) TO INDEMNIFY AND HOLD HARMLESS FROM TIME TO TIME THE
         INDEMNIFIED PARTY FROM AND AGAINST ANY AND ALL LOSSES, CLAIMS, COST
         RECOVERY ACTIONS, ADMINISTRATIVE ORDERS OR PROCEEDINGS, DAMAGES AND
         LIABILITIES TO WHICH ANY SUCH PERSON MAY BECOME SUBJECT (I) UNDER ANY
         ENVIRONMENTAL LAW APPLICABLE TO THE BORROWER OR ANY OF ITS PROPERTIES,
         INCLUDING WITHOUT LIMITATION, THE TREATMENT OR DISPOSAL OF HAZARDOUS
         SUBSTANCES ON ANY OF THEIR PROPERTIES, (II) AS A RESULT OF THE BREACH
         OR NONCOMPLIANCE BY THE BORROWER WITH ANY ENVIRONMENTAL LAW APPLICABLE
         TO THE BORROWER, (III) DUE TO PAST OWNERSHIP BY THE BORROWER OF ANY OF
         ITS PROPERTIES OR PAST ACTIVITY ON ANY OF ITS PROPERTIES WHICH, THOUGH
         LAWFUL AND FULLY PERMISSIBLE AT THE TIME, RESULTS IN PRESENT LIABILITY,
         (IV) THE PRESENCE, USE, RELEASE, STORAGE, TREATMENT OR DISPOSAL OF
         HAZARDOUS SUBSTANCES ON OR AT ANY OF THE PROPERTIES OWNED OR OPERATED
         BY THE BORROWER OR (V) ANY OTHER ENVIRONMENTAL, HEALTH OR SAFETY
         CONDITION IN CONNECTION WITH THE LOAN DOCUMENTS, PROVIDED, HOWEVER, NO
         INDEMNITY SHALL BE AFFORDED UNDER THIS SECTION 12.03(C) IN RESPECT OF
         ANY PROPERTY FOR ANY OCCURRENCE ARISING FROM THE ACTS OR OMISSIONS OF
         THE AGENT OR ANY LENDER DURING THE PERIOD AFTER WHICH SUCH PERSON, ITS
         SUCCESSORS OR ASSIGNS, OR THEIR AGENTS OR REPRESENTATIVES, SHALL HAVE
         OBTAINED POSSESSION OF SUCH PROPERTY (WHETHER BY FORECLOSURE OR DEED IN
         LIEU OF FORECLOSURE, AS MORTGAGEE-IN-POSSESSION OR OTHERWISE).

              (d) No Indemnified Party may settle any claim to be indemnified
         without the consent of the indemnitor, such consent not to be
         unreasonably withheld; provided, that the indemnitor may not reasonably
         withhold consent to any



                                       73
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         settlement that an Indemnified Party proposes, if the indemnitor does
         not have the financial ability to pay all its obligations outstanding
         and asserted against the indemnitor at that time, including, without
         limitation, the maximum potential claims against the Indemnified Party
         to be indemnified pursuant to this Section 12.03.

              (e) In the case of any indemnification hereunder, the Agent or
         Lender, as appropriate shall give notice to the Borrower of any such
         claim or demand being made against the Indemnified Party and the
         Borrower shall have the non-exclusive right to join in the defense
         against any such claim or demand provided that if the Borrower provides
         a defense, the Indemnified Party shall bear its own cost of defense
         unless there is a conflict between the Borrower and such Indemnified
         Party.

              (f) THE FOREGOING INDEMNITIES SHALL EXTEND TO THE INDEMNIFIED
         PARTIES NOTWITHSTANDING THE SOLE OR CONCURRENT NEGLIGENCE OF EVERY KIND
         OR CHARACTER WHATSOEVER, WHETHER ACTIVE OR PASSIVE, WHETHER AN
         AFFIRMATIVE ACT OR AN OMISSION, INCLUDING WITHOUT LIMITATION, ALL TYPES
         OF NEGLIGENT CONDUCT IDENTIFIED IN THE RESTATEMENT (SECOND) OF TORTS OF
         ONE OR MORE OF THE INDEMNIFIED PARTIES OR BY REASON OF STRICT LIABILITY
         IMPOSED WITHOUT FAULT ON ANY ONE OR MORE OF THE INDEMNIFIED PARTIES. TO
         THE EXTENT THAT AN INDEMNIFIED PARTY IS FOUND TO HAVE COMMITTED AN ACT
         OF GROSS NEGLIGENCE OR WILLFUL MISCONDUCT, THIS CONTRACTUAL OBLIGATION
         OF INDEMNIFICATION SHALL CONTINUE BUT SHALL ONLY EXTEND TO THE PORTION
         OF THE CLAIM THAT IS DEEMED TO HAVE OCCURRED BY REASON OF EVENTS OTHER
         THAN THE GROSS NEGLIGENCE OR WILLFUL MISCONDUCT OF SUCH INDEMNIFIED
         PARTY.

              (g) The Borrower's obligations under this Section 12.03 shall
         survive any termination of this Agreement and the payment of the Notes
         and shall continue thereafter in full force and effect.

              (h) The Borrower shall pay any amounts due under this Section
         12.03 within thirty (30) days of the receipt by the Borrower of notice
         of the amount due.

         Section 12.04 Amendments, Etc. Any provision of this Agreement or any
other Loan Document may be amended, modified or waived with the Borrower's and
the Majority Lenders' written consent; provided that (i) no amendment,
modification or waiver which extends the final maturity of the Loans, increases
the Aggregate Maximum Credit Amounts, allows an increase in the Borrowing Base
without the approval of all the Lenders, forgives the principal amount of any
Indebtedness outstanding under this Agreement, releases any guarantor of the
Indebtedness or releases all or substantially all of the collateral, reduces the
interest rate applicable to the Loans or the fees payable to the Lenders
generally, affects Section 2.03(a), this





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<PAGE>   81

Section 12.04 or Section 12.06(a) or modifies the definition of "Majority
Lenders" shall be effective without consent of all Lenders; (ii) no amendment,
modification or waiver which increases the Maximum Credit Amount of any Lender
shall be effective without the consent of such Lender; and (iii) no amendment,
modification or waiver which modifies the rights, duties or obligations of the
Agent shall be effective without the consent of the Agent. No SCI Lender may
modify or amend any material term or provision of the Equity Conversion
Agreement without the consent of the BMO/Soc-Gen Majority Lenders; provided that
a waiver of a default under the Equity Conversion Agreement shall not constitute
a modification or amendment or require the consent of any BMO/Soc-Gen Lender.

         Section 12.05 Successors and Assigns. This Agreement shall be binding
upon and inure to the benefit of the parties hereto and their respective
successors and permitted assigns.

         Section 12.06 Assignments and Participations

              (a) The Borrower may not assign its rights or obligations
         hereunder or under the Notes without the prior consent of all of the
         Lenders and the Agent.

              (b) No SCI Lender may assign its rights or obligations hereunder
         or under the Notes without the prior consent of BMO and its successors
         and Soc-Gen and its successors which consents shall not be unreasonably
         withheld.

              (c) Any BMO/Soc-Gen Lender may sell, assign, transfer or negotiate
         to one or more other lenders, commercial banks, insurance companies,
         other financial institutions or any other Person all or any portion of
         its rights and obligations hereunder, and acceptance of such assignment
         by any assignee shall constitute the agreement of such assignee to be
         bound by the terms of this Agreement applicable to the assigning
         Lender.

              (d) Promptly after receiving evidence of an assignment under
         Section 12.06(c) and following the consent of the BMO/Soc-Gen Majority
         Lenders to an assignment pursuant to Section 12.06(b), the Agent shall
         send a notice of such assignment to the Borrower. Upon receipt of such
         notice and of the Notes that are the subject thereof, the Borrower
         will, at its own expense, execute and deliver new Notes to the assignor
         and/or assignee, as appropriate, in accordance with their respective
         interests. Upon receipt of such executed Assignment and of the Notes
         which are the subject thereof, the Borrower will, at its own expense,
         execute and deliver new Notes to the assignor and/or assignee, as
         appropriate, in accordance with their respective interests as they
         appear. Upon the effectiveness of any assignment pursuant to Section
         12.06(b) or (c), the assignee will become a "Lender," if not already a
         "Lender," for all purposes of this Agreement and the other Loan
         Documents. The assignor shall be relieved of its obligations hereunder
         to the extent of such assignment (and if the assigning Lender no longer
         holds any rights or obligations under this Agreement, such assigning
         Lender shall cease to be a "Lender" hereunder except that its rights
         under Sections 4.06, 5.01, 5.05 and 12.03 shall not be affected). The
         Agent will



                                       75
<PAGE>   82


         prepare on the last Business Day of each month during which an
         assignment has become effective pursuant to Section 12.06(b) or (c), a
         new Annex I giving effect to all such assignments effected during such
         month, and will promptly provide the same to the Borrower and each of
         the Lenders.

              (e) Each Lender may transfer, grant or assign participations in
         all or any part of such Lender's interests hereunder pursuant to this
         Section 12.06(e) to any Person, provided that: (i) such Lender shall
         remain a "Lender" for all purposes of this Agreement and the transferee
         of such participation shall not constitute a "Lender" hereunder; and
         (ii) no participant under any such participation shall have rights to
         approve any amendment to or waiver of any of the Loan Documents except
         to the extent such amendment or waiver would (x) forgive any principal
         owing on any Indebtedness or extend the final maturity of the Loans,
         (y) reduce the interest rate (other than as a result of waiving the
         applicability of any post-default increases in interest rates) or fees
         applicable to any of the Commitments or Loans in which such participant
         is participating, or postpone the payment of any thereof, or (z)
         release any guarantor of the Indebtedness or release all or
         substantially all of the collateral (except as provided in the Loan
         Documents) supporting any of the Commitments or Loans in which such
         participant is participating. In the case of any such participation,
         the participant shall not have any rights under this Agreement or any
         of the other Loan Documents (the participant's rights against the
         granting Lender in respect of such participation to be those set forth
         in the agreement with such Lender creating such participation), and all
         amounts payable by the Borrower hereunder shall be determined as if
         such Lender had not sold such participation, provided that such
         participant shall be entitled to receive additional amounts under
         Article V on the same basis as if it were a Lender and be indemnified
         under Section 12.03 as if it were a Lender. In addition, each agreement
         creating any participation must include an agreement by the participant
         to be bound by the provisions of Section 12.15.

              (f) The Lenders may furnish any information concerning the
         Borrower in the possession of the Lenders from time to time to
         assignees and participants (including prospective assignees and
         participants; provided that, such Persons agree to be bound by the
         provisions of Section 12.15 hereof.

              (g) Notwithstanding anything in this Section 12.06 to the
         contrary, any Lender may assign and pledge its Note to any Federal
         Reserve Bank or the United States Treasury as collateral security
         pursuant to Regulation A of the Board of Governors of the Federal
         Reserve System and any operating circular issued by such Federal
         Reserve System and/or such Federal Reserve Bank. No such assignment
         and/or pledge shall release the assigning and/or pledging Lender from
         its obligations hereunder.

              (h) Notwithstanding any other provisions of this Section 12.06, no
         transfer or assignment of the interests or obligations of any Lender or
         any grant of participations therein shall be permitted if such
         transfer, assignment or grant



                                       76
<PAGE>   83


         would require the Borrower to file a registration statement with the
         SEC or to qualify the Loans under the "Blue Sky" laws of any state.

         Section 12.07 Invalidity. In the event that any one or more of the
provisions contained in any of the Loan Documents shall, for any reason, be held
invalid, illegal or unenforceable in any respect, such invalidity, illegality or
unenforceability shall not affect any other provision of the Notes, this
Agreement or any other Loan Document.

         Section 12.08 Counterparts. This Agreement may be executed in any
number of counterparts, all of which taken together shall constitute one and the
same instrument and any of the parties hereto may execute this Agreement by
signing any such counterpart.

         Section 12.09 References. The words "herein," "hereof," "hereunder" and
other words of similar import when used in this Agreement refer to this
Agreement as a whole, and not to any particular article, section or subsection.
Any reference herein to a Section shall be deemed to refer to the applicable
Section of this Agreement unless otherwise stated herein. Any reference herein
to an exhibit or schedule shall be deemed to refer to the applicable exhibit or
schedule attached hereto unless otherwise stated herein.

         Section 12.10 Survival. The obligations of the parties under Section
4.06, Article V, and Sections 11.05 and 12.03 shall survive the repayment of the
Loans and the termination of the Commitments. To the extent that any payments on
the Indebtedness or proceeds of any collateral are subsequently invalidated,
declared to be fraudulent or preferential, set aside or required to be repaid to
a trustee, debtor in possession, receiver or other Person under any bankruptcy
law, common law or equitable cause, then to such extent, the Indebtedness so
satisfied shall be revived and continue as if such payment or proceeds had not
been received and the Agent's and the Lenders' Liens, security interests,
rights, powers and remedies under this Agreement and each other Loan Document
shall continue in full force and effect. In such event, each Loan Document shall
be automatically reinstated and the Borrower shall take such action as may be
reasonably requested by the Agent and the Lenders to effect such reinstatement.

         Section 12.11 Captions. Captions and section headings appearing herein
are included solely for convenience of reference and are not intended to affect
the interpretation of any provision of this Agreement.

         Section 12.12 NO ORAL AGREEMENTS. THE LOAN DOCUMENTS EMBODY THE ENTIRE
AGREEMENT AND UNDERSTANDING BETWEEN THE PARTIES AND SUPERSEDE ALL OTHER
AGREEMENTS AND UNDERSTANDINGS BETWEEN SUCH PARTIES RELATING TO THE SUBJECT
MATTER HEREOF AND THEREOF. THE LOAN DOCUMENTS REPRESENT THE FINAL AGREEMENT
BETWEEN THE PARTIES AND MAY NOT BE CONTRADICTED BY EVIDENCE OF PRIOR,
CONTEMPORANEOUS OR SUBSEQUENT ORAL AGREEMENTS OF THE PARTIES. THERE ARE NO
UNWRITTEN ORAL AGREEMENTS BETWEEN THE PARTIES.

         Section 12.13 GOVERNING LAW; SUBMISSION TO JURISDICTION.





                                       77
<PAGE>   84


              (a) THIS AGREEMENT, THE LOANS AND THE NOTES SHALL BE GOVERNED BY,
         AND CONSTRUED IN ACCORDANCE WITH, THE LAWS OF THE STATE OF TEXAS EXCEPT
         TO THE EXTENT THAT UNITED STATES FEDERAL LAW PERMITS ANY LENDER TO
         CHARGE INTEREST AT THE RATE ALLOWED BY THE LAWS OF THE STATE WHERE SUCH
         LENDER IS LOCATED. CHAPTER 346 OF THE TEXAS FINANCE CODE (WHICH
         REGULATES CERTAIN REVOLVING LOAN ACCOUNTS AND REVOLVING TRI-PARTY
         ACCOUNTS) SHALL NOT APPLY TO THIS AGREEMENT, THE LOANS, OR THE NOTES.

              (b) ANY LEGAL ACTION OR PROCEEDING WITH RESPECT TO THE LOAN
         DOCUMENTS SHALL BE BROUGHT IN THE COURTS OF THE STATE OF TEXAS OR OF
         THE UNITED STATES OF AMERICA FOR THE SOUTHERN DISTRICT OF TEXAS, AND,
         BY EXECUTION AND DELIVERY OF THIS AGREEMENT, THE BORROWER HEREBY
         ACCEPTS FOR ITSELF AND (TO THE EXTENT PERMITTED BY LAW) IN RESPECT OF
         ITS PROPERTY, GENERALLY AND UNCONDITIONALLY, THE JURISDICTION OF THE
         AFORESAID COURTS. THE BORROWER HEREBY IRREVOCABLY WAIVES ANY OBJECTION,
         INCLUDING, WITHOUT LIMITATION, ANY OBJECTION TO THE LAYING OF VENUE OR
         BASED ON THE GROUNDS OF FORUM NON CONVENIENS, WHICH IT MAY NOW OR
         HEREAFTER HAVE TO THE BRINGING OF ANY SUCH ACTION OR PROCEEDING IN SUCH
         RESPECTIVE JURISDICTIONS. THIS SUBMISSION TO JURISDICTION IS
         NON-EXCLUSIVE AND DOES NOT PRECLUDE THE AGENT OR ANY LENDER FROM
         OBTAINING JURISDICTION OVER THE BORROWER IN ANY COURT OTHERWISE HAVING
         JURISDICTION.

              (c) EACH OF THE BORROWER AND EACH LENDER HEREBY (I) IRREVOCABLY
         AND UNCONDITIONALLY WAIVE, TO THE FULLEST EXTENT PERMITTED BY LAW,
         TRIAL BY JURY IN ANY LEGAL ACTION OR PROCEEDING RELATING TO THIS
         AGREEMENT OR ANY OTHER LOAN DOCUMENT AND FOR ANY COUNTERCLAIM THEREIN;
         (II) IRREVOCABLY WAIVE, TO THE MAXIMUM EXTENT NOT PROHIBITED BY LAW,
         ANY RIGHT IT MAY HAVE TO CLAIM OR RECOVER IN ANY SUCH LITIGATION ANY
         SPECIAL, EXEMPLARY, PUNITIVE OR CONSEQUENTIAL DAMAGES, OR DAMAGES OTHER
         THAN, OR IN ADDITION TO, ACTUAL DAMAGES; (III) CERTIFY THAT NO PARTY
         HERETO NOR ANY REPRESENTATIVE OR AGENT OF COUNSEL FOR ANY PARTY HERETO
         HAS REPRESENTED, EXPRESSLY OR OTHERWISE, OR IMPLIED THAT SUCH PARTY
         WOULD NOT, IN THE EVENT OF LITIGATION, SEEK TO ENFORCE THE FOREGOING
         WAIVERS, AND (IV) ACKNOWLEDGE THAT IT HAS BEEN INDUCED TO ENTER INTO
         THIS AGREEMENT, THE OTHER LOAN DOCUMENTS AND



                                       78
<PAGE>   85


         THE TRANSACTIONS CONTEMPLATED HEREBY AND THEREBY BY, AMONG OTHER
         THINGS, THE MUTUAL WAIVERS AND CERTIFICATIONS CONTAINED IN THIS SECTION
         12.13.

         Section 12.14 Interest. It is the intention of the parties hereto that
each Lender shall conform strictly to usury laws applicable to it. Accordingly,
if the transactions contemplated hereby would be usurious as to any Lender under
laws applicable to it (including the laws of the United States of America and
the State of Texas or any other jurisdiction whose laws may be mandatorily
applicable to such Lender notwithstanding the other provisions of this
Agreement), then, in that event, notwithstanding anything to the contrary in any
of the Loan Documents or any agreement entered into in connection with or as
security for the Loans, it is agreed as follows: (i) the aggregate of all
consideration which constitutes interest under law applicable to any Lender that
is contracted for, taken, reserved, charged or received by such Lender under any
of the Loan Documents or agreements or otherwise in connection with the Loans
shall under no circumstances exceed the maximum amount allowed by such
applicable law, and any excess shall be cancelled automatically and if
theretofore paid shall be credited by such Lender on the principal amount of the
Indebtedness (or, to the extent that the principal amount of the Indebtedness
shall have been or would thereby be paid in full, refunded by such Lender to the
Borrower), and (ii) in the event that the maturity of the Notes is accelerated
resulting from any Event of Default under this Agreement or otherwise, or in the
event of any required or permitted prepayment, then such consideration that
constitutes interest under law applicable to any Lender may never include more
than the maximum amount allowed by such applicable law, and excess interest, if
any, provided for in this Agreement or otherwise shall be cancelled
automatically by such Lender as of the date of such acceleration or prepayment
and, if theretofore paid, shall be credited by such Lender on the principal
amount of the Indebtedness (or, to the extent that the principal amount of the
Indebtedness shall have been or would thereby be paid in full, refunded by such
Lender to the Borrower). All sums paid or agreed to be paid to any Lender for
the use, forbearance or detention of sums due hereunder or under any other Loan
Document shall, to the extent permitted by law applicable to such Lender, be
amortized, prorated, allocated and spread throughout the full term of the Loans
evidenced by the Notes until payment in full so that the rate or amount of
interest on account of any Loans hereunder does not exceed the maximum amount
allowed by such applicable law. If at any time and from time to time (i) the
amount of interest payable to any Lender on any date shall be computed at the
Highest Lawful Rate applicable to such Lender pursuant to this Section 12.14 and
(ii) in respect of any subsequent interest computation period the amount of
interest otherwise payable to such Lender would be less than the amount of
interest payable to such Lender computed at the Highest Lawful Rate applicable
to such Lender, then the amount of interest payable to such Lender in respect of
such subsequent interest computation period shall continue to be computed at the
Highest Lawful Rate applicable to such Lender until the total amount of interest
payable to such Lender shall equal the total amount of interest which would have
been payable to such Lender if the total amount of interest had been computed
without giving effect to this Section 12.14. To the extent that Chapter 303 of
the Texas Finance Code is relevant for the purpose of determining the Highest
Lawful Rate, such Lender elects to determine the applicable rate ceiling under
such Article by the weekly ceiling from time to time in effect.

         Section 12.15 Confidentiality. In the event that the Borrower or any
Guarantor (hereinafter called the "Subject Entities") provides to the Agent or
the Lenders written




                                       79
<PAGE>   86

confidential information or, if communicated as confidential, oral confidential
information belonging to any Subject Entity, the Agent and the Lenders shall
thereafter maintain such information in confidence in accordance with the
standards of care and diligence that each utilizes in maintaining its own
confidential information. This obligation of confidence shall not apply to such
portions of the information which (i) are in the public domain, (ii) hereafter
become part of the public domain without the Agent or the Lenders breaching
their obligation of confidence to any Subject Entity, (iii) are previously known
by the Agent or the Lenders from some source other than any Subject Entity, (iv)
are hereafter developed by the Agent or the Lenders without using a Subject
Entity's information, (v) are hereafter obtained by or available to the Agent or
the Lenders from a third party who owes no obligation of confidence to any
Subject Entity with respect to such information, (vi) are disclosed with a
Subject Entity's consent, (vii) must be disclosed either pursuant to any
Governmental Requirement or to Persons regulating the activities of the Agent or
the Lenders, or (viii) as may be required by law or regulation or order of any
Governmental Authority in any judicial, arbitration or governmental proceeding.
Further, the Agent or a Lender may disclose any such information to any other
Lender, any independent petroleum engineers or consultants, any independent
certified public accountants, any legal counsel employed by such Person in
connection with this Agreement or any other Loan Document, including without
limitation, the enforcement or exercise of all rights and remedies thereunder,
or, subject to Section 12.06, any assignee or participant (including prospective
assignees to which the Borrower has consented and participants) in the Loans;
provided, however, that the Agent or the Lenders shall receive a confidentiality
agreement from the Person to whom such information is disclosed such that said
Person shall have the same obligation to maintain the confidentiality of such
information as is imposed upon the Agent or the Lenders hereunder.
Notwithstanding anything to the contrary provided herein, this obligation of
confidence shall cease three (3) years from the date the information was
furnished, unless the Borrower requests in writing at least thirty (30) days
prior to the expiration of such three year period, to maintain the
confidentiality of such information for an additional three year period.

         Section 12.16 Prior Credit Agreement. The Prior Credit Agreement is
superseded by this Agreement and is of no further force or effect.

         Section 12.17 Release Regarding the Prior Notes and Related Documents.
To induce Lenders to purchase the Prior Notes and the rights under certain of
the documents securing said Prior Notes (the "Prior Security Documents"), the
Borrower hereby fully releases and discharges the Agent and the Lenders, and
each of their officers, directors, employees, representatives, agents and
affiliates, from all claims, demands, causes of action, liabilities or other
obligations of any kind whatsoever, including, without limitation, offsets,
reductions, rebatements or claims of usury, known or unknown, whether now
existing or hereafter asserted in connection with the Prior Notes and the Prior
Security Documents arising from matters occurring before the date of the
Lender's purchase.

         Section 12.18 Effectiveness. This Agreement shall be effective on the
Closing Date (the "Effective Date") upon its execution and delivery by Borrower,
BMO, Soc-Gen and SCI. Although Brigham Exploration, Brigham, Inc., Brigham
Holdings I, LLC and Brigham Holdings II, LLC, are not parties to this Agreement
they are executing this Agreement as Releasing Parties under Section 12.20 below
and Section 12.20 will become effective as to each Releasing Party as described
in Section 12.20(c).




                                       80
<PAGE>   87


         Section 12.19 EXCULPATION PROVISIONS. EACH OF THE PARTIES HERETO
SPECIFICALLY AGREES THAT IT HAS A DUTY TO READ THIS AGREEMENT AND THE OTHER LOAN
DOCUMENTS AND AGREES THAT IT IS CHARGED WITH NOTICE AND KNOWLEDGE OF THE TERMS
OF THIS AGREEMENT AND THE OTHER LOAN DOCUMENTS; THAT IT HAS IN FACT READ THIS
AGREEMENT AND IS FULLY INFORMED AND HAS FULL NOTICE AND KNOWLEDGE OF THE TERMS,
CONDITIONS AND EFFECTS OF THIS AGREEMENT; THAT IT HAS BEEN REPRESENTED BY
INDEPENDENT LEGAL COUNSEL OF ITS CHOICE THROUGHOUT THE NEGOTIATIONS PRECEDING
ITS EXECUTION OF THIS AGREEMENT AND THE OTHER LOAN DOCUMENTS; AND HAS RECEIVED
THE ADVICE OF ITS ATTORNEY IN ENTERING INTO THIS AGREEMENT AND THE OTHER LOAN
DOCUMENTS; AND THAT IT RECOGNIZES THAT CERTAIN OF THE TERMS OF THIS AGREEMENT
AND THE OTHER LOAN DOCUMENTS RESULT IN ONE PARTY ASSUMING THE LIABILITY INHERENT
IN SOME ASPECTS OF THE TRANSACTION AND RELIEVING THE OTHER PARTY OF ITS
RESPONSIBILITY FOR SUCH LIABILITY. EACH PARTY HERETO AGREES AND COVENANTS THAT
IT WILL NOT CONTEST THE VALIDITY OR ENFORCEABILITY OF ANY EXCULPATORY PROVISION
OF THIS AGREEMENT AND THE OTHER LOAN DOCUMENTS ON THE BASIS THAT THE PARTY HAD
NO NOTICE OR KNOWLEDGE OF SUCH PROVISION OR THAT THE PROVISION IS NOT
"CONSPICUOUS."

         Section 12.20 RELEASE.

              (a) Each of the Releasing Parties desires and intends fully to
         compromise, release and settle any and all of the Released Claims; and
         each of the Releasing Parties hereby covenants, warrants and represents
         unto each of the Released Parties that such Releasing Party does hereby
         FOREVER RELEASE, ACQUIT, WAIVE AND DISCHARGE each of the Released
         Parties of and from the Released Claims and each of the Releasing
         Parties hereby declares the same FOREVER RELEASED, ACQUITTED, WAIVED,
         SETTLED AND DISCHARGED. This release is effective without regard to
         whether (i) such Released Claims are known or unknown, (ii) damages
         arising out of such Released Claims have yet accrued, (iii) such
         Released Claims arose collaterally, directly, derivatively, or
         otherwise between the parties hereto or (iv) an ordinary person in the
         same or similar circumstances would or would not, through the exercise
         of due care, have discovered such claims by the date of this Agreement.
         In connection with the foregoing release:

              (b) Borrower and each of the Guarantors represents and warrants
         that it has the full power and authority to perform the release granted
         in this Section 12.20 and that it has not in any manner made any
         assignment of any Released Claim to any third party.

              (c) The release granted in this Section 12.20 by each Releasing
         Party will be effective upon execution of this Agreement by such
         Releasing Party hereto.




                                       81
<PAGE>   88


              (d) Each party executing this Agreement understands and agrees
         that the release granted in this Section 12.20 is a full, final and
         complete release of the Released Claims and that such release may be
         pleaded as an absolute and final bar to any or all suits which may
         hereafter be filed or prosecuted by any one or more of the Releasing
         Parties or anyone claiming by, through or under any one or more of the
         Releasing Parties in respect of any of the matters released hereby, and
         that no recovery on account of the Released Claims may hereafter be had
         from any of the Released Parties; and that the consideration given for
         such release is not an admission of liability or fault on the part of
         any of the Released Parties (it being the express intent of the parties
         hereto to obtain peace of mind and avoid the expense and uncertainty of
         potential litigation), and that none of the Releasing Parties or those
         claiming by, through or under any of them will ever claim that it is.

              (e) The parties hereto acknowledge that the release granted by
         this Section 12.20 does not have any effect with respect to
         relationships between the Borrower and each of the Guarantors and the
         Lenders and the Agent other than in connection with the Lending
         Relationship.





                                       82
<PAGE>   89






         The parties hereto have caused this Agreement to be duly executed as of
the day and year first above written.

BORROWER:                                BRIGHAM OIL & GAS, L.P.

                                         By: Brigham, Inc., its General Partner


                                         By:
                                            ----------------------------------
                                         Name:  Curtis F. Harrell
                                         Title:  Chief Financial Officer

                                         Address for Notices:

                                         6300 Bridge Point Parkway
                                         Building 2, Suite 500
                                         Austin, Texas 78730

                                         Telecopier No.:  (512) 427-3400
                                         Telephone No.:  (512) 427-3300

                                         Attention:  Curtis F. Harrell

GUARANTOR:                               BRIGHAM EXPLORATION COMPANY
(for purposes of Section 12.20)



                                         By:
                                            ----------------------------------
                                         Name:  Karen E. Lynch
                                         Title:  Vice President


GUARANTOR:                               BRIGHAM, INC.
(for purposes of Section 12.20)



                                         By:
                                            ----------------------------------
                                         Name:  Curtis F. Harrell
                                         Title:  Chief Financial Officer





                                       S
<PAGE>   90



GUARANTOR:                               BRIGHAM HOLDINGS I, LLC
(for purposes of Section 12.20)



                                         By:
                                            ----------------------------------
                                         Name:
                                              --------------------------------
                                         Title:
                                              --------------------------------

GUARANTOR:                               BRIGHAM HOLDINGS II, LLC
(for purposes of Section 12.20)



                                         By:
                                            ----------------------------------
                                         Name:
                                         Title:


LENDER AND AGENT:                        BANK OF MONTREAL



                                         By:
                                            ----------------------------------
                                         Name:  Thomas E. McGraw
                                         Title:  Director


                                         Lending Office for Base Rate Loans and
                                         Eurodollar Loans:
                                         115 South LaSalle
                                         Chicago, Illinois 60603

                                         With a copy to:
                                         Thomas E. McGraw
                                         Director, U.S. Corporate Banking
                                         Bank of Montreal
                                         700 Louisiana, Suite 4400
                                         Houston, Texas 77002
                                         Telecopier No.:  (713) 223-0477
                                         Telephone No.:  (713) 546-9781

                                         Address for Notices:

                                         Bank of Montreal
                                         700 Louisiana, Suite 4400
                                         Houston, Texas 77002
                                         Telecopier No.:  (713) 223-0477
                                         Telephone No.:  (713) 546-9781
                                         Attention:  Thomas E. McGraw





                                        S
<PAGE>   91



LENDER:                                  SOCIETE GENERALE, SOUTHWEST AGENCY



                                         By:
                                            ----------------------------------
                                         Name:  Mark A. Cox
                                         Title:  Director


                                         Address for Notices:

                                         1111 Bagby Street, Suite 2020
                                         Houston, Texas 77002

                                         Telecopier No.:  (713) 650-0824
                                         Telephone No.:  (713) 759-6315
                                         Attention:  Mark A. Cox

LENDER:                                  SHELL CAPITAL INC.



                                         By:
                                            ----------------------------------
                                         Name:  Robert L. Roberts
                                         Title:  Vice President


                                         Address for Notices:

                                         910 Louisiana Street, Suite 5000
                                         Houston, Texas 77002-4916

                                         Telecopier No.:  (713) 241-5222
                                         Telephone No.:  (713) 241-4130

                                         Attention:  Robert L. Roberts



                                       S
<PAGE>   92








                                     ANNEX 1


                         LIST OF MAXIMUM CREDIT AMOUNTS

<TABLE>
<CAPTION>
                       PRIOR TO AN INCREASE EVENT                                       AFTER AN INCREASE EVENT

Name of Lender         Percentage Share     Maximum Credit Amount     Percentage Share     Maximum Credit Amount
- ---------------        ----------------     ---------------------     ----------------     ---------------------
<S>                    <C>                  <C>                       <C>                  <C>
SCI                         50.00000000%              $35,000,000          53.33333333%              $40,000,000
BMO                         33.07690000%               23,153,830          30.87177333%               23,153,830
Soc-Gen                     16.92310000%               11,846,170          15.79489333%               11,846,170
</TABLE>







                                 Annex 1, Page 1
<PAGE>   93




                                    EXHIBIT A


                                  FORM OF NOTE

$______________________                      _______________ , __________



         FOR VALUE RECEIVED, BRIGHAM OIL & GAS, L.P., a Delaware limited
partnership (the "Borrower") hereby promises to pay to the order of __________
(the "Lender"), at the Principal Office of BANK OF MONTREAL (the "Agent"), at
115 South LaSalle Street, Chicago, Illinois 60603, the principal sum of
________________________ Dollars ($_______) (or such lesser amount as shall
equal the aggregate unpaid principal amount of the Loans made by the Lender to
the Borrower under the Credit Agreement, as hereinafter defined), in lawful
money of the United States of America and in immediately available funds, on the
dates and in the principal amounts provided in the Credit Agreement, and to pay
interest on the unpaid principal amount of each such Loan, at such office, in
like money and funds, for the period commencing on the date of such Loan until
such Loan shall be paid in full, at the rates per annum and on the dates
provided in the Credit Agreement.

         The date, amount, Type, interest rate, Interest Period and maturity of
each Loan made by the Lender to the Borrower, and each payment made on account
of the principal thereof, shall be recorded by the Lender on its books and,
prior to any transfer of this Note, may be endorsed by the Lender on the
schedules attached hereto or any continuation thereof or on any separate record
maintained by the Lender.

         This Note is one of the Notes referred to in the Amended and Restated
Credit Agreement dated as of February ___, 2000 among the Borrower, the Lenders
which are or become parties thereto (including the Lender) and the Agent, and
evidences Loans made by the Lender thereunder (such Amended and Restated Credit
Agreement as the same may be amended or supplemented from time to time, the
"Credit Agreement"). Capitalized terms used in this Note have the respective
meanings assigned to them in the Credit Agreement.

         This Note is issued pursuant to the Credit Agreement and is entitled to
the benefits provided for in the Credit Agreement and the other Loan Documents.
The Credit Agreement provides for the acceleration of the maturity of this Note
upon the occurrence of certain events, for prepayments of Loans upon the terms
and conditions specified therein and other provisions relevant to this Note.





                                 Exh A, Page 1
<PAGE>   94



         THIS NOTE SHALL BE GOVERNED BY, AND CONSTRUED IN ACCORDANCE WITH, THE
LAWS OF THE STATE OF TEXAS.

                                        BRIGHAM OIL & GAS, L.P.

                                        By: Brigham, Inc., its General Partner



                                        By:
                                           -----------------------------------
                                        Name:
                                             ---------------------------------
                                        Title:
                                              --------------------------------

                                 Exh A, Page 2


<PAGE>   95




                                   EXHIBIT B


             FORM OF BORROWING, CONTINUATION AND CONVERSION REQUEST

                          _____________________, 2000

                  BRIGHAM OIL & GAS, L.P., a Delaware limited partnership (the
"Borrower"), pursuant to the Amended and Restated Credit Agreement dated as of
February ____, 2000 (together with all amendments or supplements thereto, the
"Credit Agreement") among the Borrower, BANK OF MONTREAL, as Agent and the
lenders (the "Lenders") which are or become parties thereto, and such Lenders
(the "Lender"), hereby makes the requests indicated below (unless otherwise
defined herein, capitalized terms are defined in the Credit Agreement):

[ ]     1.     Loans:

               (a)  Aggregate amount of new Loans to be $ ________________ ;


               (b)  Requested funding date is _______________ , 2000;


               (c)  $___________________of such borrowings are to be Eurodollar
                     Loans;
                    $___________________of such borrowings are to be Base Rate

                     Loans; and
               (d)   Length of Interest Period for Eurodollar Loans is:
                     ___________________.

[ ]      2.    Eurodollar Loan Continuation for Eurodollar Loans maturing
               on ______________;

               (a)   Aggregate amount to be continued as Eurodollar Loans is
                     $_______________ ;

               (b)   Aggregate amount to be converted to Base Rate Loans is
                     $_________________;

               (c)   Length of Interest Period for continued Eurodollar Loans
                     is _____________.

[ ]      3.    Conversion of Outstanding Base Rate Loans to Eurodollar Loans:
               Convert $ _________________________ of the outstanding Base Rate
               Loans to Eurodollar Loans on _____________ with an Interest
               Period of ______.


[ ]      4.    Conversion of outstanding Eurodollar Loans to Base Rate Loans:
               Convert $ ________________ of the outstanding Eurodollar Loans
               with Interest Period maturing on __________________,  2000, to
               Base Rate Loans.



                                  Exh B, Page 1






<PAGE>   96

         The undersigned certifies that he is the _____________________________
of the Borrower, and that as such he is authorized to execute this certificate
on behalf of the Borrower. The undersigned further certifies, represents and
warrants on behalf of the Borrower that the Borrower is entitled to receive the
requested borrowing, continuation or conversion under the terms and conditions
of the Credit Agreement.

                                         BRIGHAM OIL & GAS, L.P.

                                         By: Brigham, Inc., its General Partner



                                         By:
                                             ---------------------------------
                                         Name:
                                              --------------------------------
                                         Title:
                                              ---------------------------------






                                  Exh B, Page 2
<PAGE>   97






                                   EXHIBIT C-1


                         FORM OF COMPLIANCE CERTIFICATE

         The undersigned hereby certifies that he is the ________________ of
BRIGHAM, INC., a Nevada corporation, as general partner of BRIGHAM OIL & GAS,
L.P., a Delaware limited partnership (the "Borrower") and that as such he is
authorized to execute this certificate on behalf of the Borrower. With reference
to the Amended and Restated Credit Agreement dated as of February ____, 2000
(together with all amendments or supplements thereto being the "Agreement")
among the Borrower, BANK OF MONTREAL, as Agent for the lenders (the "Lenders")
which are or become a party thereto, and such Lenders, the undersigned
represents and warrants as follows (each capitalized term used herein having the
same meaning given to it in the Agreement unless otherwise specified):

              (a) The representations and warranties of the Borrower contained
         in Article VII of the Agreement and in the other Loan Documents and
         otherwise made in writing by or on behalf of the Borrower pursuant to
         the Agreement and the other Loan Documents were true and correct when
         made, and are repeated at and as of the time of delivery hereof and are
         true and correct at and as of the time of delivery hereof, except to
         the extent such representations and warranties are expressly limited to
         an earlier date or the Majority Lenders have expressly consented in
         writing to the contrary.

              (b) The Borrower has performed and complied with all agreements
         and conditions contained in the Agreement and in the other Loan
         Documents required to be performed or complied with by it prior to or
         at the time of delivery hereof.

              (c) Since December 31, 1998, no change has occurred, either in any
         case or in the aggregate, in the condition, financial or otherwise, of
         the Borrower which would have a Material Adverse Effect.

              (d) There exists, and, after giving effect to the loan or loans
         with respect to which this certificate is being delivered, will exist,
         no Default under the Agreement or any event or circumstance which
         constitutes, or with notice or lapse of time (or both) would
         constitute, an event of default under any loan or credit agreement,
         indenture, deed of trust, security agreement or other agreement or
         instrument evidencing or pertaining to any Debt of the Borrower or
         under any material agreement or instrument to which the Borrower is a
         party or by which the Borrower is bound.



                                Exh C-1, Page 1


<PAGE>   98




         EXECUTED AND DELIVERED this ________day of ___________________.



                                        BRIGHAM OIL & GAS, L.P.

                                        By: Brigham, Inc., its General Partner



                                        By:
                                           -----------------------------------
                                        Name:
                                             ---------------------------------
                                        Title:
                                              ---------------------------------




                                Exh C-1, Page 2
<PAGE>   99





                                   EXHIBIT C-2

                        FORM OF CERTIFICATE ACCOMPANYING

                              FINANCIAL STATEMENTS

Reference is made to that certain Amended and Restated Credit Agreement dated as
of February ___, 2000 (as from time to time amended, the "Agreement"), by and
among BRIGHAM OIL & GAS, L.P., a Delaware limited partnership ("Borrower"), BANK
OF MONTREAL, as Agent ("Agent"), and certain financial institutions ("Lenders").
Terms which are defined in the Agreement are used herein with the meanings given
them in the Agreement.

         This Certificate is furnished pursuant to Section 8.01 of the
Agreement. Together herewith Borrower is furnishing to Agent and each Lender
Borrower's *[audited/unaudited] financial statements (the "Financial
Statements") as at ____________ (the "Reporting Date"). Borrower hereby
represents and warrants to Agent and each Lender that:

              (a) The officer of Borrower signing this instrument is the duly
         elected, qualified and acting _________ of Borrower and as such is a
         Responsible Officer.

              (b) No Default existed on the Reporting Date or otherwise exists
         on the date of this certificate [EXCEPT AS SPECIFIED ON A SCHEDULE
         ATTACHED HERETO]. [EXCEPT AS SPECIFIED ON A SCHEDULE ATTACHED HERETO,]
         the representations and warranties of Borrower set forth in the
         Agreement and the other Loan Documents are true and correct in all
         material respects on and as of the date hereof (except to the extent
         that such representations and warranties are expressly limited to an
         earlier date or the Majority Lenders have expressly consented in
         writing to the contrary).

              (c) The Borrower has performed and complied with all agreements
         and conditions contained in the Agreement and in the other Loan
         Documents required to be performed or complied with by it prior to or
         at the time of delivery hereof.

              (d) No change or event has occurred which has caused a Material
         Adverse Effect that is continuing.

              (e) Attached hereto is a schedule of computations showing Brigham
         Exploration's compliance with Sections 5.2(q), (r) and (s) of its
         Guaranty Agreement as of the Reporting Date.

              (f) The Financial Statements fairly present the consolidated and
         consolidating financial condition and consolidated results of
         operations of Brigham Exploration and its Consolidated Subsidiaries in


                                Exh C-2, Page 1





<PAGE>   100


         accordance with GAAP, as at the end of, and for, the period indicated
         therein (subject to normal year-end audit adjustments).

         The undersigned officer is executing this certificate in his capacity
as an officer of General Partner and not in any individual capacity.

         IN WITNESS WHEREOF, this certificate is executed as of
_________________________.

                                       BRIGHAM OIL & GAS COMPANY

                                       By: Brigham, Inc., its General Partner



                                        By:
                                           -----------------------------------
                                        Name:
                                             ---------------------------------
                                        Title:
                                              ---------------------------------




                                Exh C-2, Page 2
<PAGE>   101






                                   EXHIBIT D-1


                             LIST OF LOAN DOCUMENTS

1.   Assignment of Note and Liens among the Borrower, Bank One, Texas, N.A. and
     the Agent and corresponding Financing Statement Assignments

2.   Amended and Restated Mortgage, Deed of Trust, Assignment of Production,
     Security Agreement and Financing Statement execute by the Borrower and the
     Agent

3.   Guaranty Agreement executed by Brigham, Inc.

4.   Guaranty Agreement executed by Brigham Holding I, L.L.C.

5.   Guaranty Agreement executed by Brigham Holding II, L.L.C.

6.   Guaranty Agreement executed by Brigham Exploration Company

7.   Security Agreement executed by Brigham Exploration Company covering stock
     in Brigham, Inc.

8.   Financing Statement executed by Brigham Exploration Company with respect to
     item 7 above

9.   Stock power executed by Brigham Exploration Company and related stock
     certificate of Brigham, Inc. issued in the name of Brigham Exploration
     Company

10.  Security Agreement executed by the Borrower covering accounts, general
     intangibles, equipment and inventory

11.  Financing Statement executed by the Borrower with respect to item 10 above

12.  Mortgage, Deed of Trust, Assignment of Production, Security Agreement and
     Financing Statement executed by Borrower and Agent in substantially the
     form attached hereto as Exhibit F.

13.  Mortgage, Deed of Trust, Assignment of Production, Security Agreement and
     Financing Statement executed by both Borrower and Agent in substantially
     the form attached hereto as Exhibit G.

14.  Second Amendment to Security Agreement (Accounts) - Borrower.

15.  Second Amendment to Security Agreement (Stock) - Borrower.





                                Exh D-1, Page 1


<PAGE>   102

16.  Third Supplement to Mortgage (1998) - Borrower.

17.  Supplement to Mortgage (August 1998) - Borrower.

18.  Supplement to Mortgage (January 1999) - Borrower.

19.  Supplement to Mortgage (March 1999) - Borrower.

20.  Supplement to Mortgage (June 1999) - Borrower.

21.  Supplement to Mortgage (September 1999) - Borrower.

22.  Amendment to January 26, 1998 Security Agreement - Brigham Exploration.

23.  Amendment to August 20, 1998 Security Agreement - Brigham Exploration.

24.  First Amendment to Guaranty Agreement - Brigham, Inc.

25.  Second Amendment to Guaranty Agreement - Brigham, Inc.

26.  First Amendment to Guaranty Agreement - Brigham Holdings II, LLC.

27.  Second Amendment to Security Agreement - Brigham Holdings II, LLC.

28.  First Amendment to Guaranty Agreement - Brigham Holdings I, LLC.

29.  Second Amendment to Security Agreement - Brigham Holdings I, LLC.

30.  Amended and Restated Guaranty Agreement executed by Brigham Exploration
     Company

31.  Amended and Restated Credit Agreement

32.  Lenders' Partial Assignment of Notes

33.  Second Amendment to Intercreditor and Subordination Agreement executed by
     Enron/Chase Bank of Texas, National Association





                                Exh D-1, Page 2



<PAGE>   103




                                    EXHIBIT E


                                     FORM OF


                              ASSIGNMENT AGREEMENT

         THIS ASSIGNMENT AGREEMENT ("Agreement") dated as of _________________,
_________ is between __________________________ (the "Assignor") and
___________________(the "Assignee").


                                    RECITALS

         A. The Assignor is a party to the Amended and Restated Credit Agreement
dated as of February ___, 2000 (as amended and supplemented and in effect from
time to time, the "Credit Agreement") among BRIGHAM OIL & GAS, L.P., a
______________ limited partnership (the "Borrower"), each of the lenders that is
or becomes a party thereto as provided in Section 12.06 of the Credit Agreement
(individually, together with its successors and assigns, a "Lender", and
collectively, together with their successors and assigns, the "Lenders"), and
BANK OF MONTREAL, in its individual capacity ("BMO"), and as agent for the
Lenders (in such capacity, together with its successors in such capacity, the
"Agent").

         B. The Assignor proposes to sell, assign and transfer to the Assignee,
and the Assignee proposes to purchase and assume from the Assignor, [all] [a
portion] of the Assignor's Maximum Credit Amount, outstanding Loans, all on the
terms and conditions of this Agreement.

         C. In consideration of the foregoing and the mutual agreements
contained herein, and for other good and valuable consideration, the receipt and
sufficiency of which are hereby acknowledged, the parties hereto agree as
follows:


                                    ARTICLE I

                                  Definitions.

         Section 1.01 Definitions. All capitalized terms used but not defined
herein have the respective meanings given to such terms in the Credit Agreement.

         Section 1.02 Other Definitions. As used herein, the following terms
have the following respective meanings:

                  "Assigned Interest" shall mean all of Assignor's (in its
         capacity as a "Lender") rights and obligations (i) under the





                                Exh E, Page 1
<PAGE>   104


         Credit Agreement and the other Loan Documents in respect of the Maximum
         Credit Amount of the Assignor in the principal amount equal to $ , and
         (ii) to make Loans under the Maximum Credit Amount and any right to
         receive payments for the Loans outstanding under the Maximum Credit
         Amount $ (the "Loan Balance"), plus the interest and fees which will
         accrue from and after the Assignment Date.

                           "Assignment Date" shall mean ________________,2000.


                                   ARTICLE II


                              SALE AND ASSIGNMENT.

         Section 2.01 Sale and Assignment. On the terms and conditions set forth
herein, effective on and as of the Assignment Date, the Assignor hereby sells,
assigns and transfers to the Assignee, and the Assignee hereby purchases and
assumes from the Assignor, all of the right, title and interest of the Assignor
in and to, and all of the obligations of the Assignor in respect of, the
Assigned Interest. Such sale, assignment and transfer is without recourse and,
except as expressly provided in this Agreement, without representation or
warranty.

         Section 2.02 Assumption of Obligations. The Assignee agrees with the
Assignor (for the express benefit of the Assignor and the Borrower) that the
Assignee will, from and after the Assignment Date, perform all of the
obligations of the Assignor in respect of the Assigned Interest. From and after
the Assignment Date: (a) the Assignor shall be released from the Assignor's
obligations in respect of the Assigned Interest, and (b) the Assignee shall be
entitled to all of the Assignor's rights, powers and privileges under the Credit
Agreement and the other Loan Documents in respect of the Assigned Interest.

         Section 2.03 Acknowledgement by Agent and Borrower. By executing this
Agreement as provided below, in accordance with Section 12.06(b) of the Credit
Agreement, the Agent and the Borrower hereby acknowledge notice of the
transactions contemplated by this Agreement.




                                Exh E-1, Page 2
<PAGE>   105


                                   ARTICLE III


                                    PAYMENTS.

     Section 3.01 Payments. As consideration for the sale, assignment and
transfer contemplated by Section 2.01 hereof, the Assignee shall, on the
Assignment Date, assume Assignor's obligations in respect of the Assigned
Interest and pay to the Assignor an amount equal to the Loan Balance, if any. An
amount equal to all accrued and unpaid interest and fees shall be paid to the
Assignor as provided in Section 3.02 (iii) below. Except as otherwise provided
in this Agreement, all payments hereunder shall be made in Dollars and in
immediately available funds, without setoff, deduction or counterclaim.

     Section 3.02 Allocation of Payments. The Assignor and the Assignee agree
that (i) the Assignor shall be entitled to any payments of principal with
respect to the Assigned Interest made prior to the Assignment Date, together
with any interest and fees with respect to the Assigned Interest accrued prior
to the Assignment Date, (ii) the Assignee shall be entitled to any payments of
principal, with respect to the Assigned Interest made from and after the
Assignment Date, together with any and all interest and fees with respect to the
Assigned Interest accruing from and after the Assignment Date, and (iii) the
Agent is authorized and instructed to allocate payments received by it for
account of the Assignor and the Assignee as provided in the foregoing clauses.
Each party hereto agrees that it will hold any interest, fees or other amounts
that it may receive to which the other party hereto shall be entitled pursuant
to the preceding sentence for account of such other party and pay, in like money
and funds, any such amounts that it may receive to such other party promptly
upon receipt.

     Section 3.03 Delivery of Notes. Promptly following the receipt by the
Assignor of the consideration required to be paid under Section 3.01 hereof, the
Assignor shall, in the manner contemplated by Section 12.06(b) of the Credit
Agreement, (i) deliver to the Agent (or its counsel) the Note held by the
Assignor and (ii) notify the Agent to request that the Borrower execute and
deliver new Notes to the Assignor, if Assignor continues to be a Lender, and the
Assignee, dated the date of this Agreement in respective principal amounts equal
to the respective Maximum Credit Amounts of the Assignor (if appropriate) and
the Assignee after giving effect to the sale, assignment and transfer
contemplated hereby.

     Section 3.04 Further Assurances. The Assignor and the Assignee hereby agree
to execute and deliver such other instruments, and take such other actions, as
either party may reasonably request in connection with the transactions
contemplated by this Agreement.


                                 Exh E, Page 3
<PAGE>   106


                                   ARTICLE IV


                              CONDITIONS PRECEDENT.

     Section 4.01 Conditions Precedent. The effectiveness of the sale,
assignment and transfer contemplated hereby is subject to the satisfaction of
each of the following conditions precedent:

          (a) the execution and delivery of this Agreement by the Assignor and
     the Assignee;

          (b) the receipt by the Assignor of the payment required to be made by
     the Assignee under Section 3.01 hereof; and

          (c) the acknowledgment by the Agent and the Borrower contemplated by
     Section 2.03 hereof.


                                    ARTICLE V


                         REPRESENTATIONS AND WARRANTIES.

     Section 5.01 Representations and Warranties of the Assignor. The Assignor
represents and warrants to the Assignee as follows:

          (a) it has all requisite power and authority, and has taken all action
     necessary to execute and deliver this Agreement and to fulfill its
     obligations under, and consummate the transactions contemplated by, this
     Agreement;

          (b) the execution, delivery and compliance with the terms hereof by
     Assignor and the delivery of all instruments required to be delivered by it
     hereunder do not and will not violate any Governmental Requirement
     applicable to it;

          (c) this Agreement has been duly executed and delivered by it and
     constitutes the legal, valid and binding obligation of the Assignor,
     enforceable against it in accordance with its terms;

          (d) all approvals and authorizations of, all filings with and all
     actions by any Governmental Authority necessary for the validity or
     enforceability of its obligations under this Agreement have been obtained;


                                 Exh E, Page 4
<PAGE>   107


          (e) the Assignor has good title to, and is the sole legal and
     beneficial owner of, the Assigned Interest, free and clear of all Liens,
     claims, participations or other charges of any nature whatsoever; and

          (f) the transactions contemplated by this Agreement are commercial
     banking transactions entered into in the ordinary course of the banking
     business of the Assignor.

     Section 5.02 Disclaimer. Except as expressly provided in Section 5.01
hereof, the Assignor does not make any representation or warranty, nor shall it
have any responsibility to the Assignee, with respect to the accuracy of any
recitals, statements, representations or warranties contained in the Credit
Agreement or in any certificate or other document referred to or provided for
in, or received by any Lender under, the Credit Agreement, or for the value,
validity, effectiveness, genuineness, execution, effectiveness, legality,
enforceability or sufficiency of the Credit Agreement, the Notes or any other
document referred to or provided for therein or for any failure by the Borrower
or any other Person (other than Assignor) to perform any of its obligations
thereunder or for the existence, value, perfection or priority of any collateral
security or the financial or other condition of the Borrower or the Subsidiaries
or any other obligor or guarantor, or any other matter relating to the Credit
Agreement or any other Loan Document or any extension of credit thereunder.

     Section 5.03 Representations and Warranties of the Assignee. The Assignee
represents and warrants to the Assignor as follows:

          (a) it has all requisite power and authority, and has taken all action
     necessary to execute and deliver this Agreement and to fulfill its
     obligations under, and consummate the transactions contemplated by, this
     Agreement;

          (b) the execution, delivery and compliance with the terms hereof by
     Assignee and the delivery of all instruments required to be delivered by it
     hereunder do not and will not violate any Governmental Requirement
     applicable to it;

          (c) this Agreement has been duly executed and delivered by it and
     constitutes the legal, valid and binding obligation of the Assignee,
     enforceable against it in accordance with its terms;

          (d) all approvals and authorizations of, all filings with and all
     actions by any Governmental Authority necessary for the validity or
     enforceability of its obligations under this Agreement have been obtained;

          (e) the Assignee has fully reviewed the terms of the Credit Agreement
     and the other Loan Documents and has independently and without reliance
     upon the Assignor, and based on such information as the Assignee has deemed
     appropriate, made its own credit analysis and decision to enter into this
     Agreement;


                                 Exh E, Page 5
<PAGE>   108


          (f) the Assignee hereby affirms that the representations contained in
     Section 4.06(d)(i)(1) of the Credit Agreement are true and accurate as to
     Assignee. If Section 4.06(d)(i)(2) is applicable to the Assignee, Assignee
     shall promptly deliver to the Agent and the Borrower such certifications as
     are required thereby to avoid the withholding taxes referred to in Section
     4.06; and

          (g) the transactions contemplated by this Agreement are commercial
     transactions entered into in the ordinary course of the business of the
     Assignee.


                                   ARTICLE VI


                                 MISCELLANEOUS.

     Section 6.01 Notices. All notices and other communications provided for
herein (including, without limitation, any modifications of, or waivers,
requests or consents under, this Agreement) shall be given or made in writing
(including, without limitation, by telex or telecopy) to the intended recipient
at its "Address for Notices" specified below its name on the signature pages
hereof or, as to either party, at such other address as shall be designated by
such party in a notice to the other party.

     Section 6.02 Amendment, Modification or Waiver. No provision of this
Agreement may be amended, modified or waived except by an instrument in writing
signed by the Assignor and the Assignee.

     Section 6.03 Successors and Assigns. This Agreement shall be binding upon
and inure to the benefit of the parties hereto and their respective successors
and permitted assigns. The representations and warranties made herein by the
Assignee are also made for the benefit of the Agent and the Borrower, and the
Assignee agrees that the Agent and the Borrower are entitled to rely upon such
representations and warranties.

     Section 6.04 Assignments. Neither party hereto may assign any of its rights
or obligations hereunder except in accordance with the terms of the Credit
Agreement.

     Section 6.05 Captions. The captions and section headings appearing herein
are included solely for convenience of reference and are not intended to affect
the interpretation of any provision of this Agreement.

     Section 6.06 Counterparts. This Agreement may be executed in any number of
counterparts, each of which shall be identical and all of which, taken together,
shall constitute one and the same instrument, and each of the parties hereto may
execute this Agreement by signing any such counterpart.


                                 Exh E, Page 6
<PAGE>   109


     Section 6.07 Governing Law. This Agreement shall be governed by, and
construed in accordance with, the law of the State of Texas.

     Section 6.08 Expense. To the extent not paid by the Borrower pursuant to
the terms of the Credit Agreement, each party hereto shall bear its own expenses
in connection with the execution, delivery and performance of this Agreement.

     Section 6.09 Waiver of Jury Trial. EACH OF THE PARTIES HERETO HEREBY
IRREVOCABLY WAIVES, TO THE FULLEST EXTENT PERMITTED BY LAW, ANY AND ALL RIGHT TO
TRIAL BY JURY IN ANY LEGAL PROCEEDING ARISING OUT OF OR RELATING TO THIS
AGREEMENT OR THE TRANSACTIONS CONTEMPLATED HEREBY.


                                 Exh E, Page 7
<PAGE>   110


     IN WITNESS WHEREOF, the parties hereto have caused this Assignment
Agreement to be executed and delivered as of the date first above written.

                                    ASSIGNOR



                                    By:
                                       -----------------------------------------
                                    Name:
                                         ---------------------------------------
                                    Title:
                                          --------------------------------------

                                    Address for Notices:


                                    Telecopier No.:
                                    Telephone No.:
                                    Attention:


                                    ASSIGNEE



                                    By:
                                       -----------------------------------------
                                    Name:
                                         ---------------------------------------
                                    Title:
                                          --------------------------------------

                                    Address for Notices:


                                    Telecopier No.:
                                    Telephone No.:
                                    Attention:


ACKNOWLEDGED TO:

                                                     ,
as Agent


By:
   -------------------------
Name:
     -----------------------
Title:
      ----------------------


                                 Exh E, Page 8
<PAGE>   111


                                    EXHIBIT F


                            FORM OF STANDARD MORTGAGE


               MORTGAGE, DEED OF TRUST, ASSIGNMENT OF PRODUCTION,
                   SECURITY AGREEMENT AND FINANCING STATEMENT
                               (STANDARD MORTGAGE)



                                      FROM


                             BRIGHAM OIL & GAS, L.P.


                                       TO


                          THOMAS E. MCGRAW, AS TRUSTEE



                               FOR THE BENEFIT OF


                           BANK OF MONTREAL, AS AGENT


A POWER OF SALE HAS BEEN GRANTED IN THIS INSTRUMENT. IN CERTAIN STATES, A POWER
OF SALE MAY ALLOW THE TRUSTEE OR THE AGENT TO TAKE THE MORTGAGED PROPERTY AND
SELL IT WITHOUT GOING TO COURT IN A FORECLOSURE ACTION UPON DEFAULT BY THE
GRANTOR UNDER THIS INSTRUMENT.

THIS INSTRUMENT CONTAINS AFTER-ACQUIRED PROPERTY PROVISIONS.

THIS INSTRUMENT SECURES PAYMENT OF FUTURE ADVANCES.

THIS INSTRUMENT COVERS PROCEEDS OF MORTGAGED PROPERTY.


                                    Exh F-1
<PAGE>   112


                     MORTGAGE, DEED OF TRUST, ASSIGNMENT OF
             PRODUCTION, SECURITY AGREEMENT AND FINANCING STATEMENT


     This MORTGAGE, DEED OF TRUST, ASSIGNMENT OF PRODUCTION, SECURITY AGREEMENT
AND FINANCING STATEMENT (this "Mortgage") is entered into as of the effective
time and date hereinafter stated (the "Effective Date") by BRIGHAM OIL & GAS,
L.P., a Delaware limited partnership, whose address for notice is 6300 Bridge
Point Parkway, Building 2, Suite 500, Austin, Texas 78730 ("Mortgagor"), to
THOMAS E. MCGRAW, as Trustee, whose address for notice is 700 Louisiana, Suite
4400, Houston, Texas 77002 ("Trustee") for the benefit of BANK OF MONTREAL, AS
AGENT, whose address for notice is 700 Louisiana, Suite 4400, Houston, Texas
77002 (together with any successor agents, "Agent") for the Lenders (hereinafter
defined), and for the benefit of the Lenders ("Mortgagee").

                                R E C I T A L S:

     A. Mortgagor, Mortgagee and the Lenders executed that certain Amended and
Restated Credit Agreement dated as of February 17, 2000 (such agreement, as may
from time to time be amended or supplemented, called the "Credit Agreement")
pursuant to which the Lenders have made or agreed to make certain advances to
and on behalf of the Mortgagor.

     B. Pursuant to the Credit Agreement, Mortgagor has agreed to enter into
this Mortgage.

     C. Therefore, in order to comply with the terms and conditions of the
Credit Agreement and for other good and valuable consideration, the receipt and
sufficiency of which are hereby acknowledged, Mortgagor hereby agrees as
follows:


                                    ARTICLE I

                     Grant of Lien and Indebtedness Secured

     Section 1.01 Grant of Liens. To secure payment of the Indebtedness (as
hereinafter defined) and the performance of the covenants and obligations herein
contained, Mortgagor does by these presents hereby, subject to the reservations
and restrictions set forth herein below, (i) GRANT, BARGAIN, SELL, ASSIGN, SET
OVER, TRANSFER and CONVEY unto Thomas E. McGraw, as Trustee, whose address for
notice hereunder is 700 Louisiana, Suite 4400, Houston, Texas 77002 ("Trustee")
and the Trustee's successors and substitutes in trust hereunder with power of
sale, for the use and benefit of Agent and the Lenders, all of the following
described real and personal property, rights, titles, interests and estates
which are located in (or cover properties located in) the State of Texas or
which are located within (or cover properties located within) the offshore area
over which the United States of America asserts jurisdiction and to which the
laws of such state are applicable with respect to this Mortgage and/or the


                                    Exh F-2
<PAGE>   113


liens or security interests created hereby (the "Deed of Trust Mortgaged
Property") and (ii) GRANT, MORTGAGE, PLEDGE AND HYPOTHECATE to Mortgagee, for
its benefit and the benefit of the Lenders, with respect to, all of the
following described real and personal property, rights, titles, interests and
estates which were not granted to Trustee in clause (i) above (the "Other
Mortgaged Property") (the Deed of Trust Property and the Other Mortgaged
Property herein collectively called the "Mortgaged Property"):

     (a) All rights, titles, interests and estates now owned or hereafter
acquired by Mortgagor in and to the oil and gas leases and/or oil, gas and other
mineral leases and other interests and estates and the lands and premises
covered or affected thereby which are described on Exhibit A attached hereto
(collectively called the "Hydrocarbon Property") or which Hydrocarbon Property
is otherwise referred to herein, and specifically, but without limitation, the
undivided interests of Mortgagor which are more particularly described on
Exhibit A hereto.

     (b) All rights, titles, interests and estates now owned or hereafter
acquired by Mortgagor in and to (i) the properties now or hereafter pooled or
unitized with the Hydrocarbon Property; (ii) all presently existing or future
unitization, communitization, pooling agreements and declarations of pooled
units and the units created thereby (including, without limitation, all units
created under orders, regulations, rules or other official acts of any Federal,
State or other governmental body or agency having jurisdiction and any units
created solely among working interest owners pursuant to operating agreements or
otherwise) which may affect all or any portion of the Hydrocarbon Property
including, without limitation, those units which may be described or referred to
on attached Exhibit A; (iii) all operating agreements, production sales or other
contracts, farmout agreements, farm-in agreements, area of mutual interest
agreements, equipment leases and other agreements described or referred to in
this Mortgage or which relate to any of the Hydrocarbon Property or interests in
the Hydrocarbon Property described or referred to herein or on Exhibit A or to
the production, sale, purchase, exchange, processing, handling, storage,
transporting or marketing of the Hydrocarbons (hereinafter defined) from or
attributable to such Hydrocarbon Property or interests; and (iv) subject to
applicable restrictions on disclosure and/or transfer, all geological,
geophysical, engineering, accounting, title, legal, and other technical or
business data concerning the Mortgaged Property, the Hydrocarbons, or any other
item of Property which are in the possession of Mortgagor or in which Mortgagor
can otherwise grant a security interest, and all books, files, records, magnetic
media, computer records, and other forms of recording or obtaining access to
such data.

     (c) All rights, titles, interests and estates now owned or hereafter
acquired by Mortgagor in and to all oil, gas, casinghead gas, condensate,
distillate, liquid hydrocarbons, gaseous hydrocarbons and all products refined
therefrom and all other minerals (collectively called the "Hydrocarbons") in and
under and which may be produced and saved from or attributable to the
Hydrocarbon Property, the lands pooled or unitized therewith and Mortgagor's
interests therein, including all oil in tanks and all rents, issues, profits,
proceeds, products, revenues and other income from or attributable to the
Hydrocarbon Property, the lands pooled or unitized therewith and Mortgagor's


                                    Exh F-3
<PAGE>   114


interests therein which are subjected or required to be subjected to the liens
and security interests of this Mortgage.

     (d) All tenements, hereditaments, appurtenances and properties in anywise
appertaining, belonging, affixed or incidental to the Hydrocarbon Property,
rights, titles, interests and estates described or referred to in paragraphs (a)
and (b) above, which are now owned or which may hereafter be acquired by
Mortgagor, including, without limitation, any and all property, real or
personal, now owned or hereafter acquired and situated upon, used, held for use,
or useful in connection with the operating, working or development of any of
such Hydrocarbon Property or the lands pooled or unitized therewith (excluding
drilling rigs, trucks, automotive equipment or other personal property which may
be taken to the premises for the purpose of drilling a well or for other similar
temporary uses) and including any and all oil wells, gas wells, injection wells
or other wells, buildings, structures, field separators, liquid extraction
plants, plant compressors, pumps, pumping units, pipelines, sales and flow
lines, gathering systems, field gathering systems, salt water disposal
facilities, tanks and tank batteries, fixtures, valves, fittings, machinery and
parts, engines, boilers, meters, apparatus, equipment, appliances, tools,
implements, cables, wires, towers, casing, tubing and rods, surface leases,
rights-of-way, easements, servitudes, licenses and other surface and subsurface
rights together with all additions, substitutions, replacements, accessions and
attachments to any and all of the foregoing properties.

     (e) Any property that may from time to time hereafter, by delivery or by
writing of any kind, be subjected to the lien and security interest hereof by
Mortgagor or by anyone on Mortgagor's behalf; and the Trustee is hereby
authorized to receive the same at any time as additional security hereunder.

     (f) All of the rights, titles and interests of every nature whatsoever now
owned or hereafter acquired by Mortgagor in and to the Hydrocarbon Property
rights, titles, interests and estates and every part and parcel thereof,
including, without limitation, the Hydrocarbon Property rights, titles,
interests and estates as the same may be enlarged by the discharge of any
payments out of production or by the removal of any charges or Permitted
Encumbrances (as hereinafter defined in Section 3.01) to which any of the
Hydrocarbon Property rights, titles, interests or estates are subject, or
otherwise; all rights of Mortgagor to liens and security interests securing
payment of proceeds from the sale of production from the Mortgaged Property,
including, but not limited to, those liens and security interests provided in
Tex. Bus. & Com. Code Ann.Section.9.319 (Tex. UCC) (Vernon Supp. 1989)
("Section.9.319 Tex. UCC"), as amended from time to time; together with any and
all renewals and extensions of any of the Hydrocarbon Property rights, titles,
interests or estates; all contracts and agreements supplemental to or amendatory
of or in substitution for the contracts and agreements described or mentioned
above; and any and all additional interests of any kind hereafter acquired by
Mortgagor in and to the Hydrocarbon Property rights, titles, interests or
estates.

     (g) All accounts, contract rights, inventory, general intangibles,
insurance contracts and insurance proceeds constituting a part of, relating to
or arising out of those portions of the Mortgaged Property which are described
in paragraphs (a) through (f)


                                    Exh F-4
<PAGE>   115


above and all proceeds and products of all such portions of the Mortgaged
Property and payments in lieu of production (such as "take or pay" payments),
whether such proceeds or payments are goods, money, documents, instruments,
chattel paper, securities, accounts, general intangibles, fixtures, real
property, or other assets.

     Notwithstanding any provision hereof to the contrary, this Mortgage does
not cover, and there is expressly excepted and excluded from the definition of
Mortgaged Property, any properties, rights and interests as may now or hereafter
be beneficially or equitable owned by (or contractually owing to) a third party
under any one or more of the agreements or other arrangements described in
Schedule 7.10 of the Credit Agreement (the "Participating Third Parties"), but
only to the extent any such exception and exclusion does not cause the undivided
interests specified in Exhibit A to be reduced or otherwise adversely affected.
Without limitation of the generality of the foregoing, any undivided interest
(a) with respect to which Mortgagor holds legal title (whether of record or
not), and (b) that is in excess of the undivided interests in such Mortgaged
Property as are specified in Exhibit A hereto shall be excluded from the
definition of Mortgaged Property to the extent a Participating Third Party now
or hereafter has an interest therein and, to that extent, shall otherwise be
free and clear of this Mortgage (and any security agreement and/or financing
statement associated herewith).

     TO HAVE AND TO HOLD the Mortgaged Property unto the Trustee and to his
successors and assigns forever to secure the payment of the Indebtedness
(hereinafter defined) and to secure the performance of the covenants,
agreements, and obligations of the Mortgagor herein contained.

     Section 1.02 Grant of Security Interest. To further secure the
Indebtedness, Mortgagor hereby grants to Mortgagee, subject to the reservations
and restrictions set forth herein below, a security interest in and to the
Mortgaged Property (whether now or hereafter acquired by operation of law or
otherwise) insofar as the Mortgaged Property consists of equipment, accounts,
contract rights, general intangibles (subject in the case of geological and
geophysical data (including without limitation raw data and interpretations)
contract rights and general intangibles to any existing restrictions on
disclosure and/or transfer), insurance contracts, insurance proceeds, inventory,
Hydrocarbons, fixtures and any and all other personal property of any kind or
character defined in and subject to the provisions of the Uniform Commercial
Code presently in effect in the jurisdiction in which the Mortgaged Property is
situated ("Applicable UCC"), including the proceeds and products from any and
all of such personal property. Upon the happening of any of the Events of
Default, Mortgagee is and shall be entitled to all of the rights, powers and
remedies afforded a secured party by the Applicable UCC with reference to the
personal property and fixtures in which Mortgagee has been granted a security
interest herein, or the Trustee or Mortgagee may proceed as to both the real and
personal property covered hereby in accordance with the rights and remedies
granted under this Mortgage in respect of the real property covered hereby. Such
rights, powers and remedies shall be cumulative and in addition to those granted
to the Trustee or Mortgagee under any other provision of this Mortgage or under
any other Security Instrument. Written notice mailed to Mortgagor as provided
herein at least five (5) days prior to the date of public sale of any part of
the Mortgaged Property which is personal


                                    Exh F-5
<PAGE>   116


property subject to the provisions of the Applicable UCC, or prior to the date
after which private sale of any such part of the Mortgaged Property will be
made, shall constitute reasonable notice.

     Section 1.03 Indebtedness Secured. This Mortgage is executed and delivered
by Mortgagor to secure and enforce the following (the "Indebtedness"):

     (a) Payment of and performance of any and all indebtedness, obligations and
liabilities of Mortgagor pursuant to the Credit Agreement, whether now existing
or hereafter arising, including without limitation, (i) that certain promissory
note by Mortgagor in favor of Bank of Montreal and being in the principal amount
of $23,153,830, dated February 17, 2000 with final maturity on or before
December 31, 2002 and all other notes given in substitution therefor or in
modification, renewal or extension thereof, in whole or in part (such notes, as
from time to time supplemented, amended or modified and all other notes given in
substitution therefor or in modification, renewal or extension thereof, in whole
or in part, being hereafter called the "BMO Note"), (ii) that certain promissory
note by Mortgagor in favor of Societe Generale, Southwest Agency and being in
the principal amount of $11,846,170, dated February 17, 2000 with final maturity
on or before December 31, 2002 and all other notes given in substitution
therefor or in modification, renewal or extension thereof, in whole or in part
(such notes, as from time to time supplemented, amended or modified and all
other notes given in substitution therefor or in modification, renewal or
extension thereof, in whole or in part, being hereafter called the "Soc-Gen
Note,") (iii) that certain promissory note by Mortgagor in favor of Shell
Capital Inc. and being in the principal amount of $40,000,000, dated February
17, 2000 with final maturity on or before December 31, 2002 and all other notes
given in substitution therefor or in modification, renewal or extension thereof,
in whole or in part (such notes, as from time to time supplemented, amended or
modified and all other notes given in substitution therefor or in modification,
renewal or extension thereof, in whole or in part, being hereafter called the
"SCI Note" and, together with the BMO Note and the Soc-Gen Note, the "Notes")
and (iv) any commodity, interest rate or currency swap, cap, floor, collar,
forward agreement or other exchange or protection agreements or any option with
respect to any such transaction in existence as of the date hereof or hereafter
arising between (i) Mortgagor and Bank of Montreal and its successors or assigns
(a "BMO Hedge Party") and Soc-Gen and its successors or assigns (a "Soc-Gen
Hedge Party") entered into while such BMO Hedge Party or such Soc-Gen Hedge
Party is a Lender; and (ii) Mortgagor and SCI and its successors or assigns
(with Loans or Commitments of $20 million or more) or any Affiliate of SCI (SCI
and any Affiliate of SCI a "SCI Hedge Party") entered into while such SCI Hedge
Party or Fathom Energy Capital I, L.L.C, is a Lender. For purposes of this
Section 1.03, the parties intend that any commodity, interest rate or currency
swap, cap, floor, collar, forward agreement or other exchange or protection
agreements or any option entered into between the Mortgagor and a Lender or in
the case of SCI, a SCI Hedge Party, while such Person was a party to the Credit
Agreement shall continue to be secured even after the time such Person ceases to
be a party to the Credit Agreement as a Lender.


                                    Exh F-6
<PAGE>   117


     (b) Any sums which may be advanced or paid by Mortgagee under the terms
hereof or of the Credit Agreement on account of the failure of Mortgagor to
comply with the covenants of Mortgagor contained herein or in the Credit
Agreement; and all other indebtedness of Mortgagor arising pursuant to the
provisions of this Mortgage.

     Section 1.04 Fixture Filing, Etc. Without in any manner limiting the
generality of any of the other provisions of this Mortgage: (i) some portions of
the goods described or to which reference is made herein are or are to become
fixtures on the land described or to which reference is made herein or on
attached Exhibit A; (ii) the security interests created hereby under applicable
provisions of the Applicable UCC will attach to Hydrocarbons (minerals including
oil and gas) or the accounts resulting from the sale thereof at the wellhead or
minehead located on the land described or to which reference is made herein;
(iii) this Mortgage is to be filed of record in the real estate records as a
financing statement, and (iv) Mortgagor is the record owner of the real estate
or interests in the real estate comprised of the Mortgaged Property.

     Section 1.05 Defined Terms. Any capitalized term used in this Mortgage and
not defined in this Mortgage shall have the meaning assigned to such term in the
Credit Agreement.

                                   ARTICLE II

                            Assignment of Production

     Section 2.01 Assignment. Mortgagor has absolutely and unconditionally
assigned, transferred, and conveyed, and does hereby absolutely and
unconditionally assign, transfer and convey unto Mortgagee, its successors and
assigns, all of the Hydrocarbons and all products obtained or processed
therefrom, and the revenues and proceeds now and hereafter attributable to the
Hydrocarbons and said products and all payments in lieu of the Hydrocarbons such
as "take or pay" payments or settlements. The Hydrocarbons and products are to
be delivered into pipe lines connected with the Mortgaged Property, or to the
purchaser thereof, to the credit of Mortgagee, free and clear of all taxes,
charges, costs, and expenses; and all such revenues and proceeds shall be paid
directly to Mortgagee, at its banking quarters in Chicago, Illinois with no duty
or obligation of any party paying the same to inquire into the rights of
Mortgagee to receive the same, what application is made thereof, or as to any
other matter. Mortgagor agrees to perform all such acts, and to execute all such
further assignments, transfers and division orders, and other instruments as may
be required or desired by Mortgagee or any party in order to have said proceeds
and revenues so paid to Mortgagee. Mortgagee is fully authorized to receive and
receipt for said revenues and proceeds; to endorse and cash any and all checks
and drafts payable to the order of Mortgagor or Mortgagee for the account of
Mortgagor received from or in connection with said revenues or proceeds and to
hold the proceeds thereof in a bank account as additional collateral securing
the Indebtedness; and to execute transfer and division orders in the name of
Mortgagor, or otherwise, with warranties binding Mortgagor. All proceeds
received by the Mortgagee pursuant to this assignment shall be applied as
provided in the other Loan Documents. Mortgagee shall not be liable for any
delay, neglect, or failure to effect collection of any


                                    Exh F-7
<PAGE>   118


proceeds or to take any other action in connection therewith or hereunder; but
Mortgagee shall have the right, at its election, in the name of Mortgagor or
otherwise, to prosecute and defend any and all actions or legal proceedings
deemed advisable by Mortgagee in order to collect such funds and to protect the
interests of Mortgagee, and/or Mortgagor, with all costs, expenses and
attorneys' fees incurred in connection therewith being paid by Mortgagor.
Mortgagor hereby appoints Mortgagee as its attorney-in-fact to pursue any and
all rights of Mortgagor to liens on and security interests in the Hydrocarbons
securing payment of proceeds of runs attributable to the Hydrocarbons. In
addition to the rights granted to Trustee and/or Mortgagee in Section 1.01 (f)
of this Mortgage, Mortgagor hereby further transfers and assigns to Mortgagee
any and all such liens, security interests, financing statements or similar
interests of Mortgagor attributable to its interest in the Hydrocarbons and
proceeds of runs therefrom arising under or created by said statutory provision,
judicial decision or otherwise. The power of attorney granted to Mortgagee in
this Section 2.01, being coupled with an interest, shall be irrevocable so long
as the Indebtedness or any part thereof remains unpaid.

     Section 2.02 Rights Under Texas Act. Mortgagor hereby grants, sells,
assigns, sets over and mortgages unto Mortgagee during the term hereof, all of
Mortgagor's rights and interests pursuant to the provisions of Section 9.319
Tex. UCC, hereby vesting in Mortgagee all of Mortgagor's rights as an interest
owner to the continuing security interest in and lien upon the Mortgaged
Property.

     Section 2.03 No Modification of Payment Obligations. Nothing herein
contained shall modify or otherwise alter the obligation of Mortgagor to make
prompt payment of all principal and interest owing on the Indebtedness when and
as the same become due regardless of whether the proceeds of the Hydrocarbons
are sufficient to pay the same and the rights provided in accordance with the
foregoing assignment provision shall be cumulative of all other security of any
and every character now or hereafter existing to secure payment of the
Indebtedness.

                                   ARTICLE III

                    Representations, Warranties and Covenants

         Mortgagor hereby represents, warrants and covenants as follows:

     Section 3.01 Title. To the extent of the undivided interests specified on
attached Exhibit A, after reducing same on account of the "Term ORRI" created
under the Term ORRI Conveyance as hereinafter defined, Mortgagor has good and
indefeasible title to and is possessed of the Mortgaged Property. The Mortgaged
Property is free of any and all Liens (as defined in the Credit Agreement)
except Excepted Liens and Liens, if any, described in Exhibit A (collectively,
the "Permitted Encumbrances").

     Section 3.02 Defend Title. This Mortgage is, and always will be kept, a
direct first lien and security interest upon the Mortgaged Property subject only
to the Permitted Encumbrances and Mortgagor will not create or suffer to be
created or permit to exist any lien, security interest or charge prior or junior
to or on a parity with the lien and security


                                    Exh F-8
<PAGE>   119


interest of this Mortgage upon the Mortgaged Property or any part thereof or
upon the rents, issues, revenues, profits and other income therefrom. Mortgagor
will warrant and defend the title to the Mortgaged Property against the claims
and demands of all other persons whomsoever and will maintain and preserve the
lien created hereby so long as any of the Indebtedness secured hereby remains
unpaid. Should an adverse claim be made against or a cloud develop upon the
title to any part of the Mortgaged Property, Mortgagor agrees it will
immediately defend against such adverse claim or take appropriate action to
remove such cloud at Mortgagor's cost and expense, and Mortgagor further agrees
that the Trustee and/or Mortgagee may take such other action as they deem
advisable to protect and preserve their interests in the Mortgaged Property, and
in such event Mortgagor will indemnify the Trustee and Mortgagee against any and
all cost, attorney's fees and other expenses which they may incur in defending
against any such adverse claim or taking action to remove any such cloud.

     Section 3.03 Not a Foreign Person. Mortgagor is not a "foreign person"
within the meaning of the Internal Revenue Code of 1986, as amended (hereinafter
called the "Code"), Sections 1445 and 7701 (i.e. Mortgagor is not a non-resident
alien, foreign corporation, foreign partnership, foreign trust or foreign estate
as those terms are defined in the Code and any regulations promulgated
thereunder).

     Section 3.04 Power to Create Lien and Security. The Mortgagor has, in all
material respects, full power and lawful authority to grant, bargain, sell,
assign, transfer, mortgage, and convey a security interest in all of the
Mortgaged Property in the manner and form herein provided and without obtaining
the authorization, approval, consent or waiver of any lessor, sublessor,
Governmental Authority or other party or parties whomsoever.

     Section 3.05 Revenue and Cost Bearing Interest. Mortgagor's ownership of
the Hydrocarbon Property and the undivided interests therein as specified on
Exhibit A will, after giving full effect to all Permitted Encumbrances, afford
Mortgagor not less than those net interests (expressed as a fraction, percentage
or decimal) in the production from or which is allocated to such Hydrocarbon
Property specified as net revenue interest (NRI) on Exhibit A, less the Term
ORRI, and will cause Mortgagor to bear not more than that portion (expressed as
a fraction, percentage or decimal), specified as working interest (WI) on
Exhibit A, of the costs of drilling, developing and operating the wells
identified on Exhibit A.

     Section 3.06 Rentals Paid; Leases in Effect. All rentals and royalties due
and payable in accordance with the terms of any leases or subleases comprising
any material part of the Hydrocarbon Property have been duly paid or provided
for and all leases or subleases comprising any material part of the Hydrocarbon
Property are in full force and effect.

     Section 3.07 Operation By Third Parties. All or portions of the Mortgaged
Property may be comprised of interests in the Hydrocarbon Property which are
other than working interests or which may be operated by a party or parties
other than Mortgagor and with respect to all or any such interests and
properties as may be comprised of


                                    Exh F-9
<PAGE>   120


interests other than working interests or which may be operated by parties other
than Mortgagor, Mortgagor's covenants as expressed in this Article III are
modified to require that Mortgagor use its best efforts to obtain compliance
with such covenants by the working interest owners or the operator or operators
of such leases or properties.

     Section 3.08 Abandon, Sales. The Mortgagor will not sell, lease, assign,
transfer or otherwise dispose or abandon any of the Mortgaged Property except as
permitted by the Credit Agreement.

     Section 3.09 Failure to Perform. The Mortgagor agrees that if the
Mortgagor, after receipt from Mortgagee of written notice and demand, fails to
perform any act or to take any action which the Mortgagor is required to perform
or take hereunder or pay any money which the Mortgagor is required to pay
hereunder, each of the Mortgagee and the Trustee in the Mortgagor's name or its
or their own name may, but shall not be obligated to, perform or cause to
perform such act or take such action or pay such money, and any expenses so
incurred by either of them and any money so paid by either of them shall be a
demand obligation owing by the Mortgagor to the Mortgagee or the Trustee, as the
case may be, and each of the Mortgagee and the Trustee, upon making such
payment, shall be subrogated to all of the rights of the Person receiving such
payment. Each amount due and owing by Mortgagor to each of the Mortgagee and the
Trustee pursuant to this Mortgage shall bear interest from the date of such
expenditure or payment or other occurrence which gives rise to such amount being
owed to such Person until paid at the Post-Default Rate, and all such amounts
together with such interest thereon shall be a part of the Indebtedness
described in Section 1.03 hereof.

                                   ARTICLE IV

                               Rights and Remedies

     Section 4.01 Event of Default. An "Event of Default" under the Credit
Agreement shall be an Event of Default under this Mortgage.

     Section 4.02 Foreclosure and Sale. If an Event of Default shall occur and
be continuing, Mortgagee shall have the right and option to proceed with
foreclosure by directing the Trustee, or his successors or substitutes in trust,
to proceed with foreclosure and to sell, to the extent permitted by law, all or
any portion of the Mortgaged Property at one or more sales, as an entirety or in
parcels, at such place or places in otherwise such manner and upon such notice
as may be required by law, or, in the absence of any such requirement, as the
Mortgagee may deem appropriate, and to make conveyance to the purchaser or
purchasers. Where the Mortgaged Property is situated in more than one county,
notice as above provided shall be posted and filed in all such counties (if such
notices are required by law), and all such Mortgaged Property may be sold in any
such county and any such notice shall designate the county where such Mortgaged
Property is to be sold. Nothing contained in this Section 4.02 shall be
construed so as to limit in any way the Trustee's rights to sell the Mortgaged
Property, or any portion thereof, by private sale if, and to the extent that,
such private sale is permitted under the laws of the applicable jurisdiction or
by public or private sale after entry of a judgment by any court


                                    Exh F-10
<PAGE>   121


of competent jurisdiction so ordering. Mortgagor hereby irrevocably appoints the
Trustee to be the attorney of Mortgagor and in the name and on behalf of
Mortgagor to execute and deliver any deeds, transfers, conveyances, assignments,
assurances and notices which Mortgagor ought to execute and deliver and do and
perform any and all such acts and things which Mortgagor ought to do and perform
under the covenants herein contained and generally, to use the name of Mortgagor
in the exercise of all or any of the powers hereby conferred on the Trustee. At
any such sale: (i) whether made under the power herein contained or any other
legal enactment, or by virtue of any judicial proceedings or any other legal
right, remedy or recourse, it shall not be necessary for Trustee to have
physically present, or to have constructive possession of, the Mortgaged
Property (Mortgagor hereby covenanting and agreeing to deliver to Trustee any
portion of the Mortgaged Property not actually or constructively possessed by
Trustee immediately upon demand by Trustee) and the title to and right of
possession of any such property shall pass to the purchaser thereof as
completely as if the same had been actually present and delivered to purchaser
at such sale, (ii) each instrument of conveyance executed by Trustee shall
contain a general warranty of title, binding upon Mortgagor and its successors
and assigns, (iii) each and every recital contained in any instrument of
conveyance made by Trustee shall conclusively establish the truth and accuracy
of the matters recited therein, including, without limitation, nonpayment of the
Indebtedness, advertisement and conduct of such sale in the manner provided
herein and otherwise by law and appointment of any successor Trustee hereunder,
(iv) any and all prerequisites to the validity thereof shall be conclusively
presumed to have been performed, (v) the receipt of Trustee or of such other
party or officer making the sale shall be a sufficient discharge to the
purchaser or purchasers for its purchase money and no such purchaser or
purchasers, or its assigns or personal representatives, shall thereafter be
obligated to see to the application of such purchase money, or be in any way
answerable for any loss, misapplication or nonapplication thereof, (vi) to the
fullest extent permitted by law, Mortgagor shall be completely and irrevocably
divested of all of its right, title, interest, claim and demand whatsoever,
either at law or in equity, in and to the property sold and such sale shall be a
perpetual bar both at law and in equity against Mortgagor, and against any and
all other persons claiming or to claim the property sold or any part thereof,
by, through or under Mortgagor, and (vii) to the extent and under such
circumstances as are permitted by law, Mortgagee may be a purchaser at any such
sale, and shall have the right, after paying or accounting for all costs of said
sale or sales, to credit the amount of the bid upon the amount of the
Indebtedness (in the order of priority set forth in Section 4.13 hereof) in lieu
of cash payment.

     Section 4.03 Substitute Trustees and Agents. The Trustee or his successor
or substitute may appoint or delegate any one or more persons as agent to
perform any act or acts necessary or incident to any sale held by Trustee,
including the posting of notices and the conduct of sale, but in the name and on
behalf of Trustee, his successor or substitute. If Trustee or his successor or
substitute shall have given notice of sale hereunder, any successor or
substitute trustee thereafter appointed may complete the sale and the conveyance
of the property pursuant thereto as if such notice had been given by the
successor or substitute trustee conducting the sale.


                                    Exh F-11
<PAGE>   122


     Section 4.04 Judicial Foreclosure; Receivership. If any of the Indebtedness
shall become due and payable and shall not be promptly paid, the Trustee or
Mortgagee shall have the right and power to proceed by a suit or suits in equity
or at law, whether for the specific performance of any covenant or agreement
herein contained or in aid of the execution of any power herein granted, or for
any foreclosure hereunder or for the sale of the Mortgaged Property under the
judgment or decree of any court or courts of competent jurisdiction, or for the
appointment of a receiver pending any foreclosure hereunder or the sale of the
Mortgaged Property under the order of a court or courts of competent
jurisdiction or under executory or other legal process, or for the enforcement
of any other appropriate legal or equitable remedy. Any money advanced by the
Trustee and/or Mortgagee in connection with any such receivership shall be a
demand obligation (which obligation Mortgagor hereby expressly promises to pay)
owing by Mortgagor to the Trustee and/or Mortgagee and shall bear interest from
the date of making such advance by the Trustee and/or Mortgagee until paid at
the Post Default Rate.

     Section 4.05 Foreclosure for Installments. Mortgagee shall also have the
option to proceed with foreclosure in satisfaction of any installments of the
Indebtedness which have not been paid when due either through the courts or by
directing the Trustee or his successors in trust to proceed with foreclosure in
satisfaction of the matured but unpaid portion of the Indebtedness as if under a
full foreclosure, conducting the sale as herein provided and without declaring
the entire principal balance and accrued interest due; such sale may be made
subject to the unmatured portion of the Indebtedness, and any such sale shall
not in any manner affect the unmatured portion of the Indebtedness, but as to
such unmatured portion of the Indebtedness this Mortgage shall remain in full
force and effect just as though no sale had been made hereunder. It is further
agreed that several sales may be made hereunder without exhausting the right of
sale for any unmatured part of the Indebtedness, it being the purpose hereof to
provide for a foreclosure and sale of the security for any matured portion of
the Indebtedness without exhausting the power to foreclose and sell the
Mortgaged Property for any subsequently maturing portion of the Indebtedness.

     Section 4.06 Separate Sales The Mortgaged Property may be sold in one or
more parcels and in such manner and order as Mortgagee, in its sole discretion,
may elect, it being expressly understood and agreed that the right of sale
arising out of any Event of Default shall not be exhausted by any one or more
sales.

     Section 4.07 Occupancy After Foreclosure. In the event there is a
foreclosure sale hereunder and at the time of such sale Mortgagor or Mortgagor's
heirs, devisees, representatives, successors or assigns or any other person
claiming any interest in the Mortgaged Property by, through or under Mortgagor,
are occupying or using the Mortgaged Property or any part thereof, each and all
shall immediately become the tenant of the purchaser at such sale, which tenancy
shall be a tenancy from day to day, terminable at the will of either the
landlord or tenant, or at a reasonable rental per day based upon the value of
the property occupied, such rental to be due daily to the purchaser; to the
extent permitted by applicable law, the purchaser at such sale shall,
notwithstanding any language herein apparently to the contrary, have the sole
option to demand immediate possession following the sale or to permit the
occupants to remain as


                                    Exh F-12
<PAGE>   123


tenants at will. In the event the tenant fails to surrender possession of said
property upon demand, the purchaser shall be entitled to institute and maintain
a summary action for possession of the Mortgaged Property (such as an action for
forcible entry and detainer) in any court having jurisdiction.

     Section 4.08 Remedies Cumulative, Concurrent and Nonexclusive. Every right,
power and remedy herein given to the Trustee or Mortgagee shall be cumulative
and in addition to every other right, power and remedy herein specifically given
or now or hereafter existing in equity, at law or by statute (including
specifically those granted by the Applicable UCC in effect and applicable to the
Mortgaged Property or any portion thereof) each and every right, power and
remedy whether specifically herein given or otherwise existing may be exercised
from time to time and so often and in such order as may be deemed expedient by
the Trustee or Mortgagee, and the exercise, or the beginning of the exercise, of
any such right, power or remedy shall not be deemed a waiver of the right to
exercise, at the same time or thereafter any other right, power or remedy. No
delay or omission by the Trustee or Mortgagee in the exercise of any right,
power or remedy shall impair any such right, power or remedy or operate as a
waiver thereof or of any other right, power or remedy then or thereafter
existing.

     Section 4.09 No Release of Obligations. Neither Mortgagor, any guarantor
nor any other person hereafter obligated for payment of all or any part of the
Indebtedness shall be relieved of such obligation by reason of (a) the failure
of Trustee to comply with any request of Mortgagor, or any guarantor or any
other person so obligated to foreclose the lien of this Mortgage or to enforce
any provision hereunder or under the Credit Agreement; (b) the release,
regardless of consideration, of the Mortgaged Property or any portion thereof or
interest therein or the addition of any other property to the Mortgaged
Property; (c) any agreement or stipulation between any subsequent owner of the
Mortgaged Property and Mortgagee extending, renewing, rearranging or in any
other way modifying the terms of this Mortgage without first having obtained the
consent of, given notice to or paid any consideration to Mortgagor, any
guarantor or such other person, and in such event Mortgagor, guarantor and all
such other persons shall continue to be liable to make payment according to the
terms of any such extension or modification agreement unless expressly released
and discharged in writing by Mortgagee; or (d) by any other act or occurrence
save and except the complete payment of the Indebtedness and the complete
fulfillment of all obligations hereunder or under the Credit Agreement.

     Section 4.10 Release of and Resort to Collateral. Mortgagee may release,
regardless of consideration, any part of the Mortgaged Property without, as to
the remainder, in any way impairing, affecting, subordinating or releasing the
lien or security interest created in or evidenced by this Mortgage or its
stature as a first and prior lien and security interest in and to the Mortgaged
Property, and without in any way releasing or diminishing the liability of any
person or entity liable for the repayment of the Indebtedness. For payment of
the Indebtedness, Mortgagee may resort to any other security therefor held by
Mortgagee or Trustee in such order and manner as Mortgagee may elect.


                                    Exh F-13
<PAGE>   124


     Section 4.11 Waiver of Redemption, Notice and Marshalling of Assets, Etc.
To the fullest extent permitted by law, Mortgagor hereby irrevocably and
unconditionally waives and releases (a) all benefits that might accrue to
Mortgagor by virtue of any present or future moratorium law or other law
exempting the Mortgaged Property from attachment, levy or sale on execution or
providing for any appraisement, valuation, stay of execution, exemption from
civil process, redemption or extension of time for payment and (b) any right to
a marshalling of assets or a sale in inverse order of alienation. If any law
referred to in this Mortgage and now in force, of which Mortgagor or its
successor or successors might take advantage despite the provisions hereof,
shall hereafter be repealed or cease to be in force, such law shall thereafter
be deemed not to constitute any part of the contract herein contained or to
preclude the operation or application of the provisions hereof. Provided,
however, that if the laws of any state do not permit the redemption period to be
waived, the redemption period is specifically reduced to the minimum amount of
time allowable by statute.

     Section 4.12 Discontinuance of Proceedings In case Mortgagee shall have
proceeded to invoke any right, remedy or recourse permitted hereunder or under
the Credit Agreement and shall thereafter elect to discontinue or abandon same
for any reason, Mortgagee shall have the unqualified right so to do and, in such
an event, Mortgagor and Mortgagee shall be restored to their former positions
with respect to the Indebtedness, this Mortgage, the Credit Agreement, the
Mortgaged Property and otherwise, and the rights, remedies, recourses and powers
of Mortgagee shall continue as if same had never been invoked.

     Section 4.13 Application of Proceeds. The proceeds of any sale of the
Mortgaged Property or any part thereof and all other monies received by the
Trustee or Mortgagee in any proceedings for the enforcement hereof or otherwise,
whose application has not elsewhere herein been specifically provided for, shall
be applied:

     (a) first, to the payment of all reasonable expenses incurred by the
Trustee or Mortgagee incident to the enforcement of this Mortgage, the Credit
Agreement or any of the Indebtedness (including, without limiting the generality
of the foregoing, expenses of any entry or taking of possession, of any sale, of
advertisement thereof, and of conveyances, and court costs, compensation of
agents and employees, legal fees and a reasonable commission to the Trustee
acting), and to the payment of all other charges, reasonable expenses,
liabilities and advances incurred or made by the Trustee or Mortgagee under this
Mortgage or in executing any trust or power hereunder;

     (b) second to payment of the Indebtedness in such order and manner as
Mortgagee may elect; and

     (c) third, to Mortgagor; or as otherwise required by any Governmental
Requirement.

     Section 4.14 Resignation of Operator. In addition to all rights and
remedies under this Mortgage, at law and in equity, if any Event of Default
shall occur and Trustee or the Mortgagee shall exercise any possessory remedies
under this Mortgage with


                                    Exh F-14
<PAGE>   125


respect to any portion of the Hydrocarbon Property (or Mortgagor shall transfer
any Mortgaged Property "in lieu of" foreclosure), the Mortgagee or the Trustee
shall have the right to request that any operator of any Hydrocarbon Property
which is either Mortgagor or any Affiliate of Mortgagor to resign as operator
under the joint operating agreement applicable thereto, and no later than 60
days after receipt by Mortgagor of any such request, Mortgagor shall resign (or
cause such other party to resign) as operator of such Hydrocarbon Property.

     Section 4.15 Indemnity. In connection with any action taken by the Trustee
and/or Mortgagee pursuant to this Mortgage, the Trustee and/or Mortgagee and
their officers, directors, employees, representatives, agents, attorneys,
accountants and experts ("Indemnified Parties") shall not be liable for any loss
sustained by Mortgagor resulting from an assertion that Mortgagee has received
funds from the production of Hydrocarbons claimed by third persons or any act or
omission of any Indemnified Party in administering, managing, operating or
controlling the Mortgaged Property including such loss which may result from the
ordinary negligence of an Indemnified Party unless such loss is caused by the
gross negligence willful misconduct or bad faith of an Indemnified Party, nor
shall the Trustee and/or Mortgagee be obligated to perform or discharge any
obligation, duty or liability of Mortgagor. Mortgagor shall and does hereby
agree to indemnify each Indemnified Party for, and to hold each Indemnified
Party harmless from, any and all liability, loss or damage which may or might be
incurred by any Indemnified Party by reason of this Mortgage or the exercise of
rights or remedies hereunder; should the Trustee and/or Mortgagee make any
expenditure on account of any such liability, loss or damage, the amount
thereof, including costs, expenses and reasonable attorneys' fees, shall be a
demand obligation (which obligation Mortgagor hereby expressly promises to pay)
owing by Mortgagor to the Trustee and/or Mortgagee and shall bear interest from
the date expended until paid at the Post-Default Rate, shall be a part of the
Indebtedness and shall be secured by this Mortgage and any other Security
Instrument. Mortgagor hereby assents to, ratifies and confirms any and all
actions of the Trustee and/or Mortgagee with respect to the Mortgaged Property
taken under, and in compliance with the terms of, this Mortgage. The liabilities
of the Mortgagor as set forth in this Section 4.15 shall survive the termination
of this Mortgage.

                                    ARTICLE V

                                   The Trustee

     Section 5.01 Duties, Rights, and Powers of Trustee. It shall be no part of
the duty of the Trustee to see to any recording, filing or registration of this
Mortgage or any other instrument in addition or supplemental thereto, or to give
any notice thereof, or to see to the payment of or be under any duty in respect
of any tax or assessment or other governmental charge which may be levied or
assessed on the Mortgaged Property, or any part thereof, or against Mortgagor,
or to see to the performance or observance by Mortgagor of any of the covenants
and agreements contained herein. The Trustee shall not be responsible for the
execution, acknowledgment or validity of this Mortgage or of any instrument in
addition or supplemental hereto or for the sufficiency of the security purported
to be created hereby, and makes no representation in respect thereof or in


                                    Exh F-15
<PAGE>   126


respect of the rights of Mortgagee. The Trustee shall have the right to advise
with counsel upon any matters arising hereunder and shall be fully protected in
relying as to legal matters on the advice of counsel. The Trustee shall not
incur any personal liability hereunder except for Trustee's own gross
negligence, bad faith and/or willful misconduct; and the Trustee shall have the
right to rely on any instrument, document or signature authorizing or supporting
any action taken or proposed to be taken by him hereunder, believed by him in
good faith to be genuine.

     Section 5.02 Successor Trustee. The Trustee may resign by written notice
addressed to Mortgagee or be removed at any time with or without cause by an
instrument in writing duly executed on behalf of Mortgagee. In case of the
death, resignation or removal of the Trustee, a successor trustee may be
appointed by Mortgagee by instrument of substitution complying with any
applicable requirements of law, or, in the absence of any such requirement,
without other formality than appointment and designation in writing. Written
notice of such appointment and designation shall be given by Mortgagee to
Mortgagor, but the validity of any such appointment shall not be impaired or
affected by failure to give such notice or by any defect therein. Such
appointment and designation shall be full evidence of the right and authority to
make the same and of all the facts therein recited, and, upon the making of any
such appointment and designation, this Mortgage shall vest in the successor
trustee all the estate and title in and to all of the Mortgaged Property, and
the successor trustee shall thereupon succeed to all of the rights, powers,
privileges, immunities and duties hereby conferred upon the Trustee named
herein, and one such appointment and designation shall not exhaust the right to
appoint and designate a successor trustee hereunder but such right may be
exercised repeatedly as long as any Indebtedness remains unpaid hereunder. To
facilitate the administration of the duties hereunder, Mortgagee may appoint
multiple trustees to serve in such capacity or in such jurisdictions as
Mortgagee may designate.

     Section 5.03 Retention of Moneys. All moneys received by Trustee shall,
until used or applied as herein provided, be held in trust for the purposes for
which they were received, but need not be segregated in any manner from any
other moneys (except to the extent required by law), and Trustee shall be under
no liability for interest on any moneys received by him hereunder.

                                   ARTICLE VI

                                  Miscellaneous

     Section 6.01 Instrument Construed as Mortgage, Etc. With respect to any
portions of the Mortgaged Property located in any state or other jurisdiction
the laws of which do not provide for the use or enforcement of a deed of trust
or the office, rights and authority of the Trustee as herein provided, the
general language of conveyance hereof to the Trustee is intended and the same
shall be construed as words of mortgage unto and in favor of Mortgagee and the
rights and authority granted to the Trustee herein may be enforced and asserted
by Mortgagee in accordance with the laws of the jurisdiction in which such
portion of the Mortgaged Property is located and the same may be foreclosed at
the option of Mortgagee as to any or all such portions of the Mortgaged Property
in


                                    Exh F-16
<PAGE>   127


any manner permitted by the laws of the jurisdiction in which such portions of
the Mortgaged Property is situated. This Mortgage may be construed as a
mortgage, deed of trust, chattel mortgage, conveyance, assignment, security
agreement, pledge, financing statement, hypothecation or contract, or any one or
more of them, in order fully to effectuate the lien hereof and the purposes and
agreements herein set forth.

     Section 6.02 Release of Mortgage. If all Indebtedness secured hereby shall
be paid and the Credit Agreement terminated, Mortgagee shall forthwith cause
satisfaction and discharge of this Mortgage to be entered upon the record at the
expense of Mortgagor and shall execute and deliver or cause to be executed and
delivered such instruments of satisfaction and reassignment as may be
appropriate. Otherwise, this Mortgage shall remain and continue in full force
and effect.

     Section 6.03 Severability. If any provision hereof is invalid or
unenforceable in any jurisdiction, the other provisions hereof shall remain in
full force and effect in such jurisdiction and the remaining provisions hereof
shall be liberally construed in favor of the Trustee and Mortgagee in order to
effectuate the provisions hereof, and the invalidity or unenforceability of any
provision hereof in any jurisdiction shall not affect the validity or
enforceability of any such provision in any other jurisdiction.

     Section 6.04 Successors and Assigns of Parties. The term "Mortgagee" as
used herein shall mean and include any legal owner, holder, assignee or pledgee
of any of the Indebtedness secured hereby. The terms used to designate Trustee,
Mortgagee and Mortgagor shall be deemed to include the respective heirs, legal
representatives, successors and assigns of such parties.

     Section 6.05 Satisfaction of Prior Encumbrance. To the extent that proceeds
of the Credit Agreement are used to pay indebtedness secured by any outstanding
lien, security interest, charge or prior encumbrance against the Mortgaged
Property, such proceeds have been advanced by Mortgagee at Mortgagor's request,
and Mortgagee shall be subrogated to any and all rights, security interests and
liens owned by any owner or holder of such outstanding liens, security
interests, charges or encumbrances, irrespective of whether said liens, security
interests, charges or encumbrances are released, and it is expressly understood
that, in consideration of the payment of such other indebtedness by Mortgagee,
Mortgagor hereby waives and releases all demands and causes of action for
offsets and payments to, upon and in connection with the said indebtedness.

     Section 6.06 Subrogation of Trustee. This Mortgage is made with full
substitution and subrogation of the Trustee and his successors in this trust and
his and their assigns in and to all covenants and warranties by others
heretofore given or made in respect of the Mortgaged Property or any part
thereof.

     Section 6.07 Nature of Covenants. The covenants and agreements herein
contained shall constitute covenants running with the land and interests covered
or affected hereby and shall be binding upon the heirs, legal representatives,
successors and assigns of the parties hereto.


                                    Exh F-17
<PAGE>   128


     Section 6.08 Notices. All notices, requests, consents, demands and other
communications required or permitted hereunder shall be in writing and shall be
deemed sufficiently given or furnished if delivered by registered or certified
United States mail, postage prepaid, or by personal service (including express
or courier service) at the addresses specified in the first paragraph of this
Mortgage (unless changed by similar notice in writing given by the particular
party whose address is to be changed). Any such notice or communication shall be
deemed to have been given either at the time of personal delivery or, in the
case of delivery at the address and in the manner provided herein, upon receipt;
provided that, service of notice as required by the laws of any state in which
portions of the Mortgaged Property may be situated shall for all purposes be
deemed appropriate and sufficient with the giving of such notice.

     Section 6.09 Counterparts. This Mortgage is being executed in several
counterparts, all of which are identical, except that to facilitate recordation,
if the Mortgaged Property is situated in more than one county, descriptions of
only those portions of the Mortgaged Property located in the county in which a
particular counterpart is recorded shall be attached as Exhibit A thereto. A
complete Exhibit A will be attached to that certain counterpart to be attached
to a Financing Statement and filed with the Secretary of State of Texas in the
Uniform Commercial Code Records. Each of such counterparts shall for all
purposes be deemed to be an original and all such counterparts shall together
constitute but one and the same instrument.

     Section 6.10 Exculpation Provisions. Each of the parties hereto
specifically agrees that it has a duty to read this Mortgage; and agrees that it
is charged with notice and knowledge of the terms of this Mortgage; that it has
in fact read this Mortgage and is fully informed and has full notice and
knowledge of the terms, conditions and effects of this Mortgage; that it has
been represented by independent legal counsel of its choice throughout the
negotiations preceding its execution of this Mortgage; and has received the
advice of its attorney in entering into this Mortgage; and that it recognizes
that certain of the terms of this Mortgage result in one party assuming the
liability inherent in some aspects of the transaction and relieving the other
party of its responsibility for such liability. Each party hereto agrees and
covenants that it will not contest the validity or enforceability of any
exculpatory provision of this Mortgage on the basis that the party had no notice
or knowledge of such provision or that the provision is not "conspicuous."


                                    Exh F-18
<PAGE>   129


     WITNESS THE EXECUTION HEREOF, this 17th day of February, 2000, as of 7:01
a.m. Houston, Texas time, immediately after giving effect to the execution and
effective time of that certain Conveyance of Adjustable Term Overriding Royalty
Interest of even date herewith from Mortgagor to ECT Merchant Investments Corp.
and Joint Energy Development Investments II Limited Partnership (the "Term ORRI
Conveyance") (the "Effective Date").

                                   MORTGAGOR:

                                   BRIGHAM OIL & GAS, L.P.

                                   By: Brigham, Inc., its General Partner



                                       By:
                                          --------------------------------------
                                       Name:
                                            ------------------------------------
                                       Title:
                                             -----------------------------------


                                    Exh F-19
<PAGE>   130


STATE OF TEXAS           )
                         )
COUNTY OF HARRIS         )


                                      TEXAS


     This instrument was acknowledged before me on February 17, 2000 by
____________________________, ______________________ of BRIGHAM, INC., a Nevada
corporation, as general partner of BRIGHAM OIL & GAS, L.P., a Delaware limited
partnership, on behalf of such corporation, as general partner of the limited
partnership.



                                                --------------------------------
                                                Notary Public in and for the
                                                State of Texas

                                                Notarial Seal:

                                    OKLAHOMA


     Before me, a Notary Public in and for said county and state, on this 17th
day of February, 2000, personally appeared ____________________________, to me
known to be the identical person who subscribed the name of the maker thereof to
the foregoing instrument as ______________________ of BRIGHAM, INC., a Nevada
corporation, as general partner of BRIGHAM OIL & GAS, L.P., a Delaware limited
partnership, and acknowledged to me that ______ executed the same as _______
free and voluntary act and deed, and as the free and voluntary act and deed of
such corporation for the uses and purposes therein set forth.




                                                --------------------------------
                                                Notary Public in and for the
                                                State of Texas

                                                Notarial Seal:


                                    Exh F-20
<PAGE>   131


                                    EXHIBIT G

                              FORM OF NEW MORTGAGE



               MORTGAGE, DEED OF TRUST, ASSIGNMENT OF PRODUCTION,
                   SECURITY AGREEMENT AND FINANCING STATEMENT



                                      FROM


                             BRIGHAM OIL & GAS, L.P.


                                       TO

                            THOMAS MCGRAW, AS TRUSTEE



                               FOR THE BENEFIT OF

                           BANK OF MONTREAL, AS AGENT


     A POWER OF SALE HAS BEEN GRANTED IN THIS INSTRUMENT. A POWER OF SALE MAY
ALLOW THE TRUSTEE OR THE AGENT TO TAKE THE MORTGAGED PROPERTY AND SELL IT
WITHOUT GOING TO COURT IN A FORECLOSURE ACTION UPON DEFAULT BY THE GRANTOR UNDER
THIS INSTRUMENT.

THIS INSTRUMENT CONTAINS AFTER-ACQUIRED PROPERTY PROVISIONS.

THIS INSTRUMENT SECURES PAYMENT OF FUTURE ADVANCES.

THIS INSTRUMENT COVERS PROCEEDS OF MORTGAGED PROPERTY.

THIS IS DEEMED TO BE A LINE OF CREDIT MORTGAGE UNDER THE PROVISIONS OF SECTION
48-7-4 N.M.S.A.


                                    Exh G-1
<PAGE>   132


                     MORTGAGE, DEED OF TRUST, ASSIGNMENT OF
             PRODUCTION, SECURITY AGREEMENT AND FINANCING STATEMENT


     This MORTGAGE, DEED OF TRUST, ASSIGNMENT OF PRODUCTION, SECURITY AGREEMENT
AND FINANCING STATEMENT (this "Mortgage") is entered into as of the effective
time and date hereinafter stated (the "Effective Date") by BRIGHAM OIL & GAS,
L.P., a Delaware limited partnership, whose address for notice is 6300 Bridge
Point Parkway, Building 2, Suite 500, Austin, Texas 78730 ("Mortgagor"), to
THOMAS McGRAW, as Trustee, whose address for notice is 700 Louisiana, Suite
4400, Houston, Texas 77002 ("Trustee") for the benefit of BANK OF MONTREAL, AS
AGENT, whose address for notice is 700 Louisiana, Suite 4400, Houston, Texas
77002 ("Mortgagee").

                                R E C I T A L S:

     A. Mortgagor, Mortgagee and the Lenders (herein so called) described
therein executed that certain Amended and Restated Credit Agreement dated as of
February 17, 2000, (as so amended and as the same may be further amended or
supplemented from time to time, the "Credit Agreement") pursuant to which the
Lenders have made or agreed to make certain advances to and on behalf of the
Mortgagor.

     B. Therefore, in order to comply with the terms and conditions of the
Credit Agreement and for other good and valuable consideration, the receipt and
sufficiency of which are hereby acknowledged, Mortgagor hereby agrees as
follows:

                                    ARTICLE I

                     Grant of Lien and Indebtedness Secured

          Section 1.1 Grant of Liens. To secure payment of the Indebtedness (as
hereinafter defined) and the performance of the covenants and obligations herein
contained, Mortgagor does by these presents hereby, subject to the reservations
and restrictions set forth herein below, (i) GRANT, BARGAIN, SELL, ASSIGN, SET
OVER, TRANSFER and CONVEY unto Trustee and the Trustee's successors and
substitutes in trust hereunder with power of sale, for the use and benefit of
Agent and the Lenders, all of the following described Oil and Gas Leasehold
interests, personal property, rights, titles, interests and estates which are
located in (or cover properties located in) the State of Texas or which are
located within (or cover properties located within) the offshore area over which
the United States of America asserts jurisdiction and to which the laws of such
state are applicable with respect to this Mortgage and/or the liens or security
interests created hereby (the "Deed of Trust Mortgaged Property") and (ii)
GRANT, MORTGAGE, PLEDGE, HYPOTHECATE AND GRANT A POWER OF SALE to Mortgagee, for
its benefit and the benefit of the Lenders, with respect to all of the following
described Oil and Gas Leasehold interests, personal property, rights, titles,
interests and estates which were not granted to Trustee in clause (i) above but
which are located in (or cover properties located in) the State of [       ] or
which are located within (or cover properties located within) the offshore area
over which the United States of America asserts jurisdiction and to which the
laws of the aforementioned states are applicable with respect to this


                                    Exh G-2
<PAGE>   133


Mortgage and/or the liens or security interests created hereby (collectively,
the "Other Mortgaged Property") (the Deed of Trust Property and the Other
Mortgaged Property are hereinafter collectively referred to as the "Mortgaged
Property"):

               (a) All rights, titles, interests and estates now owned or
hereafter acquired by Mortgagor in and to the oil and gas leases and/or oil, gas
and other mineral leases and other interests and estates and the lands and
premises covered or affected thereby which are described on Exhibit A attached
hereto (the "Hydrocarbon Property") or which Hydrocarbon Property is otherwise
referred to herein.

               (b) All rights, titles, interests and estates now owned or
hereafter acquired by Mortgagor in and to (i) the properties now or hereafter
pooled or unitized with the Hydrocarbon Property; (ii) all presently existing or
future unitization, communitization, pooling agreements and declarations of
pooled units and the units created thereby (including, without limitation, all
units created under orders, regulations, rules or other official acts of any
Federal, State or other governmental body or agency having jurisdiction and any
units created solely among working interest owners pursuant to operating
agreements or otherwise) which may affect all or any portion of the Hydrocarbon
Property including, without limitation, those units which may be described or
referred to on attached Exhibit A attached hereto; (iii) all operating
agreements, production sales or other contracts, farm-out agreements, farm-in
agreements, area of mutual interest agreements, equipment leases and other
agreements described or referred to in this Mortgage or which relate to any of
the Hydrocarbon Property or interests in the Hydrocarbon Property described or
referred to herein or on Exhibit A attached hereto or to the production, sale,
purchase, exchange, processing, handling, storage, transporting or marketing of
the Hydrocarbons (hereinafter defined) from or attributable to such Hydrocarbon
Property or interests including, without limitation, all agreements and
arrangements described in Schedule 7.10 of the Credit Agreement; and (iv)
subject to applicable restrictions on disclosure and/or transfer, all
geological, geophysical, engineering, accounting, title, legal, and other
technical or business data concerning the Mortgaged Property, the Hydrocarbons,
or any other item of property which are in the possession of Mortgagor or in
which Mortgagor can otherwise grant a security interest, and all books, files,
records, magnetic media, computer records, and other forms of recording or
obtaining access to such data.

               (c) All rights, titles, interests and estates now owned or
hereafter acquired by Mortgagor in and to all oil, gas, casinghead gas,
condensate, distillate, liquid hydrocarbons, gaseous hydrocarbons and all
products refined therefrom and all other minerals (collectively called the
"Hydrocarbons") in and under and which may be produced and saved from or
attributable to the Hydrocarbon Property, the lands pooled or unitized therewith
and Mortgagor's interests therein, including all oil in tanks and all rents,
issues, profits, proceeds, products, revenues and other income from or
attributable to the Hydrocarbon Property, the lands pooled or unitized therewith
and Mortgagor's interests therein which are subjected or required to be
subjected to the liens and security interests of this Mortgage.

               (d) All tenements, hereditaments, appurtenances and properties in
anywise appertaining, belonging, affixed or incidental to the Hydrocarbon
Property rights, titles, interests and estates described or referred to in
paragraphs (a) and (b) above, which are now owned or which may hereafter be
acquired by Mortgagor, including, without limitation, any and


                                    Exh G-3
<PAGE>   134


all property, real or personal, now owned or hereafter acquired and situated
upon, used, held for use, or useful in connection with the operating, working or
development of any of such Hydrocarbon Property or the lands pooled or unitized
therewith (excluding drilling rigs, trucks, automotive equipment or other
personal property which may be taken to the premises for the purpose of drilling
a well or for other similar temporary uses) and including any and all oil wells,
gas wells, injection wells or other wells, buildings, structures, field
separators, liquid extraction plants, plant compressors, pumps, pumping units,
pipelines, sales and flow lines, gathering systems, field gathering systems,
salt water disposal facilities, tanks and tank batteries, fixtures, valves,
fittings, machinery and parts, engines, boilers, meters, apparatus, equipment,
appliances, tools, implements, cables, wires, towers, casing, tubing and rods,
surface leases, rights-of-way, easements, servitudes, licenses and other surface
and subsurface rights together with all additions, substitutions, replacements,
accessions and attachments to any and all of the foregoing properties.

               (e) Any property that may from time to time hereafter, by
delivery or by writing of any kind, be subjected to the lien and security
interest hereof by Mortgagor or by anyone on Mortgagor's behalf; and the Trustee
is hereby authorized to receive the same at any time as additional security
hereunder.

               (f) All of the rights, titles and interests of every nature
whatsoever now owned or hereafter acquired by Mortgagor in and to the
Hydrocarbon Property rights, titles, interests and estates and every part and
parcel thereof, including, without limitation, the Hydrocarbon Property rights,
titles, interests and estates as the same may be enlarged by the discharge of
any payments out of production or by the removal of any charges or Permitted
Encumbrances (as hereinafter defined) to which any of the Hydrocarbon Property
rights, titles, interests or estates are subject, or otherwise; all rights of
Mortgagor to liens and security interests securing payment of proceeds from the
sale of production from the Mortgaged Property, including, but not limited to,
those liens and security interests provided in Tex. Bus. & Com. Code Ann.
Section 9.319 (Tex. UCC) (Vernon Supp. 1989) ("Section 9.319 Tex. UCC"), as
amended from time to time; together with any and all renewals and extensions of
any of the Hydrocarbon Property rights, titles, interests or estates; all
contracts and agreements supplemental to or amendatory of or in substitution for
the contracts and agreements described or mentioned above; and any and all
additional interests of any kind hereafter acquired by Mortgagor in and to the
Hydrocarbon Property rights, titles, interests or estates.

               (g) All accounts, contract rights, inventory, general
intangibles, insurance contracts and insurance proceeds constituting a part of,
relating to or arising out of those portions of the Mortgaged Property which are
described in paragraphs (a) through (f) above and all proceeds and products of
all such portions of the Mortgaged Property and payments in lieu of production
(such as "take or pay" payments), whether such proceeds or payments are goods,
money, documents, instruments, chattel paper, securities, accounts, general
intangibles, fixtures, real property, or other assets.

     Notwithstanding any provision hereof to the contrary, this Mortgage does
not cover, and there is expressly excepted and excluded from the definition of
Mortgaged Property, any properties, rights and interests as may be beneficially
or equitably owned by (or contractually owing or potentially owing to), or
otherwise as may become owing a third party (the


                                    Exh G-4
<PAGE>   135


"Participating Third Parties") whether in an absolute or in a contingent manner,
under any one or more of the agreements or other arrangements described in
Schedule 7.10 of the Credit Agreement as such agreements or arrangements are in
effect at the date hereof, as read notwithstanding the last sentence of such
Schedule 7.10, to the extent only that such agreement or arrangement has
heretofore been entered into by Mortgagor and any such Participating Third
Parties, until such time, if ever, as the interest or potential interest of such
Participating Third Party vests in Mortgagor; without limiting the generality of
the foregoing, any undivided interest with respect to which Mortgagor holds
legal title (whether of record or not), shall be excluded from the definition of
Mortgaged Property to the extent a Participating Third Party now has an
interest, whether beneficial or equitable, vested or contingent, therein.

     TO HAVE AND TO HOLD the Mortgaged Property unto the Trustee and to his
successors and assigns forever to secure the payment of the Indebtedness
(hereinafter defined) and to secure the performance of the covenants,
agreements, and obligations of the Mortgagor herein contained, subject to (i)
all Excepted Liens (as defined in the Credit Agreement) and any other Liens
described in Exhibit A attached hereto and (ii) all other agreements described
in Schedule 7.10 of the Credit Agreement as such agreements or arrangements are
in effect at the date hereof as read notwithstanding the last sentence thereof,
only to the extent that such agreement or arrangement has heretofore been
entered into by Mortgagor and any Participating Third Party (items (i) and (ii)
above are hereinafter collectively referred to as the "Permitted Encumbrances").

          Section 1.2 Grant of Security Interest. To further secure the
Indebtedness, Mortgagor hereby grants to Mortgagee, subject to the reservations
and restrictions set forth herein below, a security interest in and to the
Mortgaged Property (whether now or hereafter acquired by operation of law or
otherwise) insofar as the Mortgaged Property consists of equipment, accounts,
contract rights, general intangibles (subject in the case of geological and
geophysical data (including without limitation raw data and interpretations),
contract rights and general intangibles to any existing restrictions on
disclosure and/or transfer), insurance contracts, insurance proceeds, inventory,
Hydrocarbons, fixtures and any and all other personal property of any kind or
character defined in and subject to the provisions of the Uniform Commercial
Code presently in effect in the jurisdiction in which the Mortgaged Property is
situated ("Applicable UCC"), including the proceeds and products from any and
all of such Mortgaged Property. Upon the happening of any of the Events of
Default, Mortgagee is and shall be entitled to all of the rights, powers and
remedies afforded a secured party by the Applicable UCC with reference to the
personal property and fixtures in which Mortgagee has been granted a security
interest herein, or the Trustee or Mortgagee may proceed as to both the real and
personal property covered hereby in accordance with the rights and remedies
granted under this Mortgage in respect of the real property covered hereby. Such
rights, powers and remedies shall be cumulative and in addition to those granted
to the Trustee or Mortgagee under any other provision of this Mortgage or under
any other Security Instrument. Written notice mailed to Mortgagor as provided
herein at least five (5) days prior to the date of public sale of any part of
the Mortgaged Property which is personal property subject to the provisions of
the Applicable UCC, or prior to the date after which private sale of any such
part of the Mortgaged Property will be made, shall constitute reasonable notice.


                                    Exh G-5
<PAGE>   136


          Section 1.3 Indebtedness Secured. This Mortgage is executed and
delivered by Mortgagor to secure and enforce the following (the "Indebtedness"):

               (a) Payment of and performance of any and all indebtedness,
obligations and liabilities of Mortgagor pursuant to the Credit Agreement,
whether now existing or hereafter arising, including without limitation, (i)
that certain promissory note by Mortgagor in favor of Bank of Montreal and being
in the principal amount of $23,153,830, dated February 17, 2000 with final
maturity on or before December 31, 2002 and all other notes given in
substitution therefor or in modification, renewal or extension thereof, in whole
or in part (such notes, as from time to time supplemented, amended or modified
and all other notes given in substitution therefor or in modification, renewal
or extension thereof, in whole or in part, being hereafter called the "BMO
Note"), (ii) that certain promissory note by Mortgagor in favor of Societe
Generale, Southwest Agency and being in the principal amount of $11,846,170,
dated February 17, 2000 with final maturity on or before December 31, 2002 and
all other notes given in substitution therefor or in modification, renewal or
extension thereof, in whole or in part (such notes, as from time to time
supplemented, amended or modified and all other notes given in substitution
therefor or in modification, renewal or extension thereof, in whole or in part,
being hereafter called the "Soc-Gen Note,") (iii) that certain promissory note
by Mortgagor in favor of Shell Capital Inc. and being in the principal amount of
$40,000,000, dated February 17, 2000 with final maturity on or before December
31, 2002 and all other notes given in substitution therefor or in modification,
renewal or extension thereof, in whole or in part (such notes, as from time to
time supplemented, amended or modified and all other notes given in substitution
therefor or in modification, renewal or extension thereof, in whole or in part,
being hereafter called the "SCI Note" and, together with the BMO Note and the
Soc-Gen Note, the "Notes") and (iv) any commodity, interest rate or currency
swap, cap, floor, collar, forward agreement or other exchange or protection
agreements or any option with respect to any such transaction in existence as of
the date hereof or hereafter arising between (i) Mortgagor and Bank of Montreal
and its successors or assigns (a "BMO Hedge Party") and Soc-Gen and its
successors or assigns (a "Soc-Gen Hedge Party") entered into while such BMO
Hedge Party or such Soc-Gen Hedge Party is a Lender; and (ii) Mortgagor and SCI
and its successors or assigns (with Loans or Commitments of $20 million or more)
or any Affiliate of SCI (SCI and any Affiliate of SCI a "SCI Hedge Party")
entered into while such SCI Hedge Party or Fathom Energy Capital I, L.L.C, is a
Lender. For purposes of this Section 1.03, the parties intend that any
commodity, interest rate or currency swap, cap, floor, collar, forward agreement
or other exchange or protection agreements or any option entered into between
the Mortgagor and a Lender or in the case of SCI, a SCI Hedge Party, while such
Person was a party to the Credit Agreement shall continue to be secured even
after the time such Person ceases to be a party to the Credit Agreement as a
Lender.

               (b) Any sums which may be advanced or paid by Mortgagee or any
Lender under the terms hereof or of the Credit Agreement or the other Loan
Documents on account of the failure of Mortgagor to comply with the covenants of
Mortgagor contained herein or in the Credit Agreement or such other Loan
Documents; and all other indebtedness of Mortgagor arising pursuant to the
provisions of this Mortgage.

          Section 1.4 Fixture Filing, Etc. Without in any manner limiting the
generality of any of the other provisions of this Mortgage: (i) some portions of
the goods described or to which reference is made herein are or are to become
fixtures on the land described or to which


                                    Exh G-6
<PAGE>   137


reference is made herein or on attached Exhibit A; (ii) the security interests
created hereby under applicable provisions of the Applicable UCC will attach to
Hydrocarbons (minerals including oil and gas) or the accounts resulting from the
sale thereof at the wellhead or minehead located on the land described or to
which reference is made herein; (iii) this Mortgage is to be filed of record in
the real estate records as a financing statement; and (iv) Mortgagor is the
record owner of the real estate or interests in the real estate comprised of the
Mortgaged Property.

          Section 1.5 Defined Terms. Any capitalized term used in this Mortgage
and not defined in this Mortgage shall have the meaning assigned to such term in
the Credit Agreement.

                                   ARTICLE II

                            Assignment of Production

          Section 2.1 Assignment. Mortgagor has absolutely and unconditionally
assigned, transferred, and conveyed, and does hereby absolutely and
unconditionally assign, transfer and convey unto Mortgagee, its successors and
assigns, all of the Hydrocarbons and all products obtained or processed
therefrom, and the revenues and proceeds now and hereafter attributable to the
Hydrocarbons and said products and all payments in lieu of the Hydrocarbons such
as "take or pay" payments or settlements. The Hydrocarbons and products are to
be delivered into pipe lines connected with the Mortgaged Property, or to the
purchaser thereof, to the credit of Mortgagee, free and clear of all taxes,
charges, costs, and expenses; and all such revenues and proceeds shall be paid
directly to Mortgagee, at its banking quarters in Chicago, Illinois, with no
duty or obligation of any party paying the same to inquire into the rights of
Mortgagee to receive the same, what application is made thereof, or as to any
other matter. Mortgagor agrees to perform all such acts, and to execute all such
further assignments, transfers and division orders, and other instruments as may
be required or desired by Mortgagee or any party in order to have said proceeds
and revenues so paid to Mortgagee. Mortgagee is fully authorized to receive and
receipt for said revenues and proceeds; to endorse and cash any and all checks
and drafts payable to the order of Mortgagor or Mortgagee for the account of
Mortgagor received from or in connection with said revenues or proceeds and to
hold the proceeds thereof in a bank account as additional collateral securing
the Indebtedness; and to execute transfer and division orders in the name of
Mortgagor, or otherwise, with warranties binding Mortgagor. All proceeds
received by the Mortgagee pursuant to this assignment shall be applied as
provided in the other Loan Documents. Mortgagee shall not be liable for any
delay, neglect, or failure to effect collection of any proceeds or to take any
other action in connection therewith or hereunder; but Mortgagee shall have the
right, at its election, in the name of Mortgagor or otherwise, to prosecute and
defend any and all actions or legal proceedings deemed advisable by Mortgagee in
order to collect such funds and to protect the interests of Mortgagee, and/or
Mortgagor, with all costs, expenses and attorneys' fees incurred in connection
therewith being paid by Mortgagor. Mortgagor hereby appoints Mortgagee as its
attorney-in-fact to pursue any and all rights of Mortgagor to liens on and
security interests in the Hydrocarbons securing payment of proceeds of runs
attributable to the Hydrocarbons. In addition to the rights granted to Trustee
and/or Mortgagee in Section 1.1(f) of this Mortgage, Mortgagor hereby further
transfers and assigns to Mortgagee any and all such liens, security interests,
financing statements or similar interests of Mortgagor attributable to its
interest in the Hydrocarbons and proceeds of


                                    Exh G-7
<PAGE>   138


runs therefrom arising under or created by said statutory provision, judicial
decision or otherwise. The power of attorney granted to Mortgagee in this
Section 2.1, being coupled with an interest, shall be irrevocable so long as the
Indebtedness or any part thereof remains unpaid.

          Section 2.2 Rights Under Texas Act. Mortgagor hereby grants, sells,
assigns, sets over and mortgages unto Mortgagee during the term hereof, all of
Mortgagor's rights and interests pursuant to the provisions of Section 9.319
Tex. UCC, hereby vesting in Mortgagee all of Mortgagor's rights as an interest
owner to the continuing security interest in and lien upon the Deed of Trust
Mortgaged Property.

          Section 2.3 No Modification of Payment Obligations. Nothing herein
contained shall modify or otherwise alter the obligation of Mortgagor to make
prompt payment of all principal and interest owing on the Indebtedness when and
as the same become due, regardless of whether the proceeds of the Hydrocarbons
are sufficient to pay the same, and the rights provided in accordance with the
foregoing assignment provision shall be cumulative of all other security of any
and every character now or hereafter existing to secure payment of the
Indebtedness.

                                   ARTICLE III

                    Representations, Warranties and Covenants

         Mortgagor hereby represents, warrants and covenants as follows:

          Section 3.1 Defend Title. The Mortgaged Property is free of any and
all Liens (as defined in the Credit Agreement) created by, through or under
Mortgagor (but not otherwise) except the Permitted Encumbrances. Mortgagor will
not create or suffer to be created or permit to exist any lien, security
interest or charge prior or junior to or on a parity with the lien and security
interest of this Mortgage upon the Mortgaged Property or any part thereof or
upon the rents, issues, revenues, profits and other income therefrom, excluding
only Permitted Encumbrances. Mortgagor will maintain and preserve the lien
created hereby so long as any of the Indebtedness secured hereby remains unpaid.

          Section 3.2 Not a Foreign Person. Mortgagor is not a "foreign person"
within the meaning of the Internal Revenue Code of 1986, as amended (hereinafter
called the "Code"), Sections 1445 and 7701 (i.e. Mortgagor is not a non-resident
alien, foreign corporation, foreign partnership, foreign trust or foreign estate
as those terms are defined in the Code and any regulations promulgated
thereunder).

          Section 3.3 Power to Create Lien and Security. The Mortgagor has, in
all material respects, full power and lawful authority to grant, bargain, sell,
assign, transfer, mortgage, and convey a security interest in all of the
Mortgaged Property in the manner and form herein provided and without obtaining
the authorization, approval, consent or waiver of any lessor, sublessor,
Governmental Authority or other party or parties whomsoever.

          Section 3.4 Operation By Third Parties. All or portions of the
Mortgaged Property may be comprised of interests in the Hydrocarbon Property
which are other than working interests or which may be operated by a party or
parties other than Mortgagor and with


                                    Exh G-8
<PAGE>   139


respect to all or any such interests and properties as may be comprised of
interests other than working interests or which may be operated by parties other
than Mortgagor, Mortgagor's covenants as expressed in this Article III are
modified to require that Mortgagor use its best efforts to obtain compliance
with such covenants by the working interest owners or the operator or operators
of such leases or properties.

          Section 3.5 Abandonment; Sales. The Mortgagor will not sell, lease,
assign, transfer or otherwise dispose or abandon any of the Mortgaged Property
except as permitted by the Credit Agreement.

          Section 3.6 Failure to Perform. The Mortgagor agrees that if the
Mortgagor, after receipt from Mortgagee of written notice and demand, fails to
perform any act or to take any action which the Mortgagor is required to perform
or take hereunder or pay any money which the Mortgagor is required to pay
hereunder, each of the Mortgagee and the Trustee in the Mortgagor's name or its
or their own name may, but shall not be obligated to, perform or cause to
perform such act or take such action or pay such money, and any expenses so
incurred by either of them and any money so paid by either of them shall be a
demand obligation owing by the Mortgagor to the Mortgagee or the Trustee, as the
case may be, and each of the Mortgagee and the Trustee, upon making such
payment, shall be subrogated to all of the rights of the Person receiving such
payment. Each amount due and owing by Mortgagor to each of the Mortgagee and the
Trustee pursuant to this Mortgage shall bear interest from the date of such
expenditure or payment or other occurrence which gives rise to such amount being
owed to such Person until paid at the Post-Default Rate, and all such amounts
together with such interest thereon shall be a part of the Indebtedness
described in Section 1.3 hereof.

                                   ARTICLE IV

                               Rights and Remedies

          Section 4.1 Event of Default. An "Event of Default" under the Credit
Agreement shall be an Event of Default under this Mortgage.

          Section 4.2 Foreclosure and Sale. If an Event of Default shall occur
and be continuing, Mortgagee shall have the right and option to proceed with
foreclosure by directing the Trustee, or his successors or substitutes in trust,
to proceed with foreclosure and to sell, to the extent permitted by governing
law, all or any portion of the Mortgaged Property at one or more sales, as an
entirety or in parcels, at such place or places in otherwise such manner and
upon such notice as may be required by governing law, or, in the absence of any
such requirement, as the Mortgagee may deem appropriate, and to make conveyance
to the purchaser or purchasers. Where the Mortgaged Property is situated in more
than one county, notice as above provided shall be posted and filed in all such
counties (if such notices are required by governing law), and all such Mortgaged
Property may be sold in any such county and any such notice shall designate the
county where such Mortgaged Property is to be sold. Nothing contained in this
Section 4.2 shall be construed so as to limit in any way the Trustee's rights to
sell the Mortgaged Property, or any portion thereof, by private sale if, and to
the extent that, such private sale is permitted under the laws of the applicable
jurisdiction or by public or private sale after entry of a judgment by any court
of competent jurisdiction so ordering. Mortgagor hereby irrevocably appoints the


                                    Exh G-9
<PAGE>   140


Trustee to be the attorney of Mortgagor and in the name and on behalf of
Mortgagor to execute and deliver any deeds, transfers, conveyances, assignments,
assurances and notices which Mortgagor ought to execute and deliver and do and
perform any and all such acts and things which Mortgagor ought to do and perform
under the covenants herein contained and generally, to use the name of Mortgagor
in the exercise of all or any of the powers hereby conferred on the Trustee. At
any such sale: (i) whether made under the power herein contained or any other
legal enactment, or by virtue of any judicial proceedings or any other legal
right, remedy or recourse, it shall not be necessary for Trustee to have
physically present, or to have constructive possession of, the Mortgaged
Property (Mortgagor hereby covenanting and agreeing to deliver to Trustee any
portion of the Mortgaged Property not actually or constructively possessed by
Trustee immediately upon demand by Trustee) and the title to and right of
possession of any such property shall pass to the purchaser thereof as
completely as if the same had been actually present and delivered to purchaser
at such sale, (ii) each instrument of conveyance executed by Trustee shall
contain a general warranty of title, binding upon Mortgagor and its successors
and assigns, (iii) each and every recital contained in any instrument of
conveyance made by Trustee shall conclusively establish the truth and accuracy
of the matters recited therein, including, without limitation, nonpayment of the
Indebtedness, advertisement and conduct of such sale in the manner provided
herein and otherwise by law and appointment of any successor Trustee hereunder,
(iv) any and all prerequisites to the validity thereof shall be conclusively
presumed to have been performed, (v) the receipt of Trustee or of such other
party or officer making the sale shall be a sufficient discharge to the
purchaser or purchasers for its purchase money and no such purchaser or
purchasers, or its assigns or personal representatives, shall thereafter be
obligated to see to the application of such purchase money, or be in any way
answerable for any loss, misapplication or nonapplication thereof, (vi) to the
fullest extent permitted by governing law, Mortgagor shall be completely and
irrevocably divested of all of its right, title, interest, claim and demand
whatsoever, either at law or in equity, in and to the property sold and such
sale shall be a perpetual bar both at law and in equity against Mortgagor, and
against any and all other persons claiming or to claim the property sold or any
part thereof, by, through or under Mortgagor, and (vii) to the extent and under
such circumstances as are permitted by governing law, Mortgagee may be a
purchaser at any such sale, and shall have the right, after paying or accounting
for all costs of said sale or sales, to credit the amount of the bid upon the
amount of the Indebtedness (in the order of priority set forth in Section 4.13
hereof) in lieu of cash payment.

          Section 4.3 Substitute Trustees and Agents. The Trustee or his
successor or substitute may appoint or delegate any one or more persons as agent
to perform any act or acts necessary or incident to any sale held by Trustee,
including the posting of notices and the conduct of sale, but in the name and on
behalf of Trustee, his successor or substitute. If Trustee or his successor or
substitute shall have given notice of sale hereunder, any successor or
substitute trustee thereafter appointed may complete the sale and the conveyance
of the property pursuant thereto as if such notice had been given by the
successor or substitute trustee conducting the sale.

          Section 4.4 Judicial Foreclosure; Receivership. If any of the
Indebtedness shall become due and payable and shall not be promptly paid, the
Trustee or Mortgagee shall have the right and power to proceed by a suit or
suits in equity or at law, whether for the specific performance of any covenant
or agreement herein contained or in aid of the execution of any


                                    Exh G-10
<PAGE>   141


power herein granted, or for any foreclosure hereunder or for the sale of the
Mortgaged Property under the judgment or decree of any court or courts of
competent jurisdiction, the appointment of (and Trustee or Mortgagee shall be
entitled to the appointment of) a receiver pending any foreclosure hereunder or
the sale of the Mortgaged Property under the order of a court or courts of
competent jurisdiction or under executory or other legal process, or for the
enforcement of any other appropriate legal or equitable remedy. Any money
advanced by the Trustee and/or Mortgagee in connection with any such
receivership shall be a demand obligation (which obligation Mortgagor hereby
expressly promises to pay) owing by Mortgagor to the Trustee and/or Mortgagee
and shall bear interest from the date of making such advance by the Trustee
and/or Mortgagee until paid at the Post Default Rate.

          Section 4.5 Foreclosure for Installments. Mortgagee shall also have
the option to proceed with foreclosure in satisfaction of any installments of
the Indebtedness which have not been paid when due either through the courts of
competent jurisdiction or by directing the Trustee or his successors in trust to
proceed with foreclosure in satisfaction of the matured but unpaid portion of
the Indebtedness as if under a full foreclosure, conducting the sale as herein
provided and without declaring the entire principal balance and accrued interest
due; such sale may be made subject to the unmatured portion of the Indebtedness,
and any such sale shall not in any manner affect the unmatured portion of the
Indebtedness, but as to such unmatured portion of the Indebtedness, this
Mortgage shall remain in full force and effect just as though no sale had been
made hereunder. It is further agreed that several sales may be made hereunder
without exhausting the right of sale for any unmatured part of the Indebtedness,
it being the purpose hereof to provide for a foreclosure and sale of the
security for any matured portion of the Indebtedness without exhausting the
power to foreclose and sell the Mortgaged Property for any subsequently maturing
portion of the Indebtedness.

          Section 4.6 Separate Sales. The Mortgaged Property may be sold in one
or more parcels and in such manner and order as Mortgagee, in its sole
discretion, may elect, it being expressly understood and agreed that the right
of sale arising out of any Event of Default shall not be exhausted by any one or
more sales.

          Section 4.7 Occupancy After Foreclosure. In the event there is a
foreclosure sale hereunder and at the time of such sale Mortgagor or Mortgagor's
heirs, devisees, representatives, successors or assigns or any other person
claiming any interest in the Mortgaged Property by, through or under Mortgagor,
are occupying or using the Mortgaged Property or any part thereof, each and all
shall immediately become the tenant of the purchaser at such sale, which tenancy
shall be a tenancy from day to day, terminable at the will of either the
landlord or tenant, or at a reasonable rental per day based upon the value of
the property occupied, such rental to be due daily to the purchaser; to the
extent permitted by applicable law, the purchaser at such sale shall,
notwithstanding any language herein apparently to the contrary, have the sole
option to demand immediate possession following the sale or to permit the
occupants to remain as tenants at will. In the event the tenant fails to
surrender possession of said property upon demand, the purchaser shall be
entitled to institute and maintain a summary action for possession of the
Mortgaged Property (such as an action for forcible entry and detainer) in any
court having jurisdiction.


                                    Exh G-11
<PAGE>   142


          Section 4.8 Remedies Cumulative, Concurrent and Nonexclusive. Every
right, power and remedy herein given to the Trustee or Mortgagee shall be
cumulative and in addition to every other right, power and remedy herein
specifically given or now or hereafter existing in equity, at law or by statute
(including specifically those granted by the Applicable UCC in effect and
applicable to the Mortgaged Property or any portion thereof) each and every
right, power and remedy whether specifically herein given or otherwise existing
may be exercised from time to time and so often and in such order as may be
deemed expedient by the Trustee or Mortgagee, and the exercise, or the beginning
of the exercise, of any such right, power or remedy shall not be deemed a waiver
of the right to exercise, at the same time or thereafter, any other right, power
or remedy. No delay or omission by the Trustee or Mortgagee in the exercise of
any right, power or remedy shall impair any such right, power or remedy or
operate as a waiver thereof or of any other right, power or remedy then or
thereafter existing.

          Section 4.9 No Release of Obligations. Neither Mortgagor, any
guarantor nor any other person hereafter obligated for payment of all or any
part of the Indebtedness shall be relieved of such obligation by reason of (a)
the failure of Trustee to comply with any request of Mortgagor, or any guarantor
or any other person so obligated to foreclose the lien of this Mortgage or to
enforce any provision hereunder or under the Credit Agreement; (b) the release,
regardless of consideration, of the Mortgaged Property or any portion thereof or
interest therein or the addition of any other property to the Mortgaged
Property; (c) any agreement or stipulation between any subsequent owner of the
Mortgaged Property and Mortgagee extending, renewing, rearranging or in any
other way modifying the terms of this Mortgage without first having obtained the
written consent of, given notice to or paid any consideration to Mortgagor, any
guarantor or such other person, and in such event Mortgagor, guarantor and all
such other persons shall continue to be liable to make payment according to the
terms of any such extension or modification agreement unless expressly released
and discharged in writing by Mortgagee; or (d) by any other act or occurrence
save and except the complete payment of the Indebtedness and the complete
fulfillment of all obligations hereunder or under the Credit Agreement.

          Section 4.10 Release of and Resort to Collateral. Mortgagee may
release, regardless of consideration, any part of the Mortgaged Property
without, as to the remainder, in any way impairing, affecting, subordinating or
releasing the lien or security interest created in or evidenced by this Mortgage
or its stature as a first and prior lien and security interest in and to the
Mortgaged Property, and without in any way releasing or diminishing the
liability of any person or entity liable for the repayment of the Indebtedness.
For payment of the Indebtedness, Mortgagee may resort to any other security
therefor held by Mortgagee or Trustee in such order and manner as Mortgagee may
elect.

          Section 4.11 Waiver of Redemption, Notice and Marshalling of Assets,
Etc. To the fullest extent permitted by applicable law, Mortgagor hereby
irrevocably and unconditionally waives and releases (a) all benefits that might
accrue to Mortgagor by virtue of any present or future moratorium law or other
law exempting the Mortgaged Property from attachment, levy or sale on execution
or providing for any appraisement (except as otherwise provided in Section 4.16
of this Mortgage), valuation (except as otherwise provided in Section 4.16 of
this Mortgage), stay of execution, exemption from civil process, redemption or
extension of time for payment and (b) any right to a marshalling of assets or a
sale in inverse order of alienation. If any law referred to in this Mortgage and
now in force, of which Mortgagor or its successor or


                                    Exh G-12
<PAGE>   143


successors might take advantage despite the provisions hereof, shall hereafter
be repealed or cease to be in force, such law shall thereafter be deemed not to
constitute any part of the contract herein contained or to preclude the
operation or application of the provisions hereof. Provided, however, that if
the laws of any state do not permit the redemption period to be waived, the
redemption period is specifically reduced to the minimum amount of time
allowable by governing statute, and specifically for any property located in the
State of New Mexico, the redemption period hereunder shall be reduced to one
month.

          Section 4.12 Discontinuance of Proceedings. In case Mortgagee shall
have proceeded to invoke any right, remedy or recourse permitted hereunder or
under the Credit Agreement and shall thereafter elect to discontinue or abandon
same for any reason, Mortgagee shall have the unqualified right so to do and, in
such an event, Mortgagor and Mortgagee shall be restored to their former
positions with respect to the Indebtedness, this Mortgage, the Credit Agreement,
the Mortgaged Property and otherwise, and the rights, remedies, recourses and
powers of Mortgagee shall continue as if same had never been invoked.

          Section 4.13 Application of Proceeds. The proceeds of any sale of the
Mortgaged Property or any part thereof and all other monies received by the
Trustee or Mortgagee in any proceedings for the enforcement hereof or otherwise,
whose application has not elsewhere herein been specifically provided for, shall
be applied:

               (a) first, to the payment of all reasonable expenses incurred by
the Trustee or Mortgagee incident to the enforcement of this Mortgage, the
Credit Agreement or any of the Indebtedness (including, without limiting the
generality of the foregoing, expenses of any entry or taking of possession, of
any sale, of advertisement thereof, and of conveyances, and court costs,
compensation of agents and employees, legal fees and a reasonable commission to
the Trustee acting), and to the payment of all other charges, reasonable
expenses, liabilities and advances incurred or made by the Trustee or Mortgagee
under this Mortgage or in executing any trust or power hereunder;

               (b) second to payment of the Indebtedness in such order and
manner as Mortgagee may elect; and

               (c) third, to Mortgagor; or as otherwise required by any
Governmental Requirement.

          Section 4.14 Resignation of Operator. In addition to all rights and
remedies under this Mortgage, at law and in equity, if any Event of Default
shall occur and Trustee or the Mortgagee shall exercise any possessory remedies
under this Mortgage with respect to any portion of the Hydrocarbon Property (or
Mortgagor shall transfer any Mortgaged Property "in lieu of" foreclosure), the
Mortgagee or the Trustee shall have the right to request that any operator of
any Hydrocarbon Property which is either Mortgagor or any Affiliate of Mortgagor
to resign as operator under the joint operating agreement applicable thereto,
and no later than 60 days after receipt by Mortgagor of any such request,
Mortgagor shall resign (or cause such other party to resign) as operator of such
Hydrocarbon Property.


                                    Exh G-13
<PAGE>   144


          Section 4.15 INDEMNITY. IN CONNECTION WITH ANY ACTION TAKEN BY THE
TRUSTEE AND/OR MORTGAGEE PURSUANT TO THIS MORTGAGE, THE TRUSTEE AND/OR MORTGAGEE
AND THEIR OFFICERS, DIRECTORS, EMPLOYEES, REPRESENTATIVES, AGENTS, ATTORNEYS,
ACCOUNTANTS AND EXPERTS ("INDEMNIFIED PARTIES") SHALL NOT BE LIABLE FOR ANY LOSS
SUSTAINED BY MORTGAGOR RESULTING FROM AN ASSERTION THAT MORTGAGEE HAS RECEIVED
FUNDS FROM THE PRODUCTION OF HYDROCARBONS CLAIMED BY THIRD PERSONS OR ANY ACT OR
OMISSION OF ANY INDEMNIFIED PARTY IN ADMINISTERING, MANAGING, OPERATING OR
CONTROLLING THE MORTGAGED PROPERTY, INCLUDING SUCH LOSS WHICH MAY RESULT FROM
THE ORDINARY NEGLIGENCE OF AN INDEMNIFIED PARTY, UNLESS SUCH LOSS IS CAUSED BY
THE GROSS NEGLIGENCE, WILLFUL MISCONDUCT OR BAD FAITH OF AN INDEMNIFIED PARTY,
NOR SHALL THE TRUSTEE AND/OR MORTGAGEE BE OBLIGATED TO PERFORM OR DISCHARGE ANY
OBLIGATION, DUTY OR LIABILITY OF MORTGAGOR. MORTGAGOR SHALL AND DOES HEREBY
AGREE TO INDEMNIFY EACH INDEMNIFIED PARTY FOR, AND TO HOLD EACH INDEMNIFIED
PARTY HARMLESS FROM, ANY AND ALL LIABILITY, LOSS OR DAMAGE WHICH MAY OR MIGHT BE
INCURRED BY ANY INDEMNIFIED PARTY BY REASON OF THIS MORTGAGE OR THE EXERCISE OF
RIGHTS OR REMEDIES HEREUNDER. SHOULD THE TRUSTEE AND/OR MORTGAGEE MAKE ANY
EXPENDITURE ON ACCOUNT OF ANY SUCH LIABILITY, LOSS OR DAMAGE, THE AMOUNT
THEREOF, INCLUDING COSTS, EXPENSES AND REASONABLE ATTORNEYS' FEES, SHALL BE A
DEMAND OBLIGATION (WHICH OBLIGATION MORTGAGOR HEREBY EXPRESSLY PROMISES TO PAY)
OWING BY MORTGAGOR TO THE TRUSTEE AND/OR MORTGAGEE AND SHALL BEAR INTEREST FROM
THE DATE EXPENDED UNTIL PAID AT THE POST-DEFAULT RATE, SHALL BE A PART OF THE
INDEBTEDNESS AND SHALL BE SECURED BY THIS MORTGAGE AND ANY OTHER SECURITY
INSTRUMENT. MORTGAGOR HEREBY ASSENTS TO, RATIFIES AND CONFIRMS ANY AND ALL
ACTIONS OF THE TRUSTEE AND/OR MORTGAGEE WITH RESPECT TO THE MORTGAGED PROPERTY
TAKEN UNDER, AND IN COMPLIANCE WITH THE TERMS OF, THIS MORTGAGE. THE LIABILITIES
OF THE MORTGAGOR AS SET FORTH IN THIS SECTION 4.15 SHALL SURVIVE THE TERMINATION
OF THIS MORTGAGE.

          Section 4.16 Power of Sale in Oklahoma. Any sale of any part of the
Mortgaged Property located in the State of Oklahoma shall be made in conformity
to the laws thereof, and it is agreed that the appraisement of any such
properties is expressly waived or not waived at the option of the Agent, and any
such option may be exercised prior to the time judgment is rendered in any
foreclosure hereon. A POWER OF SALE HAS BEEN GRANTED IN THIS MORTGAGE. A POWER
OF SALE MAY ALLOW THE AGENT TO TAKE THE MORTGAGED PROPERTY AND SELL IT WITHOUT
GOING TO COURT IN A FORECLOSURE ACTION UPON DEFAULT BY GRANTOR UNDER THIS
MORTGAGE. The parties hereto are cognizant of and acknowledge the Oklahoma Power
of Sale Mortgage Foreclosure Act which went into effect November 1, 1986.
Notwithstanding any provision of Article IV to the contrary, it is the intent of
the parties that the provisions herein relating to the power of sale which are
applicable to the Mortgaged Property located in the State of Oklahoma are
subject to the provisions of the Oklahoma Power of Sale


                                    Exh G-14
<PAGE>   145


Mortgage Foreclosure Act. In addition, it is the intent of the parties that the
power of sale granted herein may be exercised by the Mortgagee pursuant to the
terms and provisions of the Oklahoma Power of Sale Mortgage Foreclosure Act. To
that end, Mortgagor hereby confers and grants to the Agent and Trustee the power
to sell the Mortgaged Property and the interests of persons therein in the
manner provided in the Oklahoma Power of Sale Mortgage Foreclosure Act. No
action of the Agent or the Trustee based on the provisions in this Mortgage or
the Oklahoma Power of Sale Mortgage Foreclosure Act, including the giving of the
Notice of Intent to Foreclose by Power of Sale or the Notice of Sale, shall
constitute an election of remedies that would preclude the Agent or Trustee from
pursuing judicial foreclosure before or at any time after commencement of the
power of sale foreclosure procedure mandated by the Oklahoma Power of Sale
Mortgage Foreclosure Act.

                                    ARTICLE V

                                   The Trustee

          Section 5.1 Duties, Rights, and Powers of Trustee. It shall be no part
of the duty of the Trustee to see to any recording, filing or registration of
this Mortgage or any other instrument in addition or supplemental thereto, or to
give any notice thereof, or to see to the payment of or be under any duty in
respect of any tax or assessment or other governmental charge which may be
levied or assessed on the Mortgaged Property, or any part thereof, or against
Mortgagor, or to see to the performance or observance by Mortgagor of any of the
covenants and agreements contained herein. The Trustee shall not be responsible
for the execution, acknowledgment or validity of this Mortgage or of any
instrument in addition or supplemental hereto or for the sufficiency of the
security purported to be created hereby, and makes no representation in respect
thereof or in respect of the rights of Mortgagee. The Trustee shall have the
right to advise with counsel upon any matters arising hereunder and shall be
fully protected in relying as to legal matters on the advice of counsel. The
Trustee shall not incur any personal liability hereunder except for Trustee's
own gross negligence, bad faith and/or willful misconduct; and the Trustee shall
have the right to rely on any instrument, document or signature authorizing or
supporting any action taken or proposed to be taken by him hereunder, believed
by him in good faith to be genuine.

          Section 5.2 Successor Trustee. The Trustee may resign by written
notice addressed to Mortgagee or be removed at any time with or without cause by
an instrument in writing duly executed on behalf of Mortgagee. In case of the
death, resignation or removal of the Trustee, a successor trustee may be
appointed by Mortgagee by instrument of substitution complying with any
applicable requirements of law, or, in the absence of any such requirement,
without other formality than appointment and designation in writing. Written
notice of such appointment and designation shall be given by Mortgagee to
Mortgagor, but the validity of any such appointment shall not be impaired or
affected by failure to give such notice or by any defect therein. Such
appointment and designation shall be full evidence of the right and authority to
make the same and of all the facts therein recited, and, upon the making of any
such appointment and designation, this Mortgage shall vest in the successor
trustee all the estate and title in and to all of the Mortgaged Property, and
the successor trustee shall thereupon succeed to all of the rights, powers,
privileges, immunities and duties hereby conferred upon the Trustee named
herein, and one such appointment and designation shall not exhaust the right to
appoint and


                                    Exh G-15
<PAGE>   146


designate a successor trustee hereunder but such right may be exercised
repeatedly as long as any Indebtedness remains unpaid hereunder. To facilitate
the administration of the duties hereunder, Mortgagee may appoint multiple
trustees to serve in such capacity or in such jurisdictions as Mortgagee may
designate.

          Section 5.3 Retention of Moneys. All moneys received by Trustee shall,
until used or applied as herein provided, be held in trust for the purposes for
which they were received, but need not be segregated in any manner from any
other moneys (except to the extent required by applicable law), and Trustee
shall be under no liability for interest on any moneys received by him
hereunder.

                                   ARTICLE VI

                                  Miscellaneous

          Section 6.1 Instrument Construed as Mortgage, Etc. With respect to any
portions of the Mortgaged Property located in any state or other jurisdiction
the laws of which do not provide for the use or enforcement of a deed of trust
or the office, rights and authority of the Trustee as herein provided, the
general language of conveyance hereof to the Trustee is intended and the same
shall be construed as words of mortgage unto and in favor of Mortgagee and the
rights and authority granted to the Trustee herein may be enforced and asserted
by Mortgagee in accordance with the laws of the jurisdiction in which such
portion of the Mortgaged Property is located, and the same may be foreclosed at
the option of Mortgagee as to any or all such portions of the Mortgaged Property
in any manner permitted by the laws of the jurisdiction in which such portions
of the Mortgaged Property is situated. This Mortgage may be construed as a
mortgage, deed of trust, chattel mortgage, conveyance, assignment, security
agreement, pledge, financing statement, hypothecation or contract, or any one or
more of them, in order fully to effectuate the lien hereof and the purposes and
agreements herein set forth.

          Section 6.2 Release of Mortgage. If all Indebtedness secured hereby
shall be paid and the Credit Agreement terminated, Mortgagee shall forthwith
cause satisfaction and discharge of this Mortgage to be entered upon the record
at the expense of Mortgagor and shall execute and deliver or cause to be
executed and delivered such instruments of satisfaction and reassignment as may
be appropriate. Otherwise, this Mortgage shall remain and continue in full force
and effect.

          Section 6.3 Severability. If any provision hereof is invalid or
unenforceable in any jurisdiction, the other provisions hereof shall remain in
full force and effect in such jurisdiction and the remaining provisions hereof
shall be liberally construed in favor of the Trustee and Mortgagee in order to
effectuate the provisions hereof, and the invalidity or unenforceability of any
provision hereof in any jurisdiction shall not affect the validity or
enforceability of any such provision in any other jurisdiction.

          Section 6.4 Successors and Assigns of Parties. The term "Mortgagee" as
used herein shall mean and include any legal owner, holder, assignee or pledgee
of any of the Indebtedness secured hereby. The terms used to designate Trustee,
Mortgagee and Mortgagor


                                    Exh G-16
<PAGE>   147


shall be deemed to include the respective heirs, legal representatives,
successors and assigns of such parties.

          Section 6.5 Satisfaction of Prior Encumbrance. To the extent that
proceeds of the Credit Agreement are used to pay indebtedness secured by any
outstanding lien, security interest, charge or prior encumbrance against the
Mortgaged Property, such proceeds have been advanced by Mortgagee at Mortgagor's
request, Mortgagee shall be subrogated to any and all rights, security interests
and liens owned by any owner or holder of such outstanding liens, security
interests, charges or encumbrances, irrespective of whether said liens, security
interests, charges or encumbrances are released, and it is expressly understood
that, in consideration of the payment of such other indebtedness by Mortgagee,
Mortgagor hereby waives and releases all demands and causes of action for
offsets and payments to, upon and in connection with the said indebtedness.

          Section 6.6 Subrogation of Trustee. This Mortgage is made with full
substitution and subrogation of the Trustee and his successors in this trust and
his and their assigns in and to all covenants and warranties by others
heretofore given or made in respect of the Mortgaged Property or any part
thereof.

          Section 6.7 Nature of Covenants. The covenants and agreements herein
contained shall constitute covenants running with the land and interests covered
or affected hereby and shall be binding upon the heirs, legal representatives,
successors and assigns of the parties hereto.

          Section 6.8 Notices. All notices, requests, consents, demands and
other communications required or permitted hereunder shall be in writing and
shall be deemed sufficiently given or furnished if delivered by registered or
certified United States mail, postage prepaid, or by personal service (including
express or courier service) at the addresses specified in the first paragraph of
this Mortgage (unless changed by similar notice in writing given by the
particular party whose address is to be changed). Any such notice or
communication shall be deemed to have been given either at the time of personal
delivery or, in the case of delivery at the address and in the manner provided
herein, upon receipt; provided that service of notice as required by the laws of
any state in which portions of the Mortgaged Property may be situated shall for
all purposes be deemed appropriate and sufficient with the giving of such
notice.

          Section 6.9 Counterparts. This Mortgage is being executed in several
counterparts, all of which are identical, except that to facilitate recordation,
if the Mortgaged Property is situated in more than one county, descriptions of
only those portions of the Mortgaged Property located in the county in which a
particular counterpart is recorded shall be attached as Exhibit A thereto. A
complete Exhibit A will be attached to that certain counterpart to be attached
to a Financing Statement and filed (a) with respect to the Deed of Trust
Mortgaged Property, with the Secretary of State of [        ] in the Uniform
Commercial Code Records, and (b) with respect to the Other Mortgaged Property,
with the [                    ]. Each of such counterparts shall for all
purposes be deemed to be an original, and all such counterparts shall together
constitute but one and the same instrument.


                                    Exh G-17
<PAGE>   148


          Section 6.10 Exculpation Provisions. Each of the parties hereto
specifically agrees that it has a duty to read this Mortgage; and agrees that it
is charged with notice and knowledge of the terms of this Mortgage; that it has
in fact read this Mortgage and is fully informed and has full notice and
knowledge of the terms, conditions and effects of this Mortgage; that it has
been represented by independent legal counsel of its choice throughout the
negotiations preceding its execution of this Mortgage; that it has received the
advice of its attorney in entering into this Mortgage; and that it recognizes
that certain of the terms of this Mortgage result in one party assuming the
liability inherent in some aspects of the transaction and relieving the other
party of its responsibility for such liability. Each party hereto agrees and
covenants that it will not contest the validity or enforceability of any
exculpatory provision of this Mortgage on the basis that the party had no notice
or knowledge of such provision or that the provision is not "conspicuous."


                                    Exh G-18
<PAGE>   149


     WITNESS THE EXECUTION HEREOF, this 17th day of February, 2000, as of 7:01
a.m. Houston, Texas time, immediately after giving effect to the execution and
effective time of that certain Conveyance of Adjustable Term Overriding Royalty
Interest of even date herewith from Mortgagor to ECT Merchant Investments Corp.
and Joint Energy Development Investments II Limited partnership (the "Term ORRI
Conveyance") (the "Effective Date").

                                   MORTGAGOR:

                                   BRIGHAM OIL & GAS, L.P.

                                   By: Brigham, Inc., its General Partner


                                       By:
                                          --------------------------------------
                                          Name:
                                          Title:


EXECUTION
WITNESSED BY:


- -------------------------------
Name:
     --------------------------


- -------------------------------
Name:
     --------------------------



                                    Exh G-19
<PAGE>   150



STATE OF TEXAS               )
                             )
COUNTY OF HARRIS             )



                                    OKLAHOMA


     Before me, a Notary Public in and for said county and state, on this 17th
day of February, 2000, personally appeared _________________________________, to
me known to be the identical person who subscribed the name of the maker thereof
to the foregoing instrument as _______________________ of BRIGHAM, INC., a
Nevada corporation, as general partner of BRIGHAM OIL & GAS, L.P., a Delaware
limited partnership, and acknowledged to me that ______ executed the same as
_____ free and voluntary act and deed, and as the free and voluntary act and
deed of such corporation for the uses and purposes therein set forth.

                                      TEXAS


     This instrument was acknowledged before me on February 17, 2000, by
___________________________, _____________ of BRIGHAM, INC., a Nevada
corporation, as general partner of BRIGHAM OIL & GAS, L.P., a Delaware limited
partnership, on behalf of such corporation, as general partner of the limited
partnership.

                                                 ------------------------------
                                                 Notary Public in and for the
                                                 State of Texas

                                                 Notarial Seal:



                                    Exh G-20
<PAGE>   151



                                    EXHIBIT A

                               MORTGAGED PROPERTY


                                    Exh G-21
<PAGE>   152


                                    EXHIBIT B

                                   ASSIGNMENTS


                                    Exh G-22
<PAGE>   153


                                  SCHEDULE 7.02


                                   LIABILITIES

Any matter disclosed in any Schedule hereto and any additional matter disclosed
in Brigham Exploration Company's financial statements and/or any cash budget
heretofore delivered to the Agent.


                                   Sch 7.2-1
<PAGE>   154


                                  SCHEDULE 7.03


                                   LITIGATION

                                      NONE


                                   Sch 7.03-1
<PAGE>   155


                                  SCHEDULE 7.09


                                      TAXES

                                      NONE


                                   Sch 7.09-1
<PAGE>   156


                                  SCHEDULE 7.10


                                  TITLES, ETC.

(a) The rights and interests afforded Gasco Limited Partnership ("Gasco") and
its successors and assigns under the terms of (i) that certain Expense
Allocation and Participation Agreement dated as of April 1, 1996, by and between
Gasco and Borrower, as heretofore and/or hereafter amended, expanded,
supplemented, renewed and/or extended, and (ii) that certain Expense Allocation
and Participation Agreement II dated as of April 1, 1997, by and between Gasco
and Borrower, as heretofore and/or hereafter amended, expanded, supplemented,
renewed and/or extended, and (iii) that certain Expense Allocation and
Participation Agreement III dated as of March 1, 1998, by and between Gasco and
Borrower, as heretofore and/or hereafter amended, expanded, supplemented,
renewed and/or extended.

(b) The rights and interests afforded Middle Bay Oil Company ("Middle Bay") and
its successors and assigns under the terms of that certain Expense Allocation
and Participation Agreement dated as of April 1, 1996, by and between Middle Bay
and Borrower, as heretofore and/or hereafter amended, modified, expanded,
supplemented, renewed and/or extended.

(c) The rights and interests afforded Stephens Production Company ("Stephens")
and its successors and assigns under the terms of that certain Anadarko Basin
Joint Participation Agreement dated as of May 1, 1996, by and between Borrower
and Stephens, as heretofore and/or hereafter amended, modified, expanded,
supplemented, renewed and/or extended.

(d) The rights and interests afforded Vintage Petroleum, Inc. ("Vintage") and
its successors and assigns under the terms of that certain Anadarko Basin Joint
Participation Agreement dated as of May 1, 1996, by and between Borrower and
Vintage, as heretofore and/or hereafter amended, modified, expanded,
supplemented, renewed and/or extended.

(e) The rights and interests afforded Brigham-Duke (Delaware) LLC ("Duke") and
its successors and assigns under the terms of that certain Joint Development
Agreement dated as of February 17, 1999, by and between Duke and Borrower, as
heretofore amended.

(f) The rights and interests afforded third parties under the terms of various
farmout, exploration, joint participation and/or operating agreements, whether
now existing or hereafter entered into and further as heretofore and/or
hereafter amended, modified, expanded, supplemented, renewed and/or extended,
under or in relation to which Borrower agrees to farm-out to one or more third
parties one or more Oil and Gas Property and/or undertakes with one or more
third party(ies) the joint exploration and/or development of one or more Oil and
Gas Properties (which rights and interests may


                                   Sch 7.10-1
<PAGE>   157


include, without limitation, rights under Area of Mutual Interests agreements
and rights in respect of forfeiture of all or a portion of Borrower's interests
in an Oil and Gas Property, or part thereof or interest therein, that is
triggered by an election not to participate in a proposed operation);

(g) consulting agreements, whether now existing or hereafter entered into and
further as heretofore and/or hereafter amended, expanded, supplemented, renewed
and/or extended, with third party geologists, landmen or other oil and gas
industry participants who agree to perform services in return, in whole or in
part, for an overriding royalty interest or other interest in or relating to any
Oil and Gas Properties; and

(h) the Term ORRI.

In no event will any agreement or other matter referred to in this Schedule
7.10, other than the Term ORRI, cause the Borrower's net interest in production
or net cost and expense obligation with respect to Hydrocarbon Interests as
reflected in a Standard Mortgage to be reduced or otherwise adversely affected.


                                   Sch 7.10-2
<PAGE>   158


                                 SCHEDULE 7.14


                         SUBSIDIARIES AND PARTNERSHIPS

Brigham, Inc.
Brigham Oil & Gas, L.P.
Brigham Holdings I, LLC
Brigham Holdings II, LLC

Quest Resources, LLC

Venture Acquisitions, LP

Each of the foregoing is owned 100% (directly by or indirectly) by Seller, other
than Venture Acquisitions, LP.

The address for each of the foregoing is:

6300 Bridge Point Parkway
Building 2, Suite 500
Austin, TX  78730
Attention:  Curtis Harrell


                                   Sch 7.14-1
<PAGE>   159


                                  SCHEDULE 7.17


                              ENVIRONMENTAL MATTERS

                                      NONE


                                   Sch 7.17-1
<PAGE>   160


                                  SCHEDULE 7.19


                                    INSURANCE

<TABLE>
<S>                                   <C>
INTEREST Property Coverage
         Carrier                      Security Insurance Company of Hartford
         Policy Period                         August 1, 1999 to August 1, 2000
         Policy No.                            CTPPG30231
         Limits                                $1,520,000 (Austin), $100,000 (Houston)-personal;

                                               $2,515,000 computer equipment
         Deductible                            $1,000

INTEREST Commercial General
         Carrier                      Northfield Insurance Company (Chubb)
         Policy Period                         August 1, 1999 to August 1, 2000
         Policy No.                            NN100139
         Limits                                $2,000,000 general aggregate
                                               $1,000,000 product/completed ops
                                                      injury each occurrence/underground
                                               $100,000 fire to rended properties
                                               $5,000 medical expenses
         Deductible                            $5,000 per claim

INTEREST Pollution Coverage
         Carrier
         Policy Period                         August 1, 1999 to August 1, 2000
         Policy No.                            NN100139
         Limits                                $1,000,000 each pollution incident
                                               $2,000,000 annual aggregate
         Deductible                            $5,000

INTEREST Workers' Comp/Employee
         Carrier                      Texas Workers' Compensation Fund
         Policy Period                         August 1, 1999 to August 1, 2000
         Policy No.                            TSF0012623201-19990801
         Limits                                $1,000,000
         Deductible                            None

INTEREST Primary Umbrella Liability
         Carrier                      Northfield Insurance Company
         Policy Period                         August 1, 1999 to August 1, 2000
         Policy No.                            NU101446
         Limits                                $10,000,000 per occurrence
                                               $10,000,000 annual aggregate
         Retention                             $25,000
</TABLE>


                                   Sch 7.19-1
<PAGE>   161


<TABLE>
<S>                                   <C>
INTEREST Excess Primary Umbrella
         Carrier                      Westchester Fire Insurance Company
         Policy Period                         August 1, 1999 to August 1, 2000
         Policy No.                            XLS310890
         Limits                                $20,000,000 per occurrence and aggregate, except

                                               $2,000,000 over the pollution coverage

INTEREST Control of Well
         Carrier                      Lexington Insurance Company
         Policy Period                         August 1, 1999 to August 1, 2000
         Policy No.                            8799881
         Limits                                $5,000,000 control of well
                                               $500,000 care, custody and control
                                               $50,000 control of well
                                               $25,000 care, custody and control

INTEREST Directors and Officers
         Carrier                      Executive Risk Speciality Insurance Company

         Policy Period                         May 30, 1997 to May 30, 2000
         Policy No.                            75106733497
         Limits                                $5,000,000
         Retention                             $0-250,000 per claim

</TABLE>


                                   Sch 7.19-2
<PAGE>   162


                                  SCHEDULE 7.20


                               HEDGING AGREEMENTS

 ISDA Master Agreement dated as of February 26, 1998, as amended, together with
                  any confirmations and written call options.


                                   Sch 7.20-1
<PAGE>   163


                                  SCHEDULE 7.22


                               MATERIAL AGREEMENTS

(a) the Senior Loan Documents (and the loan relating thereto).

(b) Two Bridge Point Lease Agreement dated as of September 20, 1996, by and
between Investors Life Insurance Company of North America and Brigham Oil & Gas,
L.P., as amended (office lease).

(c) Paragon One Lease Agreement dated as of December 14, 1996, covering the
Houston office space.

(d) Capital Lease/Financing Agreements for purchase of software and/or
equipment, more particularly described as follows:

<TABLE>
<CAPTION>
                                                              CURRENT
                                                              PRINCIPAL
                                        ENDING       BALANCE

LESSOR                                   DATE        AS OF 2/1/00      DESCRIPTION
- -------------------------------------------------------------------------------------------
<S>                                     <C>          <C>               <C>
Siemens Credit Corp                     12/1/99      $7,112.51         Houston Phone System

Siemens Credit Corp                     7/1/02       $81,149.02        Austin Phone System

Universal Finance & Leasing
Equipment                               8/1/00       $18,779.88        Workstation

Universal Finance & Leasing
Equipment                               1/10/01      $21,282.13        Workstation

Universal Finance & Leasing
Equipment                               4/21/01      $77,421.75        Workstation

Geoquest Equipment                      8/1/00       $11,026.14        Workstation

Universal Finance & Leasing
Equipment                               9/22/00      $5,517.90         Workstation

BA Credit Corp                          8/18/01      $57,141.05        Workstation

First Sierra Financial, Inc.            2/1/02       $34,955.28        Workstation

TOTAL CURRENT PRINCIPAL BALANCE         $314,025.66
</TABLE>

(e) Insurance premium financing agreements:


                                   Sch 7.22-1
<PAGE>   164

     Premium financing agreement dated June 1, 1997 relating to 3-year O&D
policy. [Payoff at December 31, 1999 was $16,855.14]

     Premium financing agreement dated August 1, 1999 relating to G.L.,
Property, Umbrella and OEE policies.

(f) The matters disclosed in the other Schedules.

(g) The Subordinated Debt.


                                   Sch 7.22-2
<PAGE>   165


                                  SCHEDULE 7.23


                                 GAS IMBALANCES

                                      NONE


                                   Sch 7.23-1
<PAGE>   166


                                  SCHEDULE 9.01


                                      DEBT

     The matters disclosed in other Schedules hereto and those divulged in
Brigham Exploration Company's financial statements or any cash budget provided
to the Agent.


                                  Sch. 9.01-1
<PAGE>   167


                                SCHEDULE 9.01(h)

              The matters described in Schedules 7.22 and/or 9.01.


                                 Sch 9.01(h)-1
<PAGE>   168


                                  SCHEDULE 9.02


                                      LIENS


                                      None


                                   Sch 9.02-1
<PAGE>   169


                                  SCHEDULE 9.03


                         INVESTMENTS, LOANS AND ADVANCES

                                      NONE


                                   Sch 9.03-1

<PAGE>   1
                                                                    EXHIBIT 10.2

                                                                  EXECUTION COPY



                     AMENDED AND RESTATED GUARANTY AGREEMENT



                                       BY


                           BRIGHAM EXPLORATION COMPANY


                                   IN FAVOR OF


                           BANK OF MONTREAL, AS AGENT
                             AND EACH OF THE LENDERS
               PARTY TO THE AMENDED AND RESTATED CREDIT AGREEMENT





                                FEBRUARY 17, 2000






<PAGE>   2
                                TABLE OF CONTENTS
<TABLE>
<CAPTION>

                                                                                                      PAGE


<S>     <C>       <C>      <C>                                                                      <C>
Article I         General Terms.........................................................................2

         Section 1.1        Terms Defined Above.........................................................2

         Section 1.2        Certain Definitions.........................................................2

         Section 1.3        Credit Agreement Definitions................................................3

Article II        The Guaranty..........................................................................3

         Section 2.1        Liabilities Guaranteed......................................................3

         Section 2.2        Nature of Guaranty..........................................................3

         Section 2.3        Agent's Rights..............................................................4

         Section 2.4        Guarantor's Waivers.........................................................4

         Section 2.5        Maturity of Liabilities; Payment............................................5

         Section 2.6        Agent's Expenses............................................................5

         Section 2.7        Liability...................................................................5

         Section 2.8        Events and Circumstances Not Reducing or Discharging
                            Guarantor's Obligations.....................................................5

Article III       Representations, Warranties And Covenants.............................................7

         Section 3.1        By Guarantor................................................................7

         Section 3.2        No Representation by Lenders...............................................11

Article IV        Subordination Of Indebtedness........................................................11

         Section 4.1        Subordination of All Guarantor Claims......................................11

         Section 4.2        Claims in Bankruptcy.......................................................12

         Section 4.3        Payments Held in Trust.....................................................12

         Section 4.4        Liens Subordinate..........................................................12

         Section 4.5        Guarantor's Enforcement Rights.............................................12

Article V         Certain Additional Covenants.........................................................13

         Section 5.1        Affirmative Covenants......................................................13

         Section 5.2        Negative Covenants.........................................................13

Article VI        Miscellaneous........................................................................19

         Section 6.1        Successors and Assigns.....................................................19

         Section 6.2        Notices....................................................................19

         Section 6.3        Business and Financial Information.........................................19

         Section 6.4        Construction...............................................................19

         Section 6.5        Invalidity.................................................................20

         Section 6.6        ENTIRE AGREEMENT...........................................................20
</TABLE>

                                        i
<PAGE>   3




                     AMENDED AND RESTATED GUARANTY AGREEMENT

         THIS AMENDED AND RESTATED GUARANTY AGREEMENT by BRIGHAM EXPLORATION
COMPANY (hereinafter called "Guarantor"), is in favor of BANK OF MONTREAL, as
agent (the "Agent") for the lenders (the "Lenders") that are or become parties
to the Credit Agreement defined below, and the Lenders (as defined below).

                              W I T N E S S E T H:


         WHEREAS, BRIGHAM OIL & GAS, L.P., a Delaware limited partnership
(hereinafter called "Borrower"), Bank of Montreal, as agent and Societe
Generale, Southwest Agency (the "Prior Lenders") entered into that certain
Credit Agreement dated as of January 26, 1998, as amended (the "Prior Credit
Agreement") pursuant to which the Prior Lenders provided to the Borrower loans
and extensions of credit, which loans and extensions of credit are evidenced by
those certain promissory notes from the Borrower in the aggregate principal
amount of $75,000,000 (the "Prior Notes"); and

         WHEREAS, one of the terms and conditions stated in the Prior Credit
Agreement for the making of the loans described therein was the execution of
that certain Guaranty Agreement dated as of January 26, 1998 in favor of the
Prior Lenders (as amended the "Guaranty Agreement"); and

         WHEREAS, by Partial Assignment of Notes of even date herewith Shell
Capital Inc. ("SCI") has acquired a portion of the Prior Notes (the "Acquired
Notes Interest") and security for the payment of the Acquired Notes Interest and
the performance of the Borrower's obligations under the Prior Credit Agreement;
and

         WHEREAS, the Prior Lenders and SCI together with their successors and
assigns (collectively, the "Lenders") have agreed to provide senior secured debt
in the amount of up to $75,000,000 consisting of a rearrangement of the Prior
Notes and advances to the Borrower, and the Borrower, the Agent and the Lenders
of even date herewith are entering into that certain Amended and Restated Credit
Agreement (the "Credit Agreement") which amends and restates in its entirety the
Prior Credit Agreement and Prior Notes;

         NOW, THEREFORE, (i) in order to comply with the terms and conditions of
the Credit Agreement, (ii) to induce the Lenders, at any time or from time to
time, to loan monies, with or without security to or for the account of Borrower
in accordance with the terms of the Credit Agreement, (iii) at the special
insistence and request of the Lenders, and (iv) for other good and valuable
consideration, the receipt and sufficiency of which is hereby acknowledged,
Guarantor hereby agrees to amend and restate the Guaranty Agreement as follows:




                                       1
<PAGE>   4


                                   ARTICLE I


                                  General Terms

         Section 1.1 Terms Defined Above. As used in this Guaranty Agreement,
the terms "Agent," "Borrower," "Credit Agreement," "Guaranty Agreement,"
"Lenders," "Prior Credit Agreement," "Prior Lenders," "Prior Notes" and
"Acquired Notes Interest" shall have the meanings indicated above.

         Section 1.2 Certain Definitions. As used in this Guaranty Agreement,
the following terms shall have the following meanings, unless the context
otherwise requires:

                  "Guarantor Claims" shall have the meaning indicated in Section
         4.1 hereof.

                  "Guaranty Agreement" shall mean this Amended and Restated
         Guaranty Agreement, as the same may from time to time be amended or
         supplemented.

                  "Indenture" shall mean that certain Indenture dated as of
         August 20, 1998, as from time to time amended, between the Guarantor,
         as issuer of the Subordinated Debt, and Chase Bank of Texas, National
         Association, as trustee.

                  "Liabilities" shall mean:

                  (a)      any and all indebtedness, obligations and liabilities
now or hereafter incurred by the Borrower pursuant to the Credit Agreement,
including without limitation, the unpaid fees and principal of and interest on
the Notes;

                  (b)      payment of and performance of any and all present or
future obligations of Borrower to a Lender according to the terms of any Hedging
Agreement now or hereafter arising between (i) Borrower and Bank of Montreal and
its successors or assigns (a "BMO Hedge Party") and Soc-Gen and its successors
or assigns (a "Soc-Gen Hedge Party") entered into while such BMO Hedge Party or
such Soc-Gen Hedge Party is a Lender; and (ii) Borrower and SCI and its
successors or assigns (with Loans or Commitments of $20 million or more) or any
Affiliate of SCI (SCI and any Affiliate of SCI a "SCI Hedge Party") entered into
while such SCI Hedge Party or Fathom Energy Capital I, L.L.C, is a Lender. For
purposes of this clause (b), the parties intend that any Hedging Agreement
entered into between the Borrower and a Lender or in the case of SCI, a SCI
Hedge Party, while such Person was a party to the Credit Agreement shall
continue to be secured even after the time such Person ceases to be a party to
the Credit Agreement as a Lender.

                  (c) any additional "Indebtedness", as defined in the Credit
Agreement, and




                                       2
<PAGE>   5


                  (d)      all renewals, rearrangements, increases, extensions
for any period, amendments or supplement in whole or in part of the Notes or any
documents evidencing the above.

                  "Securities Purchase Agreement" shall mean that certain
         Securities Purchase Agreement dated as of August 20, 1998 among the
         Guarantor, Enron Capital & Trade Resources Corp., and Joint Energy
         Development Investments II Limited Partnership regarding $50,000,000
         Senior Subordinated Secured Notes due 2003.

                  "Subordination Agreement" shall mean that certain
         Intercreditor and Subordination Agreement dated August 20, 1998, as
         from time to time amended, among Enron Capital and Trade Resources
         Corp., Joint Energy Development Investments II Limited Partnership, and
         Bank of Montreal.

                  "Subordinated Debt" shall mean the Debt in the principal
         amount not to exceed $40,000,000 (plus interest paid in kind through
         December 31, 2000 pursuant to Section 9.02 of the Indenture or
         otherwise satisfied through payment of the Term ORRI) of Guarantor
         incurred under the Indenture and expressly subordinated to the
         Indebtedness pursuant to the Subordination Agreement.

                  "Subordinated Guarantees" shall mean the Guarantees permitted
         under Section 5.2(a)(7).

                  "Subsidiary Guarantor" shall mean a Subsidiary of the
         Guarantor which is itself a "Guarantor" under the Credit Agreement.

         Section 1.3 Credit Agreement Definitions. Unless otherwise defined
herein, all terms beginning with a capital letter which are defined in the
Credit Agreement shall have the same meanings herein as therein.

                                   ARTICLE II

                                  The Guaranty

         Section 2.1 Liabilities Guaranteed. Guarantor hereby irrevocably and
unconditionally guarantees the prompt payment at maturity of the Liabilities.

         Section 2.2 Nature of Guaranty. This Guaranty Agreement is an absolute,
irrevocable, completed and continuing guaranty of payment and not a guaranty of
collection, and no notice of the Liabilities or any extension of credit already
or hereafter contracted by or extended to Borrower need be given to Guarantor.
This Guaranty Agreement may not be revoked by Guarantor and shall continue to be
effective with respect to debt under the Liabilities arising or created after
any attempted revocation by Guarantor and shall remain in full force and effect
until the Liabilities are paid in full and the Commitments are terminated,
notwithstanding that from time to time prior thereto no Liabilities may be
outstanding. Borrower and the Lenders may modify, alter,




                                       3
<PAGE>   6


rearrange, extend for any period and/or renew from time to time, the
Liabilities, and the Lenders may waive any Default or Events of Default without
notice to the Guarantor and in such event Guarantor will remain fully bound
hereunder on the Liabilities. This Guaranty Agreement shall continue to be
effective or be reinstated, as the case may be, if at any time any payment of
the Liabilities is rescinded or must otherwise be returned by any of the Lenders
upon the insolvency, bankruptcy or reorganization of Borrower or otherwise, all
as though such payment had not been made. This Guaranty Agreement may be
enforced by the Agent and any subsequent holder of any of the Liabilities and
shall not be discharged by the assignment or negotiation of all or part of the
Liabilities. Guarantor hereby expressly waives presentment, demand, notice of
non-payment, protest and notice of protest and dishonor, notice of Default or
Event of Default, and also notice of acceptance of this Guaranty Agreement,
acceptance on the part of the Lenders being conclusively presumed by the
Lenders' request for this Guaranty Agreement and delivery of the same to the
Agent.

         Section 2.3 Agent's Rights. Guarantor authorizes the Agent, without
notice or demand and without affecting Guarantor's liability hereunder, to take
and hold security for the payment of this Guaranty Agreement and/or the
Liabilities, and exchange, enforce, waive and release any such security; and to
apply such security and direct the order or manner of sale thereof as the Agent
in its discretion may determine; and to obtain a guaranty of the Liabilities
from any one or more Persons and at any time or times to enforce, waive,
rearrange, modify, limit or release any of such other Persons from their
obligations under such guaranties.

         Section 2.4 Guarantor's Waivers.


                  (a)      General. Guarantor waives any right to require any of
the Lenders to (i) proceed against Borrower or any other person liable on the
Liabilities, (ii) enforce any of their rights against any other guarantor of the
Liabilities (iii) proceed or enforce any of their rights against or exhaust any
security given to secure the Liabilities (iv) have Borrower joined with
Guarantor in any suit arising out of this Guaranty Agreement and/or the
Liabilities, or (v) pursue any other remedy in the Lenders' powers whatsoever.
The Lenders shall not be required to mitigate damages or take any action to
reduce, collect or enforce the Liabilities. Guarantor waives any defense arising
by reason of any disability, lack of corporate authority or power, or other
defense of Borrower or any other guarantor of the Liabilities, and shall remain
liable hereon regardless of whether Borrower or any other guarantor be found not
liable thereon for any reason. Whether and when to exercise any of the remedies
of the Lenders under any of the Loan Documents shall be in the sole and absolute
discretion of the Agent, and no delay by the Agent in enforcing any remedy,
including delay in conducting a foreclosure sale, shall be a defense to the
Guarantor's liability under this Guaranty Agreement.

                  (b)      Subrogation. Until the Liabilities have been paid in
full, the Guarantor waives all rights of subrogation or reimbursement against
the Borrower, whether arising by contract or operation of law (including,
without limitation, any such right arising under any federal or state bankruptcy
or insolvency laws) and waives any




                                       4
<PAGE>   7


right to enforce any remedy which the Lenders now have or may hereafter have
against the Borrower, and waives any benefit or any right to participate in any
security now or hereafter held by the Agent or any Lender.

         Section 2.5 Maturity of Liabilities; Payment. Guarantor agrees that if
the maturity of any of the Liabilities is accelerated by bankruptcy or
otherwise, such maturity shall also be deemed accelerated for the purpose of
this Guaranty Agreement without demand or notice to Guarantor. Guarantor will,
forthwith upon notice from the Agent, pay to the Agent the amount due and unpaid
by Borrower and guaranteed hereby. The failure of the Agent to give this notice
shall not in any way release Guarantor hereunder.

         Section 2.6 Agent's Expenses. If Guarantor fails to pay the Liabilities
after notice from the Agent of Borrower's failure to pay any Liabilities at
maturity, and if the Agent obtains the services of an attorney for collection of
amounts owing by Guarantor hereunder, or obtaining advice of counsel in respect
of any of their rights under this Guaranty Agreement, or if suit is filed to
enforce this Guaranty Agreement, or if proceedings are had in any bankruptcy,
probate, receivership or other judicial proceedings for the establishment or
collection of any amount owing by Guarantor hereunder, or if any amount owing by
Guarantor hereunder is collected through such proceedings, Guarantor agrees to
pay to the Agent the Agent's reasonable attorneys' fees.

         Section 2.7 Liability. It is expressly agreed that the liability of the
Guarantor for the payment of the Liabilities guaranteed hereby shall be primary
and not secondary.

         Section 2.8 Events and Circumstances Not Reducing or Discharging
Guarantor's Obligations. Guarantor hereby consents and agrees to each of the
following to the fullest extent permitted by law, and agrees that Guarantor's
obligations under this Guaranty Agreement shall not be released, diminished,
impaired, reduced or adversely affected by any of the following, and waives any
rights (including without limitation rights to notice) which Guarantor might
otherwise have as a result of or in connection with any of the following:

                  (a)      Modifications, etc. Any renewal, extension,
modification, increase, decrease, alteration or rearrangement of all or any part
of the Liabilities, or of the Notes, or the Credit Agreement or any instrument
executed in connection therewith, or any contract or understanding between
Borrower and any of the Lenders, or any other Person, pertaining to the
Liabilities;

                  (b)      Adjustment, etc. Any adjustment, indulgence,
forbearance or compromise that might be granted or given by any of the Lenders
to Borrower or Guarantor or any Person liable on the Liabilities;

                  (c)      Condition of Borrower or Guarantor. The insolvency,
bankruptcy arrangement, adjustment, composition, liquidation, disability,
dissolution, death or lack of power of Borrower or Guarantor or any other Person
at any time liable




                                       5
<PAGE>   8


for the payment of all or part of the Liabilities; or any dissolution of
Borrower or Guarantor, or any sale, lease or transfer of any or all of the
assets of Borrower or Guarantor, or any changes in the shareholders, partners,
or members of Borrower or Guarantor; or any reorganization of Borrower or
Guarantor;

                  (d)      Invalidity of Liabilities. The invalidity, illegality
or unenforceability of all or any part of the Liabilities, or any document or
agreement executed in connection with the Liabilities, for any reason
whatsoever, including without limitation the fact that the Liabilities, or any
part thereof, exceed the amount permitted by law, the act of creating the
Liabilities or any part thereof is ultra vires, the officers or representatives
executing the documents or otherwise creating the Liabilities acted in excess of
their authority, the Liabilities violate applicable usury laws, the Borrower has
valid defenses, claims or offsets (whether at law, in equity or by agreement)
which render the Liabilities wholly or partially uncollectible from Borrower,
the creation, performance or repayment of the Liabilities (or the execution,
delivery and performance of any document or instrument representing part of the
Liabilities or executed in connection with the Liabilities, or given to secure
the repayment of the Liabilities) is illegal, uncollectible, legally impossible
or unenforceable, or the Credit Agreement or other documents or instruments
pertaining to the Liabilities have been forged or otherwise are irregular or not
genuine or authentic;

                  (e)      Release of Obligors. Any full or partial release of
the liability of Borrower on the Liabilities or any part thereof, of any
co-guarantors, or any other Person now or hereafter liable, whether directly or
indirectly, jointly, severally, or jointly and severally, to pay, perform,
guarantee or assure the payment of the Liabilities or any part thereof, it being
recognized, acknowledged and agreed by Guarantor that Guarantor may be required
to pay the Liabilities in full without assistance or support of any other
Person, and Guarantor has not been induced to enter into this Guaranty Agreement
on the basis of a contemplation, belief, understanding or agreement that other
parties other than the Borrower will be liable to perform the Liabilities, or
the Lenders will look to other parties to perform the Liabilities.

                  (f)      Other Security. The taking or accepting of any other
security, collateral or guaranty, or other assurance of payment, for all or any
part of the Liabilities;

                  (g)      Release of Collateral, etc. Any release, surrender,
exchange, subordination, deterioration, waste, loss or impairment (including
without limitation negligent, willful, unreasonable or unjustifiable impairment)
of any collateral, property or security, at any time existing in connection
with, or assuring or securing payment of, all or any part of the Liabilities;

                  (h)      Care and Diligence. The failure of the Lenders or any
other Person to exercise diligence or reasonable care in the preservation,
protection, enforcement, sale or other handling or treatment of all or any part
of such collateral, property or security;


                                       6
<PAGE>   9


                  (i)      Status of Liens. The fact that any collateral,
security, security interest or lien contemplated or intended to be given,
created or granted as security for the repayment of the Liabilities shall not be
properly perfected or created, or shall prove to be unenforceable or subordinate
to any other security interest or lien, it being recognized and agreed by
Guarantor that Guarantor is not entering into this Guaranty Agreement in
reliance on, or in contemplation of the benefits of, the validity,
enforceability, collectibility or value of any of the collateral for the
Liabilities;

                  (j)      Payments Rescinded. Any payment by Borrower to the
Lenders is held to constitute a preference under the bankruptcy laws, or for any
reason the Lenders are required to refund such payment or pay such amount to
Borrower or someone else; or

                  (k)      Other Actions Taken or Omitted. Any other action
taken or omitted to be taken with respect to the Credit Agreement, the
Liabilities, or the security and collateral therefor, whether or not such action
or omission prejudices Guarantor or increases the likelihood that Guarantor will
be required to pay the Liabilities pursuant to the terms hereof; it being the
unambiguous and unequivocal intention of Guarantor that Guarantor shall be
obligated to pay the Liabilities when due, notwithstanding any occurrence,
circumstance, event, action, or omission whatsoever, whether contemplated or
uncontemplated, and whether or not otherwise or particularly described herein,
except for the full and final payment and satisfaction of the Liabilities.

                                  ARTICLE III

                    Representations, Warranties And Covenants

         Section 3.1 By Guarantor. In order to induce the Lenders to accept this
Guaranty Agreement, Guarantor represents and warrants to the Lenders (which
representations and warranties will survive the creation of the Liabilities and
any extension of credit thereunder) that:

                  (a)      Benefit to Guarantor. Guarantor's guaranty pursuant
to this Guaranty Agreement reasonably may be expected to benefit, directly or
indirectly, Guarantor.

                  (b)      Corporate Existence. Guarantor is a corporation duly
organized, legally existing and in good standing under the laws of the State of
Delaware and is duly qualified in all jurisdictions wherein the property owned
or the business transacted by it makes such qualification necessary.

                  (c)      Corporate Power and Authorization. Guarantor is duly
authorized and empowered to execute, deliver and perform this Guaranty Agreement
and all corporate action on Guarantor's part requisite for the due execution,
delivery and performance of this Guaranty Agreement has been duly and
effectively taken.

                  (d)      Binding Obligations. This Guaranty Agreement
constitutes valid and binding obligations of Guarantor, enforceable in
accordance with its terms



                                       7
<PAGE>   10


(except that enforcement may be subject to any applicable bankruptcy, insolvency
or similar laws generally affecting the enforcement of creditors' rights) or by
general principles of equity.

                  (e)      No Consent. Guarantor's execution, delivery and
performance of this Guaranty Agreement does not require the consent or approval
of any other Person, including without limitation any regulatory authority or
governmental body of the United States or any state thereof or any political
subdivision of the United States or any state thereof.

                  (f)      Solvency. The Guarantor hereby represents that (i) it
is not insolvent as of the date hereof and will not be rendered insolvent as a
result of this Guaranty Agreement, (ii) it is not engaged in business or a
transaction, or about to engage in a business or a transaction, for which any
property or assets remaining with such Guarantor is unreasonably small capital,
and (iii) it does not intend to incur, or believe it will incur, debts that will
be beyond its ability to pay as such debts mature.

                  (g)      Financial Condition. The audited consolidated balance
sheet of the Guarantor and its Consolidated Subsidiaries as at December 31, 1998
and the related consolidated statement of income, stockholders' equity and cash
flow of the Guarantor and its Consolidated Subsidiaries for the fiscal year
ended on said date, with the opinion thereon of Price Waterhouse heretofore
furnished to each of the Lenders and the unaudited consolidated balance sheet of
the Guarantor and its Consolidated Subsidiaries as at September 30, 1999 and
their related consolidated statements of income, stockholders' equity and cash
flow of the Guarantor and its Consolidated Subsidiaries for the nine-month
period ended on such date heretofore furnished to the Agent, are complete and
correct and fairly present the consolidated financial condition of the Guarantor
and its Consolidated Subsidiaries as at said dates and the results of its
operations for the fiscal year and the nine-month period on said dates, all in
accordance with GAAP, as applied on a consistent basis (subject, in the case of
the interim financial statements, to normal year-end adjustments). Neither the
Guarantor nor any of its Subsidiaries has on the Closing Date any material Debt,
Trade Payables, contingent liabilities, liabilities for taxes, unusual forward
or long-term commitments or unrealized or anticipated losses from any
unfavorable commitments, except as referred to or reflected or provided for in
the Financial Statements or in Schedule 7.02 of the Credit Agreement. Since
December 31, 1998, there has been no change or event having a Material Adverse
Effect. Since the date of the Financial Statements, neither the business nor the
Properties of the Guarantor and its Consolidated Subsidiaries, taken as a whole,
have been materially and adversely affected as a result of any fire, explosion,
earthquake, flood, drought, windstorm, accident, strike or other labor
disturbance, embargo, requisition or taking of Property or cancellation of
contracts, permits or concessions by any Governmental Authority, riot,
activities of armed forces or acts of God or of any public enemy.

                  (h)      Litigation. Except as disclosed to the Lenders in
Schedule 7.03 of the Credit Agreement, at the Closing Date there is no
litigation, legal, administrative or arbitral proceeding, investigation or other
action of any nature pending



                                       8
<PAGE>   11


or, to the knowledge of the Guarantor threatened against or affecting the
Guarantor or any of its Subsidiaries which both (a) involves the possibility of
any judgment or liability against the Guarantor or any of its Subsidiaries not
fully covered by insurance (except for normal deductibles), and (b) would be
more likely than not to have a Material Adverse Effect.

                  (i)      No Breach. Neither the execution and delivery of this
Guaranty Agreement, nor compliance with the terms and provisions hereof will
conflict with or result in a breach of, or require any consent which has not
been obtained as of the Closing Date under, the respective charter or by-laws of
the Guarantor or any of its Subsidiaries or any Governmental Requirement or any
material agreement or instrument to which the Guarantor or any of its
Subsidiaries is a party or by which it is bound or to which it or its Properties
are subject, or constitute a default under any such agreement or instrument, or
result in the creation or imposition of any Lien upon any of the material
revenues or assets of the Guarantor or any of its Subsidiaries pursuant to the
terms of any such agreement or instrument other than the Liens created by the
Loan Documents.

                  (j)      ERISA.

                           (1)      The Guarantor, its Subsidiaries and each
                  ERISA Affiliate have complied in all material respects with
                  ERISA and, where applicable, the Code regarding each Plan.

                           (2)      Each Plan is, and has been, maintained in
                  substantial compliance with ERISA and, where applicable, the
                  Code.

                           (3)      No act, omission or transaction has occurred
                  which could result in imposition on the Guarantor, any of its
                  Subsidiaries or any ERISA Affiliate (whether directly or
                  indirectly) of an amount of $100,000 or more as (i) either a
                  civil penalty assessed pursuant to section 502(c), (i) or (l)
                  of ERISA or a tax imposed pursuant to Chapter 43 of Subtitle D
                  of the Code or (ii) breach of fiduciary duty liability damages
                  under section 409 of ERISA.

                           (4)      No Plan (other than a defined contribution
                  plan) or any trust created under any such Plan has been
                  terminated since September 2, 1974. No liability to the PBGC
                  in excess of $100,000 (other than for the payment of current
                  premiums which are not past due) by the Guarantor, any of its
                  Subsidiaries or any ERISA Affiliate has been or is expected by
                  the Guarantor, any of its Subsidiaries or any ERISA Affiliate
                  to be incurred with respect to any Plan. No ERISA Event with
                  respect to any Plan has occurred which could reasonably
                  expected to result in liabilities of $100,000 or more.


                                       9
<PAGE>   12


                           (5)      Full payment when due has been made of all
                  amounts which the Guarantor, any of its Subsidiaries or any
                  ERISA Affiliate is required under the terms of each Plan or
                  applicable law to have paid as contributions to such Plan, and
                  no accumulated funding deficiency in an amount of $100,000 or
                  more (as defined in section 302 of ERISA and section 412 of
                  the Code), whether or not waived, exists with respect to any
                  Plan.

                           (6)      The actuarial present value of the benefit
                  liabilities under each Plan which is subject to Title IV of
                  ERISA does not, as of the end of the Guarantor's most recently
                  ended fiscal year, exceed the current value of the assets
                  (computed on a plan termination basis in accordance with Title
                  IV of ERISA) of such Plan allocable to such benefit
                  liabilities by $100,000 or more. The term "actuarial present
                  value of the benefit liabilities" shall have the meaning
                  specified in section 4041 of ERISA.

                           (7)      None of the Guarantor, any of its
                  Subsidiaries or any ERISA Affiliate sponsors, maintains, or
                  contributes to an employee welfare benefit plan, as defined in
                  section 3(1) of ERISA, including, without limitation, any such
                  plan maintained to provide benefits to former employees of
                  such entities, that may not be terminated by the Guarantor,
                  any of its Subsidiaries or any ERISA Affiliate in its sole
                  discretion at any time without any material liability.

                           (8)      None of the Guarantor, any of its
                  Subsidiaries or any ERISA Affiliate sponsors, maintains or
                  contributes to, or has at any time in the preceding six
                  calendar years, sponsored, maintained or contributed to, any
                  Multiemployer Plan.

                           (9)      None of the Guarantor, any of its
                  Subsidiaries or any ERISA Affiliate is required to provide
                  security under section 401(a)(29) of the Code due to a Plan
                  amendment that results in an increase in current liability for
                  the Plan.

                  (k)      Taxes. Except as set out in Schedule 7.09 of the
Credit Agreement, each of the Guarantor and its Subsidiaries has filed all
United States Federal income tax returns and all other tax returns which are
required to be filed by it and has paid all material taxes due pursuant to such
returns or pursuant to any assessment received by the Guarantor or any of its
Subsidiaries, except for any taxes which are being contested in good faith and
by proper proceedings and against which adequate reserves are being maintained.
The charges, accruals and reserves on the books of the Guarantor and its
Subsidiaries in respect of taxes and other governmental charges are, in the
opinion of the Guarantor, adequate. No tax lien has been filed and, to the
knowledge of the Guarantor, no claim is being asserted with respect to any such
tax, fee or other charge,



                                       10
<PAGE>   13


except for any taxes, fees or other charges which are being contested in good
faith and by proper proceedings and against which adequate reserves are being
maintained.

                  (l)      Title to Ownership Interest in General Partner and
Limited Partners of Borrower. The Guarantor has good and unencumbered title to
all of the capital stock of the General Partner of the Borrower and, directly or
indirectly, all of the ownership interests in the limited partners of the
Borrower, except for liens and security interests securing the Liabilities or as
permitted under Section 5.2(b)(4).

                  (m)      Investment Company Act. Neither the Guarantor nor any
of its Subsidiaries is an "investment company" or a company "controlled" by an
"investment company," within the meaning of the Investment Company Act of 1940,
as amended.

                  (n)      Public Utility Holding Company Act. Neither the
Guarantor nor any of its Subsidiaries is a "holding company," or a "subsidiary
company" of a "holding company," or an "affiliate" of a "holding company" or of
a "subsidiary company" of a "holding company," or a "public utility" within the
meaning of the Public Utility Holding Company Act of 1935, as amended.

                  (o)      Subsidiaries. Except as set forth on Schedule 1
hereto or as permitted by Section 9.16 of the Credit Agreement, the Guarantor
has no Subsidiaries.

                  (p)      Compliance with the Law. Neither the Guarantor nor
any of its Subsidiaries has violated any Governmental Requirement or failed to
obtain any license, permit, franchise or other governmental authorization
necessary for the ownership of any of its Properties or the conduct of its
business, which violation or failure would have (in the event such violation or
failure were asserted by any Person through appropriate action) a Material
Adverse Effect.

         Section 3.2 No Representation by Lenders. Neither the Lenders nor any
other Person has made any representation, warranty or statement to the Guarantor
in order to induce the Guarantor to execute this Guaranty Agreement.

                                   ARTICLE IV

                          Subordination Of Indebtedness

         Section 4.1 Subordination of All Guarantor Claims. As used herein, the
term "Guarantor Claims" shall mean all debts and liabilities of Borrower or any
Subsidiary of the Borrower to Guarantor, whether such debts and liabilities now
exist or are hereafter incurred or arise, or whether the obligation of Borrower
or such Subsidiary thereon be direct, contingent, primary, secondary, several,
joint and several, or otherwise, and irrespective of whether such debts or
liabilities be evidenced by note, contract, open account, or otherwise, and
irrespective of the person or persons in whose favor such debts or liabilities
may, at their inception, have been, or may hereafter be created, or the manner
in which they have been or may hereafter be acquired by Guarantor. The Guarantor
Claims shall include without limitation all rights and claims of Guarantor




                                       11
<PAGE>   14


against Borrower or any Subsidiary of the Borrower arising as a result of
subrogation or otherwise as a result of Guarantor's payment of all or a portion
of the Liabilities. Until the Liabilities shall be paid and satisfied in full
and Guarantor shall have performed all of its obligations hereunder, Guarantor
shall not receive or collect, directly or indirectly, from Borrower or any
Subsidiary of the Borrower or any other party any amount upon the Guarantor
Claims.

         Section 4.2 Claims in Bankruptcy. In the event of receivership,
bankruptcy, reorganization, arrangement, debtor's relief, or other insolvency
proceedings involving Borrower or any Subsidiary of the Borrower, as debtor, the
Lenders shall have the right to prove their claim in any proceeding, so as to
establish their rights hereunder and receive directly from the receiver, trustee
or other court custodian, dividends and payments which would otherwise be
payable upon Guarantor Claims. Guarantor hereby assigns such dividends and
payments to the Lenders. Should the Agent or any Lender receive, for application
upon the Liabilities, any such dividend or payment which is otherwise payable to
Guarantor, and which, as between Borrower or any Subsidiary of the Borrower and
Guarantor, shall constitute a credit upon the Guarantor Claims, then upon
payment in full of the Liabilities, Guarantor shall become subrogated to the
rights of the Lenders to the extent that such payments to the Lenders on the
Guarantor Claims have contributed toward the liquidation of the Liabilities, and
such subrogation shall be with respect to that proportion of the Liabilities
which would have been unpaid if the Agent or a Lender had not received dividends
or payments upon the Guarantor Claims.

         Section 4.3 Payments Held in Trust. In the event that notwithstanding
Sections 4.1 and 4.2 above, Guarantor should receive any funds, payments, claims
or distributions which is prohibited by such Sections, Guarantor agrees to hold
in trust for the Lenders an amount equal to the amount of all funds, payments,
claims or distributions so received, and agrees that it shall have absolutely no
dominion over the amount of such funds, payments, claims or distributions except
to pay them promptly to the Agent, and Guarantor covenants promptly to pay the
same to the Agent.

         Section 4.4 Liens Subordinate. Guarantor agrees that any liens,
security interests, judgment liens, charges or other encumbrances upon
Borrower's or any Subsidiary of the Borrower's assets securing payment of the
Guarantor Claims shall be and remain inferior and subordinate to any liens,
security interests, judgment liens, charges or other encumbrances upon
Borrower's or any Subsidiary of the Borrower's assets securing payment of the
Liabilities, regardless of whether such encumbrances in favor of Guarantor, the
Agent or the Lenders presently exist or are hereafter created or attach.

         Section 4.5 Guarantor's Enforcement Rights. Without the prior written
consent of the Lenders, Guarantor shall not (a) exercise or enforce any
creditor's right it may have against the Borrower or any Subsidiary of the
Borrower, or (b) foreclose, repossess, sequester or otherwise take steps or
institute any action or proceeding (judicial or otherwise, including without
limitation the commencement of or joinder in any liquidation, bankruptcy,
rearrangement, debtor's relief or insolvency proceeding) to enforce any lien,
mortgages, deeds of trust, security interest, collateral rights, judgments


                                       12
<PAGE>   15

or other encumbrances on assets of Borrower or any Subsidiary of the Borrower
held by Guarantor.

                                    ARTICLE V

                          Certain Additional Covenants

         Section 5.1 Affirmative Covenants.

         Financial Statements. The Guarantor shall cause the Borrower to deliver
as and when required, the financial statements and other information called for
in Section 8.01 of the Credit Agreement and Guarantor shall:

                  (i)      Notice of Default. Promptly after the Guarantor knows
         that any default in any covenant herein has occurred, the Guarantor
         will give notice of such default to the Agent, describing the same in
         reasonable detail and the action the Guarantor proposes to take with
         respect thereto.

                  (ii)     Payment of Trade Payables. The Guarantor will pay and
         cause all of its Subsidiaries to pay all of their respective Trade
         Payables now or hereafter incurred within 60 days of the invoice or
         billing date, unless subject to legal offset or unless being contested
         in good faith by appropriate proceedings and reserves adequate under
         GAAP shall have been established therefor.

         Section 5.2 Negative Covenants. The Guarantor covenants and agrees
that, so long as any of the Commitments are in effect and until payment in full
of the Liabilities hereunder, all interest thereon and all other amounts payable
by the Guarantor hereunder, without the prior written consent of the Lenders:

                  (a)      Debt. The Guarantor will not and will not permit any
of its Subsidiaries to incur, create, assume or suffer to exist any Debt,
except:

                           (1)      the Notes or other Indebtedness arising
                  under the Loan Documents or any guaranty of or suretyship
                  arrangement for the Notes or other Indebtedness arising under
                  the Loan Documents;

                           (2)      Debt existing on the Closing Date which is
                  reflected in the Financial Statements or is disclosed in
                  Schedule 9.01 to the Credit Agreement, and any renewals or
                  extensions (but not increases) thereof;

                           (3)      Debt permitted under the Credit Agreement;

                           (4)      Debt owing to the Borrower, the Guarantor or
                  a Subsidiary Guarantor which (other than Debt owing to the
                  Borrower) is subordinated to the Indebtedness as provided in
                  the


                                       13
<PAGE>   16


                  Guaranty Agreement of the Guarantor or such Subsidiary
                  Guarantor;

                           (5)      Debt of the Guarantor or any of its
                  Subsidiaries which is not described in Sections 5.2(a)(1)
                  through (4) above and which together with all Debt of the
                  Borrower allowed under Section 9.01(h) of the Credit
                  Agreement, does not exceed $1,000,000 at any one time
                  outstanding;

                           (6)      the Subordinated Debt; and

                           (7)      Guarantees by Subsidiaries of the Guarantor
                  (which also are obligated upon or otherwise guarantee the
                  Liabilities pursuant to documents in form and substance
                  satisfactory to the Agent) which guarantee the Subordinated
                  Debt permitted under Section 5.2(a)(6) above, which Guarantees
                  are subordinated consistent with the Subordination Agreement
                  and otherwise are in form and substance satisfactory to the
                  Agent consistent with the Subordination Agreement.

                  (b)      Liens. The Guarantor will not and will not permit any
of its Subsidiaries to create, incur, assume or permit to exist any Lien on any
of its Properties (now owned or hereafter acquired), except:

                           (1)      Liens securing the payment of any
                  Indebtedness;

                           (2)      Excepted Liens;

                           (3)      Liens incurred by the Borrower and the
                  Borrower's Subsidiaries as permitted under the Credit
                  Agreement;

                           (4)      Liens securing the Subordinated Debt or the
                  Subordinated Guarantees on Properties upon which prior Liens
                  have been granted to secure the Liabilities pursuant to
                  documents in form and substance satisfactory to the Agent,
                  provided that such Liens (i) are subordinated to the Liens in
                  favor of the Lenders and otherwise are in form and substance
                  satisfactory to the Agent consistent with the Subordination
                  Agreement and (ii) do not directly or indirectly secure any
                  Hedging Agreements; and

                           (5)      the Term ORRI.

                  (c)      Investments, Loans and Advances. The Guarantor will
not and will not permit any of its Subsidiaries to remain outstanding any loans
or advances to or investments in any Person, except that the foregoing
restriction shall not apply to:

                           (1)      investments, loans or advances by the
                  Guarantor or a Subsidiary Guarantor (other than a Subsidiary
                  of the Borrower)



                                       14
<PAGE>   17



                  in or to the Borrower, the Guarantor or a Subsidiary
                  Guarantor; and

                           (2)      any other investments, loans and advances by
                  the Borrower or a Subsidiary of the Borrower as permitted
                  under Section 9.03 of the Credit Agreement.

                  (d)      Dividends, Distributions and Redemptions. The
Guarantor will not declare or pay any dividend, purchase, redeem or otherwise
acquire for value any of its stock now or hereafter outstanding, return any
capital to its stockholders or make any distribution of its assets to its
stockholders.

                  (e)      Sales and Leasebacks. The Guarantor will not and will
not permit any of its Subsidiaries to enter into any arrangement, directly or
indirectly, with any Person whereby such Person shall sell or transfer any of
its Property, whether now owned or hereafter acquired, and whereby such Person
shall then or thereafter rent or lease as lessee such Property or any part
thereof or other Property which such Person intends to use for substantially the
same purpose or purposes as the Property sold or transferred.

                  (f)      Nature of Business. The Guarantor will not allow any
material change to be made in the character of its business as presently
conducted.

                  (g)      Limitation on Leases. The Guarantor will not and will
not permit any of its Subsidiaries to create, incur, assume or suffer to exist
any obligation for the payment of rent or hire of Property of any kind
whatsoever (real or personal including capital leases but excluding leases of
Hydrocarbon Interests and the equipment used thereon), under leases or lease
agreements which would cause the aggregate amount of all payments made by the
Guarantor and its Subsidiaries pursuant to all such leases or lease agreements
to exceed $2,000,000 in any period of twelve consecutive calendar months during
the life of such leases.

                  (h)      Mergers, Etc. The Guarantor will not and will not
permit any of its Subsidiaries to merge into or with or consolidate with any
other Person or sell, lease or otherwise dispose of (whether in one transaction
or in a series of transactions) all or substantially all of its Property or
assets to any other Person unless the Guarantor, the Borrower or any Subsidiary
Guarantor whose Guaranty Agreement is in full force and effect is the surviving
entity and no Default exists or will be created thereby.

                  (i)      ERISA Compliance. The Guarantor will not and will not
permit any of its Subsidiaries to at any time:

                           (1)      Engage in, or permit any ERISA Affiliate to
                  engage in, any transaction in connection with which the
                  Guarantor, any of its Subsidiaries or any ERISA Affiliate
                  could be subjected to either a civil penalty assessed pursuant
                  to section 502(c), (i) or (l) of ERISA or a tax imposed by
                  Chapter 43 of Subtitle D of the Code in excess of $100,000;



                                       15
<PAGE>   18

                           (2)      Terminate, or permit any ERISA Affiliate to
                  terminate, any Plan in a manner, or take any other action with
                  respect to any Plan, which could reasonably be expected to
                  result in any liability of the Guarantor, any of its
                  Subsidiaries or any ERISA Affiliate to the PBGC in excess of
                  $100,000;

                           (3)      Fail to make, or permit any ERISA Affiliate
                  to fail to make, full payment when due of all amounts which
                  under the provisions of any Plan, agreement relating thereto
                  or applicable law, the Guarantor, any of its Subsidiaries or
                  any ERISA Affiliate is required to pay as contributions
                  thereto;

                           (4)      Permit to exist, or allow any ERISA
                  Affiliate to permit to exist, any accumulated funding
                  deficiency in excess of $100,000 within the meaning of Section
                  302 of ERISA or section 412 of the Code, whether or not
                  waived, with respect to any Plan;

                           (5)      Permit, or allow any ERISA Affiliate to
                  permit, the actuarial present value of the benefit liabilities
                  under any Plan maintained by the Guarantor, any of its
                  Subsidiaries or any ERISA Affiliate which is regulated under
                  Title IV of ERISA to exceed the current value of the assets
                  (computed on a plan termination basis in accordance with Title
                  IV of ERISA) of such Plan allocable to such benefit
                  liabilities by an amount in excess of $100,000. The term
                  "actuarial present value of the benefit liabilities" shall
                  have the meaning specified in section 4041 of ERISA;

                           (6)      Contribute to or assume an obligation to
                  contribute to, or permit any ERISA Affiliate to contribute to
                  or assume an obligation to contribute to, any Multiemployer
                  Plan;

                           (7)      Acquire, or permit any ERISA Affiliate to
                  acquire, an interest in any Person that causes such Person to
                  become an ERISA Affiliate with respect to the Borrower or any
                  ERISA Affiliate if such Person sponsors, maintains or
                  contributes to, or at any time in the six-year period
                  preceding such acquisition has sponsored, maintained, or
                  contributed to, (a) any Multiemployer Plan, or (b) any other
                  Plan that is subject to Title IV of ERISA under which the
                  actuarial present value of the benefit liabilities under such
                  Plan exceeds the current value of the assets (computed on a
                  plan termination basis in accordance with Title IV of ERISA)
                  of such Plan allocable to such benefit liabilities;

                           (8)      Incur, or permit any ERISA Affiliate to
                  incur, a liability to or on account of a Plan under sections
                  515, 4062, 4063, 4064, 4201 or 4204 of ERISA which in the
                  aggregate for all such liability exceeds $100,000;


                                       16
<PAGE>   19

                           (9)      Contribute to or assume an obligation to
                  contribute to, or permit any ERISA Affiliate to contribute to
                  or assume an obligation to contribute to, any employee welfare
                  benefit plan, as defined in section 3(1) of ERISA, including,
                  without limitation, any such plan maintained to provide
                  benefits to former employees of such entities, that may not be
                  terminated by such entities in their sole discretion at any
                  time without any material liability; or

                           (10)     Amend or permit any ERISA Affiliate to
                  amend, a Plan resulting in an increase in current liability
                  such that the Guarantor, any of its Subsidiaries or any ERISA
                  Affiliate is required to provide security to such Plan under
                  section 401(a)(29) of the Code.

                  (j)      Sale or Discount of Receivables. The Guarantor will
not and will not permit any of its Subsidiaries to discount or sell (with or
without recourse) any of its notes receivable or accounts receivable.

                  (k)      Capital Expenditures. The Guarantor will not and will
not permit Borrower to exceed the capital expenditure limitations provided in
Section 9.22 of the Credit Agreement.

                  (l)      Environmental Matters. The Guarantor will not and
will not permit any of its Subsidiaries to cause or permit any of its Property
to be in violation of, or do anything or permit anything to be done which will
subject any such Property to any remedial obligations under any Environmental
Laws, assuming disclosure to the applicable Governmental Authority of all
relevant facts, conditions and circumstances, if any, pertaining to such
Property where such violations or remedial obligations would have a Material
Adverse Effect.

                  (m)      Transactions with Affiliates. The Guarantor will not
and will not permit any of its Subsidiaries to enter into any transaction,
including, without limitation, any purchase, sale, lease or exchange of Property
or the rendering of any service, with any Affiliate unless such transactions are
otherwise not in violation of the Credit Agreement, are in the ordinary course
of its business and are upon fair and reasonable terms no less favorable to it
(or, if the Borrower is involved, no less favorable to the Borrower) than it
would obtain in a comparable arm's length transaction with a Person not an
Affiliate.

                  (n)      Subsidiaries. The Guarantor will not and will not
permit any of its Subsidiaries to, create any additional Subsidiaries except for
the Subsidiaries of the Borrower as permitted by the Credit Agreement.

                  (o)      Negative Pledge Agreements. The Guarantor will not
and will not permit any of its Subsidiaries to create, incur, assume or suffer
to exist any contract, agreement or understanding (other than the Loan
Documents, the Indenture and the documents described in Section 4.01(a) through
(d) of the Indenture, and any other



                                       17
<PAGE>   20


documents establishing Liens permitted under Sections 5.2(b)(4) and (5)) which
in any way prohibits or restricts the granting, conveying, creation or
imposition of any Lien on any of its Property or which requires the consent of
or notice to other Persons in connection therewith.

                  (p)      Capital Stock of General Partner of Borrower. The
Guarantor will not permit any of the capital stock of the General Partner of the
Borrower or any ownership interest in any limited partner of the Borrower to be
owned or controlled by any Person other than the Guarantor or Brigham Inc.

                  (q)      Current Ratio. The Guarantor will not permit its
ratio of (i) consolidated current assets of the Guarantor and its Consolidated
Subsidiaries to (ii) their consolidated current liabilities (excluding the
Indebtedness) to be less than (A) .75 to 1.0 for the quarters ended December 31,
1999 and March 31, 2000 or (B) 1.0 to 1.0 at any time thereafter.

                  (r)      Interest Coverage Ratio. The Guarantor will not
permit its Interest Coverage Ratio as of the end of any fiscal quarter of the
Guarantor (calculated quarterly at the end of each fiscal quarter) to be less
than the ratio set forth below for such period. Interest Coverage Ratio shall
mean the ratio of (i) EBITDA to (ii) the sum of all required payments of
interest (whether paid in cash or in kind) during such period on borrowed money
(excluding any payments made on account of the Term ORRI):

                  (i)      not less than .75 to 1.0 for the twelve (12) month
         period ending September 30, 2000;

                  (ii)     not less than .90 to 1.0 for the twelve (12) month
         period ending December 31, 2000;

                  (iii)    not less than 1.1 to 1.0 for the twelve (12) month
         period ending March 31, 2001;

                  (iv)     not less than 1.3 to 1.0 for the twelve (12) month
         period ending June 30, 2001;

                  (v)      not less than 1.5 to 1.0 for the twelve (12) month
         period ending September 30, 2001;

                  (vi)     thereafter, not less than 1.7 to 1.0 for the twelve
         (12) month period ending December 31, 2001, and each twelve (12) month
         period ending at the end of each fiscal quarter of Guarantor;

                  (s)      Securities Purchase Agreement, Indenture and Equity
Conversion Agreement. The Guarantor will not agree to any amendment or
modification to the Securities Purchase Agreement, the Indenture or the Equity
Conversion Agreement without the express written consent of the Majority
Lenders; provided that a waiver of a default under the Equity Conversion
Agreement shall not constitute a modification or amendment or require the
consent of any BMO/Soc-Gen Lender.



                                       18
<PAGE>   21

                  (t)      Payments on Subordinated Debt.


                           (i)      No prepayments of principal will be made on
the Subordinated Debt unless all of the Subordinated Debt is prepaid by (a)
converting all of the Subordinated Debt into common stock and/or preferred stock
with cashless dividends of Guarantor or (b) applying the proceeds from a sale of
Guarantor's common stock and/or preferred stock with cashless dividends or (c)
refinancing the Subordinated Debt through the issuance of debt and/or common
stock and/or preferred stock with cashless dividends of Guarantor on refinancing
terms reasonably acceptable to the Majority Lenders; and

                           (ii)     No payment of interest will be made in cash
on the Subordinated Debt on or before August 20, 2000 and from and after August
20, 2000, (a) no payment of interest will be made in cash on the Subordinated
Debt if on or before November 20, 2000 Guarantor has earned the right to pay
interest in kind for such quarterly payment and (b) no payment of interest will
be made in cash on the Subordinated Debt (i) if an Event of Default under
Section 10.01(a) of the Credit Agreement has occurred, or (ii) if a Borrowing
Base deficiency is in existence under the Credit Agreement.

                                   ARTICLE VI

                                  Miscellaneous

         Section 6.1 Successors and Assigns. This Guaranty Agreement is and
shall be, in every particular, available to the successors and assigns of the
Lenders and is and shall always be fully binding upon the legal representatives,
heirs, successors and assigns of Guarantor, notwithstanding that some or all of
the monies, the repayment of which this Guaranty Agreement applies, may be
actually advanced after any bankruptcy, receivership, reorganization, death,
disability or other event affecting Guarantor.

         Section 6.2 Notices. Any notice or demand to Guarantor under or in
connection with this Guaranty Agreement may be given and shall conclusively be
deemed and considered to have been given and received in accordance with Section
12.02 of the Credit Agreement, addressed to Guarantor at the address on the
signature page hereof or at such other address provided to the Agent in writing.

         Section 6.3 Business and Financial Information. Subject to any
applicable confidentiality agreements, the Guarantor will promptly furnish to
the Agent and the Lenders from time to time upon request such information
regarding the business and affairs and financial condition of the Guarantor and
its subsidiaries as the Agent and the Lenders may reasonably request.

         Section 6.4 Construction. This Guaranty Agreement is a contract made
under and shall be construed in accordance with and governed by the laws of the
State of Texas.


                                       19
<PAGE>   22


         Section 6.5 Invalidity. In the event that any one or more of the
provisions contained in this Guaranty Agreement shall, for any reason, be held
invalid, illegal or unenforceable in any respect, such invalidity, illegality or
unenforceability shall not affect any other provision of this Guaranty
Agreement.

         Section 6.6 ENTIRE AGREEMENT. THIS WRITTEN GUARANTY AGREEMENT EMBODIES
THE ENTIRE AGREEMENT AND UNDERSTANDING BETWEEN THE LENDERS AND THE GUARANTOR AND
SUPERSEDES ALL OTHER AGREEMENTS AND UNDERSTANDINGS BETWEEN SUCH PARTIES RELATING
TO THE SUBJECT MATTER HEREOF AND THEREOF. THIS WRITTEN GUARANTY AGREEMENT
REPRESENTS THE FINAL AGREEMENT BETWEEN THE PARTIES AND MAY NOT BE CONTRADICTED
BY EVIDENCE OF PRIOR, CONTEMPORANEOUS, OR SUBSEQUENT ORAL AGREEMENTS OF THE
PARTIES. THERE ARE NO UNWRITTEN ORAL AGREEMENTS BETWEEN THE PARTIES.




                                       20
<PAGE>   23





         WITNESS THE EXECUTION HEREOF, as of this the 17th day of February,
2000.

                                              BRIGHAM EXPLORATION COMPANY



                                              By:
                                                 -------------------------------
                                              Name:    Curtis F. Harrell
                                              Title:   Chief Financial Officer

                                              Address for Notices:

                                              6300 Bridge Point Parkway
                                              Building 2, Suite 500
                                              Austin, Texas  78730
                                              Telecopier No.: (512) 427-3400
                                              Telephone No.: (512) 427-3300
                                              Attention:  Curtis F. Harrell


                                        S
<PAGE>   24




                                   SCHEDULE I

                       SUBSIDIARIES OF BRIGHAM EXPLORATION

                  Brigham Exploration has the following Subsidiaries:

         1.       Brigham, Inc., a Nevada corporation, all of whose shares are
                  owned by Brigham Exploration.

         2.       Brigham Holdings I, LLC, a Nevada limited liability company,
                  whose only member is Brigham Exploration.

         3.       Brigham Holdings II, LLC, a Nevada limited liability company,
                  whose only member is Brigham, Inc.

         4.       Borrower, a Delaware limited partnership, whose only General
                  Partner is Brigham, Inc., and whose only limited partners are
                  Brigham Holdings I, LLC and Brigham Holdings II, LLC.



                                     SCH I-1

<PAGE>   1
                                                                    EXHIBIT 10.3

                                                                  EXECUTION COPY



                           PARTIAL ASSIGNMENT OF NOTES

                  THIS PARTIAL ASSIGNMENT OF NOTES ("Agreement") dated as of
February 17, 2000, by and among Bank of Montreal, a Canadian bank (the "BMO"),
Societe Generale, Southwest Agency ("Soc-Gen"), Shell Capital Inc., a Delaware
corporation (the "Assignee") and Brigham Oil & Gas, L.P., a Delaware limited
partnership (the "Borrower").

                                    RECITALS

                  A. Pursuant to that certain Credit Agreement (the "Original
Credit Agreement") dated as of January 26, 1998 among the Borrower and BMO, as
amended by that certain First Amendment to Credit Agreement dated as of August
20, 1998 among the Borrower, BMO and Soc-Gen (the "First Amendment"), that
certain Second Amendment to Credit Agreement dated as of March 26, 1999 among
the Borrower, BMO and Soc-Gen (the "Second Amendment"), that certain Third
Amendment to Credit Agreement dated as of July 19, 1999 among the Borrower, BMO
and Soc-Gen (the "Third Amendment") and that certain Fourth Amendment to Credit
Agreement dated as of October 7, 1999 among the Borrower, BMO and Soc-Gen (the
"Fourth Amendment") (the Original Credit Agreement as amended by the First
Amendment, the Second Amendment, the Third Amendment and the Fourth Amendment
being hereafter called the "Prior Credit Agreement"), BMO and Soc-Gen provided
to the Borrower loans and extensions of credit, which loans and extensions of
credit are evidenced by those certain promissory notes from the Borrower in the
aggregate principal amount of $75,000,000 (the "Prior Notes").

                  B. BMO and Soc-Gen (collectively the "Assignors") propose to
sell, assign and transfer to the Assignee, and the Assignee proposes to purchase
and assume from the Assignors, a 53.333% interest in the Prior Notes (the
Assigned Interest, as hereinafter defined) upon the occurrence of certain
conditions provided herein, and BMO and Soc-Gen, as the case may be, propose to
sell, assign and transfer to the Assignee, and the Assignee proposes to purchase
and assume from BMO and/or Soc-Gen the Retained Interest, as hereinafter
defined, all on the terms and conditions of this Agreement.

                  C. Pursuant to that certain Amended and Restated Credit
Agreement (the "Current Credit Agreement") dated as of February 17, 2000 among
the Borrower, BMO, in its individual capacity, Soc-Gen and Assignee, and BMO, in
its capacity as Agent for Soc-Gen and Assignee (in such capacity, together with
its successors in such capacity, the "Agent") have agreed to provide senior
secured debt in the amount of up to $75,000,000 (the "Current Notes") consisting
of a rearrangement of the Prior Notes and advances to the Borrower for general
corporate purposes and the Borrower, BMO, Soc-Gen, Assignee and the Agent agree
to amend and restate in their entirety the Prior Credit Agreement by means of
the Current Credit Agreement, and the Prior Notes, by means of the Current
Notes.

                  D. In consideration of the foregoing and the mutual agreements
contained herein, and for other good and valuable consideration, the receipt and
sufficiency of which are hereby acknowledged, the parties hereto agree as
follows:


<PAGE>   2


                                   ARTICLE 1

                                  Definitions.

         Section 1.01 Definitions. All capitalized terms used but not defined
herein have the respective meanings given to such terms in the Credit Agreement
if defined therein.

         Section 1.02 Other Definitions. As used herein, the following terms
have the following respective meanings:

                 "Assigned Interest" shall mean that portion of each of BMO's
         and Soc-Gen's rights and obligations (i) under the Prior Credit
         Agreement and the other Loan Documents in respect of the Maximum Credit
         Amount of each of BMO and Soc-Gen in the principal amount as set forth
         on Schedule A to this Agreement ("Schedule A"), and (ii) to make Loans
         under the Maximum Credit Amount and any right to receive payments for
         the Loans outstanding under the Maximum Credit Amount as set forth on
         Schedule A, plus the interest and fees which will accrue on the
         Assigned Interest from and after the Assignment Date.

                 "Assignee Subordinated Indebtedness" shall mean the principal
         balance due to Assignee (excluding any Debt of the Borrower under
         Hedging Agreements made with the Assignee or an Affiliate of Assignee
         as provided in the Current Credit Agreement) of all loans advanced to
         or issued for the account of Borrower pursuant to the terms and
         conditions of the Prior Credit Agreement and the Current Credit
         Agreement, not to exceed $75,000,000 and accrued but unpaid interest
         thereon, and of all fees, expenses, reimbursement obligations,
         liabilities, indemnities or other monetary obligations of Borrower
         whether any of the foregoing is (i) absolute or contingent, direct or
         indirect, joint, several or independent, (ii) now outstanding or owing
         or which may hereafter be existing or incurred, (iii) due or to become
         due, or (iv) held or to be held by Assignee, and all renewals,
         extensions, rearrangements, refundings and modifications thereof
         permitted by the terms hereof.

                 "Assignment Date" shall mean February 17, 2000.

                 "BMO/Soc-Gen Senior Indebtedness" shall mean the principal
         balance due (i) to Assignors of all loans advanced to or issued for the
         account of Borrower pursuant to the terms and conditions of the Prior
         Credit Agreement and the Current Credit Agreement, not to exceed
         $75,000,000 and accrued but unpaid interest thereon, and of all fees,
         expenses, reimbursement obligations, liabilities, indemnities or other
         monetary obligations of Borrower under the Credit Agreement, and (ii)
         of all swap settlement amounts or other amounts due and payable under
         any Hedging Agreement in existence as of the date hereof or hereafter
         arising between (i) Borrower and BMO and its successors or assigns (a
         "BMO Hedge Party") and Soc-Gen and its successors or assigns (a
         "Soc-Gen Hedge Party") entered into while such BMO Hedge Party or such
         Soc-Gen Hedge Party is a Lender; and (ii) Borrower and SCI and its
         successors or assigns (with


                                       2
<PAGE>   3


         Loans or Commitments of $20 million or more) or any Affiliate of SCI
         (SCI and any Affiliate of SCI a "SCI Hedge Party") entered into while
         such SCI Hedge Party or Fathom Energy Capital I, L.L.C, is a Lender,
         whether any of the foregoing is (w) absolute or contingent, direct or
         indirect, joint, several or independent, (x) now outstanding or owing
         or which may hereafter be existing or incurred, (y) due or to become
         due, or (z) held or to be held by the Assignors or any Assignor, and
         all renewals, extensions, rearrangements, refundings and modifications
         thereof permitted by the terms hereof. The parties intend that any
         Hedging Agreement entered into between the Borrower and a Lender or in
         the case of SCI, a SCI Hedge Party, while such Person was a party to
         the Credit Agreement shall continue to be secured even after the time
         such Person ceases to be a party to the Credit Agreement as a Lender
         and shall be "BMO/Soc-Gen Senior Indebtedness".

                 "Retained Interest" shall mean that portion of each of BMO and
         Soc-Gen's rights and obligations (i) under the Prior Credit Agreement,
         the Current Credit Agreement and the other Loan Documents in respect of
         the BMO/Soc-Gen Senior Indebtedness of each of BMO and Soc-Gen in the
         principal amount as set forth in Schedule B to this Agreement
         ("Schedule B") and (ii) to make Loans under the BMO/Soc-Gen Senior
         Indebtedness as set forth on Schedule B (the "Retained Loan
         Commitment"), plus the interest and fees which will accrue on the
         Retained Interest from and after the Assignment Date.

                                   ARTICLE 2

                              Sale and Assignment.

         Section 2.01 Sale and Assignment.

                 (a) On the terms and conditions set forth herein, effective on
         and as of the Assignment Date, the Assignors hereby sell, assign and
         transfer to the Assignee, and the Assignee hereby purchases and assumes
         from the Assignors, all of the right, title and interest of the
         Assignors in and to, and all of the obligations of the Assignors in
         respect of, the Assigned Interest. Such sale, assignment and transfer
         is without recourse and, except as expressly provided in this
         Agreement, without representation or warranty.

                 (b) At the election of each BMO/Soc-Gen Lender, Assignee shall
         be obligated to purchase the Retained Interest of such BMO/Soc-Gen
         Lender on March 31, 2002 provided that the amount of the Borrowing Base
         on such date determined in accordance with Section 2.08 of the Credit
         Agreement is greater than the aggregate outstanding principal amounts
         of the Loans, there are no Defaults or Events of Default under the
         Current Credit Agreement, and such BMO/Soc-Gen Lender requests in
         writing no later than March 15, 2002 that the Assignee purchase the
         Retained Interest of such BMO/Soc-Gen Lender. The sale, assignment and
         transfer of such Retained Interest to Assignee will be without recourse
         and without representation or warranty, except for representations


                                       3
<PAGE>   4


         substantially the same to those provided in this Agreement and shall be
         in form substantially similar to this Agreement.

         Section 2.02 Assumption of Obligations. The Assignee agrees with the
Assignors (for the express benefit of the Assignors and the Borrower) that the
Assignee will, from and after the Assignment Date, perform all of the
obligations of the Assignors accruing after the Assignment Date in respect of
the Assigned Interest. From and after the Assignment Date: (a) the Assignors
shall be released from the Assignors' obligations in respect of the Assigned
Interest, and (b) the Assignee shall, except as otherwise provided in this
Agreement, including, without limitation, Section 3.03 which, among the
Assignors, Assignee and the Borrower, governs the allocation of payments on the
Assigned Interest and Section 3.05 which, among the Assignors, Assignee and the
Borrower, governs future obligations to make loans under the Current Credit
Agreement, be entitled to all of the Assignors' rights, powers and privileges
under the Credit Agreement and the other Loan Documents in respect of the
Assigned Interest.

         Section 2.03 Purchase Price for Assigned Interest. As consideration for
the sale, assignment and transfer of the Assigned Interest contemplated by
Section 2.01(a) hereof, the Assignee shall, on the Assignment Date, assume
Assignors' obligations accruing after the Assignment Date in respect of the
Assigned Interest and pay to BMO an amount equal to $13,892,323.85 and to
Soc-Gen an amount equal to $7,107,676.15. Except as otherwise provided in this
Agreement, all payments hereunder shall be made in Dollars and in immediately
available funds, without setoff, deduction or counterclaim.

         Section 2.04 Purchase Price for Retained Interest. Upon satisfaction of
the conditions specified in Section 2.01(b) hereof, Assignee shall pay to each
BMO/Soc-Gen Lender who makes the election to assign its Retained Interest to
Assignee an amount equal to the then outstanding principal and interest of the
Retained Loan Commitment owed to such BMO/Soc-Gen Lender in consideration of the
sale, assignment and transfer of the Retained Interest as provided herein. Such
payment shall be made in Dollars and in immediately available funds, without
setoff, deduction or counterclaim and shall be made no later than March 31,
2002.

         Section 2.05 Delivery of Notes. Promptly following the receipt by the
Assignors of the consideration required to be paid under Section 2.03 or 2.04
hereof, the Assignors shall, in the manner contemplated by Section 12.06(d) of
the Current Credit Agreement, (i) deliver to the Agent (or its counsel) a Note
corresponding to the Assigned Interest or any applicable Retained Interest, as
the case may be, and (ii) notify the Agent to request that the Borrower execute
and deliver new Notes in accordance with the terms of the Current Credit
Agreement to the Assignors and the Assignee.

                                   ARTICLE 3

                                  Subordination

         Section 3.01 Agreement to Subordinate. The payment of any and all
Assignee Subordinated Indebtedness and the rights of Assignee with respect to
the Assignee Subordinated


                                       4
<PAGE>   5


Indebtedness are expressly subordinated to the BMO/Soc-Gen Senior Indebtedness
to the extent and in the manner set forth in Sections 3.02 through 3.05 hereof.

         Section 3.02 Certain Voting Rights.

                 (a) The Assignors and Assignee agree that, except as otherwise
         expressly provided herein or in the Current Credit Agreement, on any
         date prior to March 31, 2002 any act, event, document or condition
         requiring pursuant to the terms of the Current Credit Agreement the
         consent, agreement or waiver of, or approval, notice, selection,
         designation or appointment by, or request, direction or election of,
         the Lenders, shall require the unanimous agreement of the Majority
         Lenders;

                 (b) Notwithstanding the provisions of Section 2.08(a) of the
         Current Credit Agreement, the BMO/Soc-Gen Majority Lenders shall in
         their sole discretion determine the Target Asset Value as provided in
         Section 8.13 of the Current Credit Agreement and whether to waive any
         default arising from Borrower's non-compliance with Section 8.13 of the
         Current Credit Agreement;

                 (c) The SCI Majority Lenders, in their sole discretion, shall
         determine (i) the Risk Adjusted Proved Reserve Value, (ii) the PDP
         Reserve value for purposes of subparagraph (c) of the definition of
         Increase Event, (iii) whether to waive any default under Section
         9.22(e) of the Current Credit Agreement, and (iv) whether to convert
         the Assigned Interest into equity of Borrower pursuant to the Equity
         Conversion Agreement;

                 (d) At the request of the Agent, the Assignee agrees to execute
         any consents, agreements, waivers, approvals, requests, or other
         instruments or documents necessary or desirable to give effect to the
         agreements specified in Section 3.02(b); and

                 (e) At the request of the Assignee, each of the Assignors agree
         to execute any consents, agreements, waivers, approvals, requests, or
         other instruments or documents necessary or desirable to give effect to
         the agreements specified in Section 3.02(c).

         Section 3.03 Payments on Assigned Interest.

                 (a) The Assignors, the Assignee and Borrower (to the extent
         required) agree, that:

                     (i) the Assignee Subordinated Indebtedness is subordinate
                 in right of payment, to the extent and in the manner provided
                 in this Agreement, to the prior payment in full of all
                 principal of the BMO/Soc-Gen Senior Indebtedness (whether
                 outstanding on the date hereof or hereafter created, incurred,
                 assumed or guaranteed);


                                       5
<PAGE>   6


                     (ii) the Borrower may not, except as otherwise agreed to in
                 writing by Assignors and Assignee, make any payment (whether by
                 redemption, purchase, retirement, defeasance, set-off or
                 otherwise) upon or in respect of the Assignee Subordinated
                 Indebtedness, until all principal and other obligations with
                 respect to the BMO/Soc-Gen Senior Indebtedness has been paid in
                 full:

                     (iii) the Borrower may commence payments on, and
                 distributions in respect of, the Assignee Subordinated
                 Indebtedness upon payment in full of all BMO/Soc-Gen Senior
                 Indebtedness (whether outstanding on the date hereof or
                 hereafter created, incurred, assumed or guaranteed).

                     (iv) Notwithstanding the foregoing, and provided that no
                 Event of Default has occurred and is continuing, the Borrower
                 may pay to the SCI Lenders, and the SCI Lenders may receive and
                 retain, all amounts due and payable to the SCI Lenders for
                 accrued interest on the SCI Loans and other fees due to SCI in
                 accordance with Sections 3.02 and 4.02 of the Current Credit
                 Agreement and the SCI Fee Letter.

                     (v) Upon any payment or distribution of property or
                 securities to creditors of the Borrower in a liquidation or
                 dissolution of such person or its property, or in an assignment
                 for the benefit of creditors or any marshaling of its assets
                 and liabilities:

                         (A) each of the Assignors shall be entitled to receive
                     payment in full of all BMO/Soc-Gen Senior Indebtedness
                     before the Assignee shall be entitled to receive any
                     payment with respect to the Assignee Subordinated
                     Indebtedness; and

                         (B) until the BMO/Soc-Gen Senior Indebtedness is paid
                     in full, any payment or distribution to which the Assignee
                     would be entitled shall be made to each of the Assignors
                     for its benefit.

                         (C) under the circumstances described in this clause
                     (iv), the Borrower or any receiver, trustee in bankruptcy,
                     liquidating trustee, agent or other similar Person making
                     any payment or distribution of cash or other property or
                     securities is authorized or instructed to make any payment
                     or distribution to which the Assignee would otherwise be
                     entitled (other than securities that are subordinated at
                     least to the same extent as the Assignee Subordinated
                     Indebtedness) directly to each of the Assignors for its
                     benefit to the extent necessary to pay all BMO/Soc-Gen
                     Senior Indebtedness in full, after giving effect to any
                     concurrent payment, distribution or provision therefor to
                     or for the Assignors.


                                       6
<PAGE>   7


                 (b) The foregoing provisions of this Section 3.03 shall not
         impair or prohibit the rights of the Assignee to receive payments (i)
         through conversion of any of the Assignee Subordinated Indebtedness to
         equity as provided in the Equity Conversion Agreement or (ii) in the
         form of other equity securities or additional subordinated debt that is
         subordinated to the BMO/Soc-Gen Senior Indebtedness in accordance with
         the terms substantially similar to the terms of this Agreement.

         Section 3.04 Payments Received or Made in Violation of this Agreement.
In the event the Assignee shall receive any payment or distribution on account
of the Assignee Subordinated Indebtedness which it is not entitled to receive
under the provisions of Section 3.03, the Assignee will hold any amount so
received in trust for the Assignors and will forthwith turn over such payment to
the Assignors in the form received by it (together with any necessary
endorsement) to be applied to the BMO/Soc-Gen Senior Indebtedness.

         Section 3.05 Assignee Funding. Assignors, Assignee and Borrower agree
that, subsequent to the Assignment Date, (i) Assignors shall have no further
obligation to make Loans under the Current Credit Agreement; and (ii) Assignee
shall have the sole responsibility to meet any obligation that may arise under
the Credit Agreement to make Loans under the Credit Agreement, provided,
however, Assignee's obligations to make Loans under the Current Credit Agreement
shall not exceed its Commitment.

                                   ARTICLE 4

                              Conditions Precedent.

         Section 4.01 Conditions Precedent. The effectiveness of the sale,
assignment and transfer of the Assigned Interest contemplated hereby is subject
to the satisfaction of each of the following conditions precedent:

                 (a) the execution and delivery of this Agreement by the
         Assignors and the Assignee;

                 (b) the receipt by the Assignors of the payment required to be
         made by the Assignee under Section 2.03 hereof;

                 (c) the acknowledgment by the Agent and the Borrower
         contemplated by Section 2.05 hereof;

                 (d) the execution and delivery of the Notes contemplated by
         Section 2.06 hereof;

                 (e) the satisfaction of the conditions of the Initial Funding
         set forth in Section 6.01 of the Current Credit Agreement; and

                 (f) the execution and delivery of the Current Credit Agreement.


                                       7
<PAGE>   8


                                   ARTICLE 5

                         Representations and Warranties.

         Section 5.01 Representations and Warranties of the Assignors.

                 (a) Each of the Assignors represents and warrants for itself
         that:

                     (i) it has all requisite power and authority, and has taken
                 all action necessary to execute and deliver this Agreement and
                 to fulfill its obligations under, and consummate the
                 transactions contemplated by, this Agreement;

                     (ii) the execution, delivery and compliance with the terms
                 hereof by it and the delivery of all instruments required to be
                 delivered by it hereunder do not and will not violate any
                 Governmental Requirement applicable to it;

                     (iii) this Agreement has been duly executed and delivered
                 by it and constitutes the legal, valid and binding obligation
                 of such Assignor, enforceable against it in accordance with its
                 terms;

                     (iv) all approvals and authorizations of, all filings with
                 and all actions by any Governmental Authority necessary for the
                 validity or enforceability of its obligations under this
                 Agreement have been obtained;

                     (v) it has good title, to and is the sole legal and
                 beneficial owner of, the Assigned Interest, free and clear of
                 all Liens, claims, participations or other charges of any
                 nature whatsoever and has the right to transfer to the
                 Assignee, the rights being transferred; and

                     (vi) the amounts set forth on Schedule A and Schedule B by
                 each of the respective Assignors as its portion of the Assigned
                 Interest and Retained Interest is true and correct.

                 (b) Each of the Assignors does not (i) make any representation
         or warranty or assume any responsibility with respect to any
         statements, warranties or representations made (x) by the Borrower in
         or in connection with the Credit Agreement or (y) with respect to the
         execution, legality, validity, enforceability, genuineness, sufficiency
         or value of the Credit Agreement, any other Loan Document or any other
         instrument or document furnished pursuant hereto or thereto, or any
         collateral or the legality, validity, perfection or priority of any
         Lien granted or purported to be granted pursuant to any Security
         Instrument, or (ii) make any representation or warranty or assume any
         responsibility with respect to the financial condition of Borrower or
         any other obligor or the performance or observance by Borrower or any
         other obligor of any of their respective obligations under the Credit
         Agreement or any other Loan Document or any other instrument or
         document furnished pursuant hereto or thereto.


                                       8
<PAGE>   9


         Section 5.02 Representations and Warranties of the Assignee. The
Assignee represents and warrants to each of the Assignors as follows:

                 (a) it has all requisite power and authority, and has taken all
         action necessary to execute and deliver this Agreement and to fulfill
         its obligations under, and consummate the transactions contemplated by,
         this Agreement;

                 (b) the execution, delivery and compliance with the terms
         hereof by Assignee and the delivery of all instruments required to be
         delivered by it hereunder do not and will not violate any Governmental
         Requirement applicable to it;

                 (c) this Agreement has been duly executed and delivered by it
         and constitutes the legal, valid and binding obligation of the
         Assignee, enforceable against it in accordance with its terms;

                 (d) all approvals and authorizations of, all filings with and
         all actions by any Governmental Authority necessary for the validity or
         enforceability of its obligations under this Agreement have been
         obtained; and

                 (e) the Assignee has fully reviewed the terms of the Credit
         Agreement and the other Loan Documents and has independently and
         without reliance upon the Assignors, and based on such information as
         the Assignee has deemed appropriate, made its own credit analysis and
         decision to enter into this Agreement.

                                   ARTICLE 6

                                 Miscellaneous.

         Section 6.01 Notices. All notices and other communications provided for
herein (including, without limitation, any modifications of, or waivers,
requests or consents under, this Agreement) shall be given or made in writing
(including, without limitation, by telex or telecopy) to the intended recipient
at its "Address for Notices" specified below its name on the signature pages
hereof or, as to either party, at such other address as shall be designated by
such party in a notice to the other party.

         Section 6.02 Amendment, Modification or Waiver. No provision of this
Agreement may be amended, modified or waived except by an instrument in writing
signed by the Assignors and the Assignee, and consented to by the Agent.

         Section 6.03 Further Assurances. The Assignors and the Assignee hereby
agree to execute and deliver such other instruments, and take such other
actions, as either party may reasonably request to correct any errors or as
otherwise required to accomplish the transactions contemplated by this
Agreement.

         Section 6.04 Successors and Assigns. This Agreement shall be binding
upon and inure to the benefit of the parties hereto and their respective
successors and permitted


                                       9
<PAGE>   10


assigns. The representations and warranties made herein by the Assignee are also
made for the benefit of the Agent and the Borrower, and the Assignee agrees that
the Agent and the Borrower are entitled to rely upon such representations and
warranties.

         Section 6.05 Assignments. None of the parties hereto may assign any of
its rights or obligations hereunder except in accordance with the terms of the
Credit Agreement.

         Section 6.06 Captions. The captions and section headings appearing
herein are included solely for convenience of reference and are not intended to
affect the interpretation of any provision of this Agreement.

         Section 6.07 Counterparts. This Agreement may be executed in any number
of counterparts, each of which shall be identical and all of which, taken
together, shall constitute one and the same instrument, and each of the parties
hereto may execute this Agreement by signing any such counterpart.

         Section 6.08 Governing Law. This Agreement shall be governed by, and
construed in accordance with, the law of the State of Texas.

         Section 6.09 Expense. To the extent not paid by the Borrower pursuant
to the terms of the Credit Agreement, each party hereto shall bear its own
expenses in connection with the execution, delivery and performance of this
Agreement.

         Section 6.10 Waiver of Jury Trial. EACH OF THE PARTIES HERETO HEREBY
IRREVOCABLY WAIVES, TO THE FULLEST EXTENT PERMITTED BY LAW, ANY AND ALL RIGHT TO
TRIAL BY JURY IN ANY LEGAL PROCEEDING ARISING OUT OF OR RELATING TO THIS
AGREEMENT OR THE TRANSACTIONS CONTEMPLATED HEREBY.


                                       10
<PAGE>   11


                  IN WITNESS WHEREOF, the parties hereto have caused this
Assignment Agreement to be executed and delivered as of the date first above
written.

                                          ASSIGNORS

                                          BANK OF MONTREAL



                                          By:
                                             ----------------------------------
                                          Name:   Thomas E. McGraw
                                          Title:  Director

                                          Address for Notices:
                                          700 Louisiana Street, Suite 4400
                                          Houston, Texas 77002

                                          Telecopier No.:  (713) 223-0477
                                          Telephone No.:  (713) 223-4400

                                          Attention:  Thomas E. McGraw


                                          SOCIETE GENERALE, SOUTHWEST AGENCY



                                          By:
                                             ----------------------------------
                                          Name:   Mark A. Cox
                                          Title:  Director

                                          Address for Notices:
                                          1111 Bagby Street, Suite 2020
                                          Houston, Texas 77002

                                          Telecopier No: (713) 650-0824
                                          Telephone No:  (713) 759-6315



                                       S

<PAGE>   12



                                          ASSIGNEE

                                          SHELL CAPITAL INC.

                                          By:
                                             ----------------------------------
                                          Name:  Robert L. Roberts
                                          Title: Vice President


                                          Address for Notices:

                                          910 Louisiana Street, Suite 5000
                                          Houston, Texas 77002-4916

                                          Telecopier No.:  (713) 241-5222
                                          Telephone No.:  (713) 241-4130
                                          Attention:  Robert L. Roberts

                                          BORROWER:

                                          BRIGHAM OIL & GAS, L.P.

                                          By:  Brigham, Inc., General Partner



                                          By:
                                             ----------------------------------
                                          Name:    Curtis F. Harrell
                                          Title:   Chief Financial Officer


                                          BANK OF MONTREAL, as Agent



                                          By:
                                             ----------------------------------
                                          Name:    Thomas E. McGraw
                                          Title:   Director


                                       S

<PAGE>   13



                                   SCHEDULE A


<TABLE>
<CAPTION>
                                               Principal Amount    Loan Commitment
                                               ----------------    ---------------
<S>                                            <C>                 <C>
Bank of Montreal                               $  13,892,323.85    $ 26,461,554.62
Societe Generale, Southwest Agency             $   7,107,676.15    $ 13,538,445.38
</TABLE>


                                 SCH. A, PAGE 1

<PAGE>   14




                                   SCHEDULE B

<TABLE>
<CAPTION>
                                                                Retained Loan
                                           Principal Amount      Commitment
                                           ----------------    ---------------
<S>                                        <C>                 <C>
Bank of Montreal                           $  23,153,830.00    $ 23,153,830.00
Societe Generale, Southwest Agency         $  11,846,170.00    $ 11,846,170.00
</TABLE>




                                 SCH. B, PAGE 1


<PAGE>   1

                                                                    EXHIBIT 10.4

                                                                  EXECUTION COPY


                      FIRST AMENDMENT TO WARRANT AGREEMENT


                  THIS FIRST AMENDMENT TO WARRANT AGREEMENT (this "Amendment")
dated as of February 17, 2000 is between Brigham Exploration Company, a Delaware
corporation ("Issuer") and Bank of Montreal, a Canadian bank (the "Warrant
Holder" or "BMO").

                                    RECITALS

                  A. Brigham Oil & Gas, L.P., a Delaware limited partnership
(the "Borrower"), BMO and Societe Generale Southwest Agency (the "Prior
Lenders") previously entered into that certain Credit Agreement dated as of
January 26, 1998, as amended by First Amendment to Credit Agreement dated as of
August 20, 1998, Second Amendment to Credit Agreement dated as of March 26,
1999, Third Amendment to Credit Agreement dated as of July 19, 1999 and Fourth
Amendment to Credit Agreement dated as of October 7, 1999 (such Credit Agreement
as amended called the "Prior Credit Agreement"), pursuant to which the Prior
Lenders agreed to make certain loans and extensions of credit to the Borrower as
evidenced by those certain promissory notes in the aggregate principal amount of
$75,000,000 (the "Prior Notes").

                  B. By Partial Assignment of Notes of even date herewith Shell
Capital Inc. ("SCI") has acquired an interest in the Prior Notes and a like
interest in all security for the payment of the Prior Notes and the performance
of the Borrower's obligations under the Prior Credit Agreement; and

                  C. The Prior Lenders and SCI (collectively, the "Lenders")
have agreed to provide senior secured debt in the amount of up to $75,000,000
consisting of a rearrangement of the Prior Notes and advances to the Borrower,
and the Borrower, BMO as Agent (the "Agent") and the Lenders are entering into
that certain Amended and Restated Credit Agreement (the "Credit Agreement") of
even date herewith which amends and restates in its entirety the Prior Credit
Agreement and Prior Notes; and

                  D. Issuer and BMO now desire to amend certain provisions of
the Warrant Agreement dated as of July 19, 1999 between Issuer and BMO (the
"Warrant Agreement") in recognition of the benefits Issuer will obtain under the
Credit Agreement.

                  NOW THEREFORE, in consideration of the mutual covenants and
agreements herein contained, Issuer and BMO hereby agree that the Warrant
Agreement shall be amended as follows:

                  Section 1. Certain Definitions. As used in this Amendment, the
terms "Agent", "Amendment", "Borrower", "Credit Agreement", "Issuer", "BMO",
"SCI", "Lenders", "Prior Credit Agreement", "Prior Lenders," "Prior Notes", and
"Warrant Agreement" shall have the meanings indicated above; and unless
otherwise defined herein, all terms beginning with a capital letter which are
defined in the Warrant Agreement shall have the same meanings herein as therein
unless the context hereof otherwise requires.


<PAGE>   2

                  Section 2. Amendments to Warrant Agreement.

                  Section 2.1 The definition of Current Warrant Price in section
1. of the Warrant Agreement is hereby deleted in its entirety and the following
is substituted therefor:

                  "Current Warrant Price" shall mean, in respect of a share of
                  Common Stock at any date herein specified, two dollars and two
                  cents ($2.02) per share of Common Stock, subject to adjustment
                  from time to time as provided in this Agreement."

                  Section 2.2 Exhibit A to the Warrant Agreement (Form of
Warrant Certificate) is amended as follows:

                  (a)      to change the reference "of two and 25/100 dollars
                           ($2.25)" to "of two and 02/100 dollars ($2.02)";

                  (b)      to add the following language after the date "July
                           19, 1999, to the next to the last paragraph of the
                           Form of Warrant Certificate: "as amended by that
                           certain First Amendment to Warrant Agreement dated as
                           of February 17, 2000".

                  Section 2.3 All references to the "Credit Agreement" in the
Warrant Agreement shall henceforth refer to the Credit Agreement as defined in
this Amendment, as such Credit Agreement is from time to time further amended,
supplemented or restated.

                  Section 2.4 The second sentence of Section 4.3(b) of the
Warrant Agreement is hereby deleted in its entirety and the following is
substituted therefor:

                  "No adjustment of the number of shares of Common Stock for
                  which a Warrant shall be exercised shall be made under Section
                  4.3(a) of this Agreement upon the issuance of any Additional
                  Shares of Common Stock which are issued pursuant to the
                  exercise of any warrants or other subscription or purchase
                  rights or pursuant to the exercise of any conversion or
                  exchange rights in any Convertible Securities (i) if any such
                  adjustment shall previously have been made upon the issuance
                  of such Convertible Securities (or upon the issuance of any
                  such warrants or other rights) pursuant to Section 4.4 or
                  Section 4.5 of this Agreement, (ii) if no adjustment was
                  required pursuant to such sections upon the issuance of such
                  Convertible Securities, warrants or other rights or (iii) in
                  the event the issuance of such Convertible Securities,
                  warrants or other rights predates or is of the same date as
                  this Agreement, if no adjustment would have been required
                  pursuant to such sections upon such issuance had this
                  Agreement been in effect."

                  Section 3. Representations and Warranties. Issuer hereby
reaffirms that as of the effective date of this Amendment, the representations
and warranties made by the Issuer in the Warrant Agreement will be true and
correct as though made on and as of the date of this Amendment.



                                       2
<PAGE>   3

                  Section 4. Ratification. Issuer hereby expressly ratifies and
affirms its obligations under the Warrant Agreement as amended by this Amendment
and agrees that the Warrant Agreement as amended by this Amendment remains in
full force and effect.

                  Section 5. Issuance of Warrant Certificate. Contemporaneously
with the execution of this Amendment, Issuer will deliver to BMO a Warrant
Certificate reflecting the amendments described in Section 2.2 hereof.

                  Section 6. Governing Law. This Amendment and the rights and
obligations of the parties hereunder and under the Warrant Agreement shall be
construed in accordance with and be governed by the laws of the State of Texas
and the United States of America.

                  Section 7. Descriptive Headings, Etc. The descriptive headings
of the several Sections of this Amendment are inserted for convenience only and
shall not be deemed to affect the meaning or construction of any of the
provisions hereof.

                  Section 8. Counterparts. This Amendment may be executed in any
number of counterparts and by different parties on separate counterparts and all
of such counterparts shall together constitute one and the same instrument.

                           [SIGNATURES ON NEXT PAGE.]



                                       3
<PAGE>   4

                  IN WITNESS WHEREOF, the parties hereto have caused this
Amendment to be duly executed and delivered and effective as of the date first
above written.

                                        BANK OF MONTREAL, as Warrant Holder



                                        By:
                                           -------------------------------------
                                        Name: Thomas E. McGraw
                                        Title: Director



                                        BRIGHAM EXPLORATION COMPANY,
                                        As Issuer



                                        By:
                                           -------------------------------------
                                        Name: Karen E. Lynch
                                        Title: Vice President



                                       S

<PAGE>   1
                                                                    EXHIBIT 10.5

                                                                  EXECUTION COPY


                      FIRST AMENDMENT TO WARRANT AGREEMENT


         THIS FIRST AMENDMENT TO WARRANT AGREEMENT (this "Amendment") dated as
of February 17, 2000 is between Brigham Exploration Company, a Delaware
corporation ("Issuer") and Societe Generale, Southwest Agent, a bank organized
under the laws of the Republic of France acting through its Southwest Agency
(the "Warrant Holder" or "Soc-Gen").

                                    RECITALS

         A. Brigham Oil & Gas, L.P., a Delaware limited partnership (the
"Borrower"), Bank of Montreal ("BMO") and Soc-Gen (the "Prior Lenders")
previously entered into that certain Credit Agreement dated as of January 26,
1998, as amended by First Amendment to Credit Agreement dated as of August 20,
1998, Second Amendment to Credit Agreement dated as of March 26, 1999, Third
Amendment to Credit Agreement dated as of July 19, 1999 and Fourth Amendment to
Credit Agreement dated as of October 7, 1999 (such Credit Agreement as amended
called the "Prior Credit Agreement"), pursuant to which the Prior Lenders agreed
to make certain loans and extensions of credit to the Borrower as evidenced by
those certain promissory notes in the aggregate principal amount of $75,000,000
(the "Prior Notes").

         B. By Partial Assignment of Notes of even date herewith Shell Capital
Inc. ("SCI") has acquired an interest in the Prior Notes and a like interest in
all security for the payment of the Prior Notes and the performance of the
Borrower's obligations under the Prior Credit Agreement; and

         C. The Prior Lenders and SCI (collectively, the "Lenders") have agreed
to provide senior secured debt in the amount of up to $75,000,000 consisting of
a rearrangement of the Prior Notes and advances to the Borrower, and the
Borrower, BMO as Agent (the "Agent") and the Lenders are entering into that
certain Amended and Restated Credit Agreement (the "Credit Agreement") of even
date herewith which amends and restates in its entirety the Prior Credit
Agreement and Prior Notes; and

         D. Issuer and Soc-Gen now desire to amend certain provisions of the
Warrant Agreement dated as of July 19, 1999 between Issuer and Soc-Gen (the
"Warrant Agreement") in recognition of the benefits Issuer will obtain under the
Credit Agreement.

         NOW THEREFORE, in consideration of the mutual covenants and agreements
herein contained, Issuer and Soc-Gen hereby agree that the Warrant Agreement
shall be amended as follows:

         Section 1. Certain Definitions. As used in this Amendment, the terms
"Agent", "Amendment", "Borrower", "Credit Agreement", "Issuer", "BMO", "SCI",
"Lenders", "Prior Credit Agreement", "Prior Lenders," "Prior Notes", "Soc-Gen"
and "Warrant Agreement" shall have the meanings indicated above; and unless
otherwise defined herein, all terms




<PAGE>   2

beginning with a capital letter which are defined in the Warrant Agreement shall
have the same meanings herein as therein unless the context hereof otherwise
requires.

         Section 2. Amendments to Warrant Agreement.

                  Section 2.1 The definition of Current Warrant Price in section
1. of the Warrant Agreement is hereby deleted in its entirety and the following
is substituted therefor:

                  "Current Warrant Price" shall mean, in respect of a share of
                  Common Stock at any date herein specified, two dollars and two
                  cents ($2.02) per share of Common Stock, subject to adjustment
                  from time to time as provided in this Agreement."

                  Section 2.2 Exhibit A to the Warrant Agreement (Form of
Warrant Certificate) is amended as follows:

                  (a)      to change the reference "of two and 25/100 dollars
                           ($2.25)" to "of two and 02/100 dollars ($2.02)";

                  (b)      to add the following language after the date "July
                           19, 1999, to the next to the last paragraph of the
                           Form of Warrant Certificate: "as amended by that
                           certain First Amendment to Warrant Agreement dated as
                           of February 17, 2000".

                  Section 2.3 All references to the "Credit Agreement" in the
Warrant Agreement shall henceforth refer to the Credit Agreement as defined in
this Amendment, as such Credit Agreement is from time to time further amended,
supplemented or restated.

                  Section 2.4 The second sentence of Section 4.3(b) of the
Warrant Agreement is hereby deleted in its entirety and the following is
substituted therefor:

                  "No adjustment of the number of shares of Common Stock for
                  which a Warrant shall be exercised shall be made under Section
                  4.3(a) of this Agreement upon the issuance of any Additional
                  Shares of Common Stock which are issued pursuant to the
                  exercise of any warrants or other subscription or purchase
                  rights or pursuant to the exercise of any conversion or
                  exchange rights in any Convertible Securities (i) if any such
                  adjustment shall previously have been made upon the issuance
                  of such Convertible Securities (or upon the issuance of any
                  such warrants or other rights) pursuant to Section 4.4 or
                  Section 4.5 of this Agreement, (ii) if no adjustment was
                  required pursuant to such sections upon the issuance of such
                  Convertible Securities, warrants or other rights or (iii) in
                  the event the issuance of such Convertible Securities,
                  warrants or other rights predates or is of the same date as
                  this Agreement, if no adjustment would have been required
                  pursuant to such sections upon such issuance had this
                  Agreement been in effect."




                                       2
<PAGE>   3

         Section 3. Representations and Warranties. Issuer hereby reaffirms that
as of the effective date of this Amendment, the representations and warranties
made by the Issuer in the Warrant Agreement will be true and correct as though
made on and as of the date of this Amendment.

         Section 4. Ratification. Issuer hereby expressly ratifies and affirms
its obligations under the Warrant Agreement as amended by this Amendment and
agrees that the Warrant Agreement as amended by this Amendment remains in full
force and effect.

         Section 5. Issuance of Warrant Certificate. Contemporaneously with the
execution of this Amendment, Issuer will deliver to Soc-Gen a Warrant
Certificate reflecting the amendments described in Section 2.2 hereof.

         Section 6. Governing Law. This Amendment and the rights and obligations
of the parties hereunder and under the Warrant Agreement shall be construed in
accordance with and be governed by the laws of the State of Texas and the United
States of America.

         Section 7. Descriptive Headings, Etc. The descriptive headings of the
several Sections of this Amendment are inserted for convenience only and shall
not be deemed to affect the meaning or construction of any of the provisions
hereof.

         Section 8. Counterparts. This Amendment may be executed in any number
of counterparts and by different parties on separate counterparts and all of
such counterparts shall together constitute one and the same instrument.

                           [SIGNATURES ON NEXT PAGE.]




                                       3
<PAGE>   4


         IN WITNESS WHEREOF, the parties hereto have caused this Amendment to be
duly executed and delivered and effective as of the date first above written.

                                              SOCIETE GENERALE SOUTHWEST AGENCY,
                                              as Warrant Holder



                                              By:
                                                     ---------------------------
                                              Name:  Mark A. Cox
                                              Title: Director



                                              BRIGHAM EXPLORATION COMPANY,
                                              As Issuer



                                              By:
                                                     ---------------------------
                                              Name:  Karen E. Lynch
                                              Title: Vice President




                                       S

<PAGE>   1
                                                                    EXHIBIT 10.6

                           EQUITY CONVERSION AGREEMENT


         This Equity Conversion Agreement (the "Agreement") dated as of February
17, 2000 (the "Closing Date") is entered into by and among Brigham Oil & Gas,
L.P., a Delaware limited partnership (the "Borrower"), Brigham Exploration
Company, a Delaware corporation (the "Issuer") and Shell Capital Inc., a
Delaware corporation and its successors and assigns (the "Convertible Lender").

                                     RECITAL

         WHEREAS, the Borrower and Bank of Montreal, as Agent for the Lenders
have entered into that certain Amended and Restated Credit Agreement of even
date herewith (the "Credit Agreement"), pursuant to the terms and conditions of
which the Convertible Lender has agreed to make certain revolving loans to the
Borrower with such loans to be evidenced by that certain note of even date
therewith made by the Borrower payable to the order of the Convertible Lender in
the aggregate principal amount of $40,000,000 (the "Convertible Note"); and

         WHEREAS, certain sums outstanding on the Convertible Note are to be
convertible into the common stock of the Issuer pursuant to certain terms and
provisions as fully set forth in this Agreement; and

         WHEREAS, the Issuer is the parent company of the Borrower and will
directly and indirectly benefit from the loans and extension of credit by the
Convertible Lender to the Borrower under the Credit Agreement and in
consideration therefore as agreed to enter into this Equity Conversion
Agreement.

         NOW, THEREFORE, known all men by these presents that the Borrower, the
Convertible Lender and the Issuer do hereby agree as follows:

                                    ARTICLE I

                               CERTAIN DEFINITIONS

         Section 1.01 Terms Defined Above. As used in this Agreement, the terms
Borrower, Convertible Lender, Convertible Note, Credit Agreement and Issuer
shall have the meanings indicated above. Capitalized terms not otherwise defined
herein shall have the meanings set forth in the Credit Agreement.

         Section 1.02 Certain Defined Terms. As used herein, the following terms
shall have the following meanings (all terms defined in this Article I, the
Credit Agreement or in other provisions of this Agreement in the singular shall
have the same meanings when used in the plural and vice versa):




<PAGE>   2

         "Additional Shares of Common Stock" shall mean all shares of Common
Stock issued by the Issuer after the Closing Date, other than Common Stock
issued pursuant to this Agreement or the Warrant Agreement.

         "Appraised Value" shall mean, in respect of any share of Common Stock
on any date herein specified, the fair saleable value of such share of Common
Stock (determined without giving effect to the discount for (i) a minority
interest or (ii) any lack of liquidity of the Common Stock or to the fact that
the Issuer may have no class of equity registered under the Exchange Act) as of
the last day of the most recent fiscal month to end prior to such date
specified, based on the value of the Issuer, as determined by an investment
banking firm (approved by the Convertible Lender and the Issuer) in accordance
with such firm's customary practices, divided by the number of outstanding
shares of Common Stock, after giving pro forma effect to the exercise or
conversion of all exercisable or Convertible Securities (including the Warrants)
for Common Stock and the payment of the exercise or conversion price therefor.

         "Board" means the Board of Directors of the Issuer.

         "Book Value" shall mean, in respect of any share of Common Stock on any
date herein specified, the consolidated book value of the Issuer as of the last
day of any month immediately preceding such date, divided by the number of
Outstanding shares of Common Stock, after giving pro forma effect to the
exercise or conversion of all exercisable or Convertible Securities (including
the Warrants) for Common Stock and the payment of the exercise or conversion
price therefor, as determined in accordance with GAAP by any firm of independent
certified public accountants of recognized national standing selected by the
Issuer and reasonably acceptable to the Convertible Lender.

         "Business Day" shall mean each day which is not a day on which banks in
Houston, Texas are generally authorized or obligated by law or executive order
to close.

         "Closing Price" shall mean with respect to a particular security, at
the end of a given day, the last reported sale price regular way or, in case no
such reported sale takes place on such day, the average of the last closing bid
and asked prices regular way, in either case on the principal national
securities exchange on which the applicable security is listed or admitted to
trading, or if not listed or admitted to trading on any national securities
exchange, (i) the closing sale price for such day reported by the NASDAQ Stock
Market if such security is traded over-the-counter and quoted in the NASDAQ
Stock Market, or (ii) if such security is so traded, but not so quoted, the
average of the closing reported bid and asked prices of such security as
reported by the NASDAQ Stock Market or any comparable system.

         "Common Stock" shall mean the common stock, $0.01 par value per share,
of the Issuer, as constituted on the Closing Date, and any capital stock into
which such Common Stock may thereafter be changed, and shall also include (i)
capital stock of the Issuer of any other class (regardless of how denominated)
issued to the holders of shares of Common Stock upon any reclassification
thereof




                                       2
<PAGE>   3

which is also not preferred as to dividends or assets over any other class of
stock of the Issuer and which is not subject to redemption and (ii) shares of
common stock of any successor or acquiring corporation (as defined in Section
2.04(h) of this Agreement) received by or distributed to the holders of Common
Stock of the Issuer in the circumstances contemplated by Section 2.04(h) of this
Agreement.

         "Conversion Date" shall mean the date set out in the Conversion Notice.

         "Conversion Notice" shall mean a written notice from the Convertible
Lender to the Issuer with a copy to the Borrower as provided in Section 2.01(h)
hereof.

         "Conversion Price" shall mean the applicable per share prices as set
out in subsection 2.01 (f).

         "Convertible Amount" shall mean the dollar amount of Convertible Loans
outstanding at any time under the Convertible Note.

         "Convertible Loan Threshold Amount" shall mean at any time the greater
of (i) $45,000,000 less the proceeds from asset sales made by the Issuer used to
permanently repay Loans less the amount of any SCI Loans previously converted to
Common Stock pursuant to the terms hereof and (ii) the Borrowing Base or Target
Asset Value as determined by the Convertible Lender from time to time.

         "Convertible Loans" shall mean those portions of the SCI Loans which
are convertible into Common Stock pursuant to Section 2.01 hereof.

         "Convertible Securities" shall mean evidences of indebtedness, shares
of stock or other securities which are convertible into or exchangeable, with or
without payment of additional consideration in cash or property, for Additional
Shares of Common Stock, either immediately or upon the occurrence of a specified
date or a specified event.

         "Convertible Tranches" shall mean Tranche One, Tranche Two and Tranche
Three as described in Section 2.01(f) hereof.

         "Current Market Price" shall mean, in respect of any share of Common
Stock on any date herein specified, (a) if there shall then be a public market
for the Common Stock, the average Price per share for the 20 trading days
preceding such date; or (b) at any time that there is no public market for the
Common Stock, the fair market value per share of Common Stock on such date as
determined reasonably and in good faith by the board of directors of the Issuer
(determined without giving effect to any discount for a minority interest, any
restrictions on transferability or any lack of liquidity of the Common Stock or
to the fact that the Issuer has no class of equity registered under the Exchange
Act), such fair market value to be determined by reference to the cash price
that would be paid between a fully informed buyer and seller under no compulsion
to buy or sell, provided that (i) if Current Market Price is being determined in
connection with an issuance of shares of Common Stock,




                                       3
<PAGE>   4

solely to one or more Affiliates of the Issuer, then if so requested by the
Convertible Lender, Current Market Price shall be the Appraised Value; and (ii)
Current Market Price shall never be less than Book Value.

         "Outstanding" shall mean, when used with reference to Common Stock, at
any date as of which the number of shares thereof is to be determined, all
issued shares of Common Stock, except shares then owned or held by or for the
account of the Issuer or any Subsidiary, and shall include all shares issuable
in respect of outstanding scrip or any certificates representing fractional
interests in shares of Common Stock.

         "Permitted Issuances" shall mean (i) the issuance of shares of Common
Stock upon exercise of the Warrants or pursuant to this Agreement or the
issuance of Warrants pursuant to this Agreement, (ii) the issuance of shares
relating to any benefit plan, stock option plan or any other compensation plan
offered solely to the Issuer's officers and/or employees, (iii) the issuance of
shares of Common Stock as consideration for the purchase of any property, stock,
business or securities from any Person who is not an Affiliate of the Issuer or
any Subsidiary immediately prior to such transaction whether such shares are
issued directly by the Issuer or by a Subsidiary of the Issuer in connection
with any merger, consolidation or other business combination, (iv) if there
shall then be a public market for the Common Stock, the issuance of shares of
Common Stock upon receipt by the Issuer of no less than the Current Market Price
therefor as described in clause (a) of the definition of "Current Market Price"
and (v) if there shall then be no public market for the Common Stock, the
issuance of shares of Common Stock, warrants or Convertible Securities on terms
that are at least as favorable to the Issuer as terms that could be obtained in
an arm's length transaction with third Persons not Affiliates of the Issuer or
any Subsidiary and for consideration equal to the fair value of such shares as
determined in good faith by a majority of disinterested members of the Board of
the Issuer.

         "Person" means an individual or a corporation, partnership, trust,
incorporated or unincorporated association, limited liability company, joint
venture, joint stock company, government (or an agency or political subdivision
thereof) or other entity of any kind.

         "Price" means the average of the "high" and "low" prices as reported in
The Wall Street Journal's listing for such day (corrected for obvious
typographical errors) or if such shares are not reported in such listing, the
average of the reported "high" and "low" sales prices on the largest national
securities exchange (based on the aggregate dollar value of securities listed)
on which such shares are listed or traded, or if such shares are not listed or
traded on any national securities exchange, then the average of the reported
"high" and "low" sales prices for such shares in the over-the-counter market, as
reported on the National Association of Securities Dealers Automated Quotations
System, or, if such prices shall not be reported thereon, the average of the
closing bid and asked prices so reported, or, if such prices shall not be
reported, then the average of the closing bid and asked prices reported by the
National Quotations Bureau Incorporated. The "average" Price per share for any
period shall be determined by dividing the sum of the Prices determined for the
individual trading days in such period by the number of trading days in such
period.




                                       4
<PAGE>   5

         "SCI Loans" means that portion of the Loans allocable to the
Convertible Lender from time to time, pursuant to the Credit Agreement and SCI
Assignment.

         "Subsidiary" of a Person means (i) a corporation, a majority of whose
stock with voting power, under ordinary circumstances, to elect directors is at
the time of determination, directly or indirectly, owned by such Person or by
one or more Subsidiaries of such Person, or (ii) any other entity (other than a
corporation) in which such Person or one or more Subsidiaries of such Person,
directly or indirectly, at the date of determination thereof has at least a
majority ownership interest.

         "Warrant Agreement" shall mean that certain Warrant Agreement between
Issuer and Convertible Lender of even date herewith.

         "Warrants" shall mean one or more Warrants to be issued by the Issuer
each, in the form attached as Exhibit A to the Warrant Agreement.

                                   ARTICLE II

                                   CONVERSION

         Section 2.01 Convertible Lender Elected Conversions. Up to $30,000,000
of the SCI Loans shall constitute Convertible Loans, determined as follows:

         (a) $15,000,000 of SCI Loans shall be Convertible Loans.

         (b) An additional $5,000,000 of SCI Loans shall be Convertible Loans if
the total principal amount of the Loans outstanding exceeds the Convertible Loan
Threshold Amount plus $15,000,000.

         (c) An additional $5,000,000 of SCI Loans shall be Convertible Loans if
the total principal amount of the Loans outstanding exceeds the Convertible Loan
Threshold Amount plus $20,000,000.

         (d) An additional $5,000,000 of SCI Loans shall be Convertible Loans if
the total principal amount of the Loans outstanding exceeds the Convertible Loan
Threshold Amount plus $25,000,000.

         (e) Once SCI Loans are deemed to be Convertible Loans pursuant to
clauses (a), (b), (c) and (d) above such Convertible Loans shall be the last SCI
Loans to be repaid under the Convertible Note, other than through conversion
under this Agreement.

         (f) Convertible Amounts shall be convertible at the following
Conversion Prices:

                  (i) the first $10,000,000 in Convertible Amounts (Tranche One)
         shall be convertible at $3.90 per share;




                                       5
<PAGE>   6

                  (ii) the Convertible Amounts in excess of $10,000,000 and up
         to $20,000,000 (Tranche Two) shall be convertible at $6.00 per share;
         and

                  (iii) the Convertible Amounts in excess of $20,000,000
         (Tranche Three) shall be convertible at $8.00 per share.

         (g) The Convertible Lender shall have the right to convert all or any
portion of the Convertible Amount into Common Stock at any time and from time to
time (provided, however, such portion shall not be less than $5,000,000);
provided that all of Tranche One shall be converted before any portion of
Tranche Two shall be converted, and all of Tranche Two shall be converted before
any portion of Tranche Three shall be converted.

         (h) To convert, the Convertible Lender shall deliver a Conversion
Notice not more than 60 days nor less than 15 days prior to the Conversion Date
(which must be at least 90 days after the Closing Date), which notice shall set
out the amount of the SCI Loans to be so converted, the applicable Conversion
Tranche or Tranches, Conversion Price or Prices, the number of shares of Common
Stock to be delivered upon such conversion and the Conversion Date. The number
of shares of Common Stock to be delivered upon a conversion shall be the
quotient obtained by dividing the amount of the SCI Loans (of the applicable
Conversion Tranche) to be converted by the applicable Conversion Price. If
Eurodollar Loans are outstanding and are to be repaid pursuant to any such
conversion, the Conversion Date must be a date which coincides with the last day
of the appropriate Eurodollar Interest Period.

         (i) Upon any repayment of the SCI Loans, whether at Maturity or as a
prepayment (whether or not required pursuant to Section 2.07 of the Credit
Agreement), which reduces the outstanding principal balance thereof below the
then existing Convertible Amount, Tranche One shall be deemed paid first,
Tranche Two shall be deemed paid second and Tranche Three shall be deemed paid
last, and the following shall apply:

                           (i) to the extent the provisions of clauses (ii) and
                  (iii) below are not applicable with respect to such payment,
                  the Convertible Lender's Warrants shall be exercisable in
                  accordance with the terms thereof.

                           (ii) If such repayment is made on or before the six
                  (6) month anniversary of the Closing Date, the Borrower may
                  elect to repay the outstanding principal amount of the
                  Convertible Loans so repaid at the greater of (x) 125% of par
                  or (y) $5,000,000 plus the principal amount at par less the
                  actual interest earned from the Closing Date on the
                  Convertible Amount so repaid, and in such event the conversion
                  rights with respect to the Convertible Amount so repaid shall
                  be automatically canceled.

                           (iii) From and after the six (6) month anniversary of
                  Closing Date, the Borrower may irrevocably elect by written
                  notice to the Convertible Lender, such




                                       6
<PAGE>   7

                  notice given no more than 60 or no less than 30 days prior to
                  the repayment date selected by the Borrower, subject to the
                  prior conversion of any Convertible Amount by the Convertible
                  Lender, to repay all or a portion of the Convertible Amount of
                  the SCI Loans at the following premiums to par:

                           If paid between the following dates:

                           Six month anniversary to December 31, 2000       150%
                           January 1, 2001 to June 30, 2001                 140%
                           July 1, 2001 to December 31, 2001                130%
                           January 1, 2002 to June 30, 2002                 120%
                           July 1, 2002 to December 31, 2002                110%

                  Any Convertible Amount not converted by the Convertible Lender
                  prior to the repayment date elected by the Borrower shall be
                  repaid as aforesaid. If Borrower timely repays the Convertible
                  Amount so noticed on the repayment date, the conversion rights
                  with respect to the Convertible Amount so repaid shall be
                  automatically canceled.

         Section 2.02 Borrower Forced Conversion. At any time after the first
anniversary of the Closing Date, the Borrower shall have the right to require
the conversion of all or any portion of the Convertible Amount of the SCI Loans
into Common Stock upon 5 business days' notice, provided that there exists no
Event of Default nor an event which would with the passage of time result in an
Event of Default, and provided that the following additional conditions are met:

         (a) All or any portion of the Tranche One Convertible Amount may be
converted (provided, however, such portion shall not be less than $5,000,000) if
the Closing Price of the Common Stock has (i) equaled or exceeded 200% of the
Conversion Price for Tranche One on each of the five (5) Business Days preceding
the date the forced conversion election is made and (ii) averaged 200% or more
of the Conversion Price for Tranche One for the two months preceding the date
the forced conversion election is made, provided that the first day of the two
month time period shall not occur prior to the completion of 50% of the primary
wells on the CAPEX Plan approved at Closing, as such plan is amended from time
to time with the consent of the Convertible Lender.

         (b) All or any portion of the Tranche Two Convertible Amount may be
converted (provided, however, such portion shall not be less than $5,000,000) if
the Closing Price of the Common Stock has (i) equaled or exceeded 150% of the
Conversion Price for Tranche Two on each of the five (5) Business Days preceding
the date the forced conversion election is made and (ii) has averaged 150% or
more of the Conversion Price for Tranche Two for the two months preceding the
date the forced conversion election is made, provided that the first day of the
two month time period shall not occur prior to the completion of 50% of the
primary wells on the CAPEX Plan approved at Closing, as such plan is amended
from time to time with the consent of the Convertible Lender.




                                       7
<PAGE>   8

         (c) All or any portion of the Tranche Three Convertible Amount may be
converted (provided, however, such portion shall not be less than $5,000,000) if
the Closing Price of the Common Stock has (i) equaled or exceeded 150% of the
Conversion Price for Tranche Three on each of the five (5) Business Days
preceding the date the forced conversion election is made and (ii) has averaged
150% or more of the Conversion Price for Tranche Three for the two months
preceding the date the forced conversion election is made, provided that the
first day of the two month time period shall not occur prior to the completion
of 50% of the primary wells on the CAPEX Plan approved at Closing, as such plan
is amended from time to time with the consent of the Convertible Lender.

         (d) All or any portion of the Convertible Amount (provided, however,
such portion shall not be less than $5,000,000) may be converted if the Issuer
conducts a public offering of Common Stock at a price of $9 or more per share of
Common Stock within twelve (12) months after the Closing Date, provided that the
Convertible Lender is permitted to sell in such public offering all or any
portion of the Common Stock acquired pursuant to such conversion on terms no
less favorable to the Convertible Lender than those contained in the
Registration Rights Agreement.

         (e) Notwithstanding anything stated in this Section 2.02 to the
contrary, the Borrower may not elect, pursuant to this Section 2.02, to convert
an amount of SCI Loans in excess of $20,000,000, unless any remaining balance of
the Convertible Note is repaid pursuant to the terms of the Credit Agreement.

         Section 2.03 Issuance of Common Stock on Conversion. The Issuer shall
deliver or cause to be delivered to the Convertible Lender on the Conversion
Date certificates representing the number of fully paid and nonassessable shares
of Common Stock into which Conversion Amount is to be converted in accordance
with the provisions hereof. Such conversion shall be deemed to have been made at
the close of business on the date the certificates are delivered and the
principal of the SCI Loans shall be deemed to be repaid by an amount equal to
such converted Conversion Amount on such date. Accrued interest on such SCI
Loans shall remain due and owing and payable at the time and as otherwise
provided in the Credit Agreement.

         No fractional shares of Common Stock shall be issued upon conversion.
Instead of any fractional shares of Common Stock which would otherwise be
issuable upon conversion, the Issuer shall pay a cash adjustment in respect of
such fraction in an amount equal to such fraction of a share multiplied by the
Conversion Price.

         Section 2.04 Adjustments and Other Rights. The Conversion Price and the
number of shares issuable upon conversion rights listed in this Agreement shall
be subject to adjustment from time to time as follows:

         (a) Stock Dividends, Subdivisions and Combinations. If at any time the
Issuer shall:




                                       8
<PAGE>   9

                  (i) take a record of the holders of its Common Stock for the
         purpose of entitling them to receive a dividend payable in, or other
         distribution of, Additional Shares of Common Stock,

                  (ii) subdivide its outstanding shares of Common Stock into a
         larger number of shares of Common Stock, or

                  (iii) combine its outstanding shares of Common Stock into a
         smaller number of shares of Common Stock,

then (i) the number of shares of Common Stock for which conversion rights are
exercisable immediately after the occurrence of any such event shall be adjusted
to equal the number of shares of Common Stock which a record holder of the same
number of shares of Common Stock for which Convertible Loans are exercisable
immediately prior to the occurrence of such event would own or be entitled to
receive after the happening of such event, and (ii) the Conversion Price shall
be adjusted to equal the Conversion Price multiplied by a fraction, the
numerator of which shall be the number of shares of Common Stock for which
Convertible Loans are exercisable immediately prior to the adjustment and the
denominator of which shall be the number of shares for which Convertible Loans
are exercisable immediately after such adjustment.

         (b) Certain Other Distributions. If at any time the Issuer shall take a
record of the holders of its Common Stock for the purpose of entitling them to
receive any dividend or other distribution of:

                  (i) cash;

                  (ii) any evidences of its indebtedness (other than Convertible
         Securities), any shares of its stock (other than Additional Shares of
         Common Stock or Convertible Securities) or any other securities or
         property of any nature whatsoever (other than cash); or

                  (iii) any warrants or other rights to subscribe for or
         purchase any evidences of its indebtedness (other than Convertible
         Securities), any shares of its stock (other than Additional Shares of
         Common Stock or Convertible Securities) or any other securities or
         property of any nature whatsoever;

then (i) the number of shares of Common Stock for which Convertible Loans are
exercisable shall be adjusted to equal the product obtained by multiplying the
number of shares of Common Stock for which Convertible Loans are exercisable
immediately prior to such adjustment by a fraction (A) the numerator of which
shall be the Current Market Price per share of Common Stock at the date of
taking such record and (B) the denominator of which shall be such Current Market
Price per share of Common Stock, minus the amount allocable to one share of
Common Stock of any such cash so distributable and of the fair value (as
determined reasonably and in good faith by the board of directors of the Issuer)
of any and all such evidences of indebtedness, shares of stock, other securities




                                       9
<PAGE>   10

or property or warrants or other subscription or purchase rights so
distributable, and (ii) the Conversion Price shall be adjusted to equal (A) the
Conversion Price multiplied by the number of shares of Common Stock for which
Convertible Loans are exercisable immediately prior to the adjustment divided by
(B) the number of shares for which Convertible Loans are exercisable immediately
after such adjustment. A reclassification of the Common Stock (other than a
change in par value, or from par value to no par value or from no par value to
par value) into shares of Common Stock and shares of any other class of stock
shall be deemed a distribution by the Issuer to the holders of its Common Stock
of such shares of such other class of stock within the meaning of this Section
2.04(b) and, if the outstanding shares of Common Stock shall be changed into a
larger or smaller number of shares of Common Stock as a part of such
reclassification, such change shall be deemed a subdivision or combination, as
the case may be, of the outstanding shares of Common Stock within the meaning of
Section 2.04(a) of this Agreement.

         (c) Issuance of Additional Shares of Stock.

                  (i) If at any time the Issuer shall (except as hereinafter
         provided) issue or sell any Additional Shares of Common Stock, other
         than Permitted Issuances, for consideration in an amount per Additional
         Share of Common Stock less than the Current Market Price, then the
         Conversion Price shall be adjusted by multiplying the Conversion Price
         by a fraction, the numerator of which shall be (A) an amount equal to
         the sum of (X) the number of shares of Common Stock outstanding
         immediately prior to such issuance or sale multiplied by the Current
         Market Price immediately prior to the first to occur of (i) Board
         action by the Issuer authorizing such action or (ii) the public
         announcement of an intent to take such action, plus (Y) the
         consideration, if any, received by the Issuer upon such issuance or
         sale, and the denominator of which shall be (B) the total number of
         shares of Common Stock outstanding immediately after such issuance or
         sale multiplied by the Current Market Price as determined in clause (A)
         above.

                  (ii) The provisions of Section 2.04(c)(i) of this Agreement
         shall not apply to any issuance of Additional Shares of Common Stock
         for which an adjustment is provided under Sections 2.04(a) or 2.04(b)
         of this Agreement. No adjustment of the number of shares of Common
         Stock for which Convertible Loans are exercisable shall be made under
         Section 2.04(c) of this Agreement upon the issuance of any Additional
         Shares of Common Stock which are issued pursuant to the exercise of any
         warrants or other subscription or purchase rights or pursuant to the
         exercise of any conversion or exchange rights in any Convertible
         Securities (i) if any such adjustment shall previously have been made
         upon the issuance of such warrants or other rights or upon the issuance
         of such Convertible Securities (or upon the issuance of any such
         warrants or other rights) pursuant to Section 2.04(d) or Section
         2.04(e) of this Agreement, (ii) if no adjustment was required pursuant
         to such sections upon the issuance of such Convertible Securities,
         warrants or other rights or (iii) in the event the issuance of such
         Convertible Securities, warrants or other rights predates or is of the
         same date as this Agreement, if no adjustment would have been required
         pursuant to such sections upon such issuance had this Agreement been in
         effect.




                                       10
<PAGE>   11

         (d) Issuance of Warrants or Other Rights. If at any time the Issuer
shall take a record of the holders of its Common Stock for the purpose of
entitling them to receive a distribution of, or shall in any manner (whether
directly or by assumption in a merger in which the Issuer is the surviving
corporation) issue or sell, any warrants or other rights to subscribe for or
purchase any Additional Shares of Common Stock or any Convertible Securities,
other than Permitted Issuances, whether or not the rights to exchange or convert
thereunder are immediately exercisable, and if the price per share for which
Common Stock is issuable upon the exercise of such warrants or other rights or
upon conversion or exchange of such Convertible Securities shall be less than
the Current Market Price in effect immediately prior to the time of such
distribution, issue or sale, then the Conversion Price shall be adjusted as
provided in Section 2.04(a) of this Agreement on the basis that (A) the maximum
number of Additional Shares of Common Stock issuable pursuant to all such
warrants or other rights or necessary to effect the conversion or exchange of
all such Convertible Securities shall be deemed to be outstanding immediately
following such issuance, (B) the price per share for such Additional Shares of
Common Stock shall be deemed to be the lowest possible price per share in any
range of prices per share at which such Additional Shares of Common Stock are
available to such holders, and (C) the Issuer shall be deemed to have received
all of the consideration payable therefor, if any, as of the date of the actual
issuance of such warrants or other rights. No further adjustments of the
Conversion Price shall be made upon the actual issuance of such Common Stock or
of such other rights or upon exercise of such warrants or other rights or upon
the actual issuance of such Common Stock upon such conversion or exchange of
such Convertible Securities.

         (e) Issuance of Convertible Securities. If at any time the Issuer shall
take a record of the holders of its Common Stock for the purpose of entitling
them to receive a distribution of, or shall in any manner (whether directly or
by assumption in a merger in which the Issuer is the surviving corporation)
issue or sell, any Convertible Securities, other than Permitted Issuances,
whether or not the rights to exchange or convert thereunder are immediately
exercisable, and if the price per share for which Common Stock is issuable upon
such conversion or exchange shall be less than the Current Market Price in
effect immediately prior to the time of such issue or sale of Convertible
Securities, then the Conversion Price shall be adjusted as provided in Section
2.04(a) of this Agreement on the basis that (A) the maximum number of Additional
Shares of Common Stock necessary to effect the conversion or exchange of all
such Convertible Securities shall be deemed to be outstanding immediately
following such issuance, (B) the price per share of such Additional Shares of
Common Stock shall be deemed to be the lowest possible price in any range of
prices at which such Additional Shares of Common Stock are available to such
holders, and (C) the Issuer shall be deemed to have received all of the
consideration payable therefor, if any, as of the date of actual issuance of
such Convertible Securities. No adjustment of the Conversion Price shall be made
under this Section 2.04(e) upon the issuance of any Convertible Securities which
are issued pursuant to the exercise of any warrants or other subscription or
purchase rights therefor if any such adjustments shall previously have been made
upon the issuance of such warrants or other rights pursuant to Section 2.04(d)
of this Agreement. No further adjustments of the Conversion Price shall be made
upon the actual issue of such Common Stock upon conversion or exchange of such
Convertible Securities and, if any issue or sale of such Convertible Securities
is made upon exercise of any warrant or other right to purchase any such
Convertible Securities for which adjustments of the Conversion Price have been
or are to




                                       11
<PAGE>   12

be made pursuant to other provisions of this Section 2.04, no further
adjustments of the Conversion Price shall be made by reason of such issue or
sale.

         (f) Superseding Adjustment. If, at any time after any adjustment of the
Conversion Price shall have been made pursuant to Section 2.04(d) or Section
2.04(e) of this Agreement as the result of any issuance of warrants, options,
rights or Convertible Securities, and such warrants, options or rights, or the
right of conversion or exchange in such other Convertible Securities, shall
expire, and all or a portion of such warrants, options or rights, or the right
of conversion or exchange with respect to all or a portion of such other
Convertible Securities, as the case may be, shall not have been exercised, then
such previous adjustment shall be rescinded and annulled in whole or in part, as
applicable, and, if applicable, the Conversion Price shall be recalculated as if
all such expired and unexercised warrants, options, rights or Convertible
Securities had never been issued.

         (g) Other Provisions Applicable to Adjustments Under This Section. The
following provisions shall be applicable to the making of adjustments of the
number of shares of Common Stock for which Convertible Loans are exercisable
provided for in this Section 2.04:

                  (i) Computation of Consideration. To the extent that any
         Additional Shares of Common Stock shall be issued for cash
         consideration, the consideration received by the Issuer therefor shall
         be the amount of the cash received by the Issuer therefor, or, if such
         Additional Shares of Common Stock are sold to underwriters or dealers
         for public offering without a subscription offering, the initial public
         offering price (in any such case subtracting any amounts paid or
         receivable for accrued interest or accrued dividends, but not
         subtracting any compensation, discounts or expenses paid or incurred by
         the Issuer for and in the underwriting of, or otherwise in connection
         with, the issuance thereof). To the extent that such issuance shall be
         for a consideration other than cash, then, except as herein otherwise
         expressly provided, the amount of such consideration shall be deemed to
         be the fair value of such consideration at the time of such issuance as
         determined reasonably and in good faith by a majority of the
         disinterested members of the Board of the Issuer.

                  (ii) When Adjustments to Be Made. The adjustments required by
         this Section 2.04 shall be made whenever and as often as any specified
         event requiring an adjustment shall occur, except that any adjustment
         to the number of shares for which Convertible Loans are exercisable
         that would otherwise be required may be postponed (except in the case
         of a subdivision or combination of shares of the Common Stock, as
         provided for in Section 2.04(a) of this Agreement) up to, but not
         beyond, the date and time of exercise of conversion rights if such
         adjustment either by itself or with other adjustments not previously
         made adds or subtracts less than 1% to the number of shares of Common
         Stock for which conversion rights are exercisable immediately prior to
         the making of such adjustment. Any adjustment representing a change of
         less than such minimum amount (except as aforesaid) which is postponed
         shall be carried forward and made as soon as such adjustment, together
         with other adjustments required by this Section 2.04 and not previously
         made, would result in a minimum adjustment or on the date of exercise.
         For the purpose of any adjustment, any




                                       12
<PAGE>   13

         specified event shall be deemed to have occurred at the close of
         business on the date of its occurrence.

                  (iii) Fractional Interests. In computing adjustments under
         this Section 2.04, fractional interests in Common Stock resulting from
         an issuance of additional Common Stock to Convertible Lender pursuant
         to this Section 4 shall be taken into account to the nearest 1/10th of
         a share.

                  (iv) When Adjustment Not Required. If the Issuer shall take a
         record of the holders of its Common Stock for the purpose of entitling
         them to receive a dividend or distribution or subscription or purchase
         rights and shall, thereafter and before the distribution to
         stockholders thereof, legally abandon its plan to pay or deliver such
         dividend, distribution, subscription or purchase rights, no adjustment
         shall be required by reason of the taking of such record and any such
         adjustment previously made in respect thereof shall be rescinded and
         annulled.

                  (v) Escrow of Warrant Stock. If after any property becomes
         distributable pursuant to this Section 2.04 by reason of the taking of
         any record of the holders of Common Stock, but prior to the occurrence
         of the event for which such record is taken, Convertible Lender
         exercises its conversion rights, any Additional Shares of Common Stock
         issuable upon exercise of such conversion rights by reason of such
         adjustment shall be held in escrow for Convertible Lender by the Issuer
         to be issued to Convertible Lender upon and to the extent that the
         event actually takes place, upon payment of the balance, if any, of the
         Conversion Price for such Common Stock at such date (after taking into
         account any overpayment of the Conversion Price made at any time of the
         initial exercise of conversion rights). Notwithstanding any other
         provision to the contrary herein, if the event for which such record
         was taken fails to occur or is rescinded, then such escrowed shares
         shall be canceled by the Issuer and escrowed property returned.

         (h) Reorganization, Reclassification, Merger, Consolidation or
Disposition of Assets. In the event the Issuer shall reorganize its capital,
reclassify its capital stock, consolidate or merge with and into another
corporation or entity (where the Issuer is not the surviving corporation or
where there is a change in or distribution with respect to the Common Stock of
the Issuer), or sell, transfer or otherwise dispose of all or substantially all
its property, assets or business to another corporation or entity and, pursuant
to the terms of such reorganization, reclassification, merger, consolidation or
disposition of assets, shares of common stock of the successor or acquiring
corporation or entity, or any cash, shares of stock or other securities or
property of any nature whatsoever (including warrants or other subscription or
purchase rights) in addition to or in lieu of common stock of the successor or
acquiring corporation or entity ("Other Property"), are to be received by or
distributed to the holders of Common Stock of the Issuer, then the Issuer shall,
as a condition precedent to such transaction, cause effective provisions to be
made so that the Convertible Lender shall have the right thereafter to receive,
upon exercise of its conversion rights, solely the number of shares of "common
stock of the successor or acquiring corporation" or of the Issuer, if it is the
surviving corporation, and




                                       13
<PAGE>   14

Other Property receivable upon or as a result of such reorganization,
reclassification, merger, consolidation or disposition of assets, by a holder of
the number of shares of Common Stock for which Convertible Loans are exercisable
immediately prior to such event. In case of any such reorganization,
reclassification, merger, consolidation or disposition of assets, such
provisions shall include the express assumption by the successor or acquiring
corporation or entity (if other than the Issuer) of the due and punctual
observance and performance of each and every covenant and condition of this
Agreement to be performed and observed by the Issuer and all the obligations and
liabilities hereunder, subject to such modifications as may be deemed
appropriate (as determined by resolution of the board of directors of the
Issuer) to provide for adjustments of shares of the Common Stock for which
Convertible Loans are exercisable which shall be as nearly equivalent as
practicable to the adjustments provided for in this Section 2.04. For purposes
of this Section 2.04(h), "common stock of the successor or acquiring
corporation" shall include stock of such corporation of any class which is not
preferred as to dividends or assets over any other class of stock or other
securities of such corporation or entity and which is not subject to redemption
and shall also include any evidences of indebtedness, shares of stock or other
securities which are convertible into or exchangeable for any such stock or
other securities, either immediately or upon the arrival of a specified date or
the happening of a specified event, and any warrants or other rights to
subscribe for or purchase any such stock or securities. The foregoing provisions
of this Section 2.04(h) shall similarly apply to successive reorganizations,
reclassifications, mergers, consolidations or disposition of assets.

         (i) Notice of Adjustments. Whenever the number of shares of Common
Stock for which Convertible Loans are exercisable, or whenever the price at
which a share of such Common Stock may be purchased upon exercise of conversion
rights, shall be adjusted pursuant to Section 2.04, the Issuer shall forthwith
prepare a certificate to be executed by the chief financial officer of the
Issuer setting forth, in reasonable detail, the event requiring the adjustment
and the method by which such adjustment was calculated (including a description
of the basis on which the board of directors of the Issuer determined the fair
value of any evidences of indebtedness, shares of stock, other securities or
property or warrants or other subscription or purchase rights referred to in
Section 2.04 of this Agreement), specifying the number of shares of Common Stock
for which conversion rights are exercisable and (if such adjustment was made
pursuant to Section 2.04(h) of this Agreement) describing the number and kind of
any other shares of stock or Other Property for which conversion rights are
exercisable, and any change in the purchase price or prices thereof, after
giving effect to such adjustment or change. The Issuer shall promptly cause a
signed copy of such certificate to be delivered to the Convertible Lender. The
Issuer shall keep at its office or agency copies of all such certificates and
cause the same to be available for inspection at said office during normal
business hours by the Convertible Lender.

         (j) Notice of Certain Corporate Action. The Convertible Lender shall be
entitled to the same rights to receive notice of corporate action as any holder
of Common Stock.

         (k) No Impairment. The Issuer shall not by any action including,
without limitation, amending its certificate of incorporation or through any
reorganization, transfer of assets, consolidation, merger, dissolution, issue or
sale of securities or any other voluntary action, avoid or




                                       14
<PAGE>   15

seek to avoid the observance or performance of any of the terms of this
Agreement, but will at all times in good faith assist in the carrying out of all
such terms and in the taking of all such actions as may be necessary or
appropriate to protect the rights of the Convertible Lender against impairment.
Without limiting the generality of the foregoing, the Issuer will use reasonable
good faith efforts to obtain all such authorizations, exemptions or consents
from any public regulatory body having jurisdiction thereof as may be necessary
to enable it to perform its obligations under this Agreement.

         Upon the request of the Convertible Lender, the Issuer will, at any
time during the period this Agreement is in effect, acknowledge in writing, in
form satisfactory to the Convertible Lender, the continuing validity of this
Agreement and the obligations of the Issuer hereunder.

         Section 2.05 Reservation of Shares. The Issuer covenants that it will
at all times reserve and keep available, free from preemptive rights, out of its
authorized but unissued shares of Common Stock, solely for the purpose of issue
upon conversion of the Convertible Loans as herein provided, such number of
shares of Common Stock as shall then be issuable upon the conversion of the full
potential Conversion Amount. The Issuer covenants that all shares of Common
Stock which shall be so issuable shall, upon issuance, be duly and validly
issued and fully paid and non-assessable. The Issuer shall from time to time, in
accordance with applicable law, increase the authorized amount of its Common
Stock if at any time the authorized amount of shares of Common Stock remaining
unissued shall not be sufficient to permit the conversion of the full potential
Conversion Amount.

         Section 2.06 Certain Covenants. Before taking any action which would
cause an adjustment reducing the Conversion Price below the then stated or par
value of the Common Stock issuable upon conversion, the Issuer will take any
corporate action which may, in the opinion of its counsel, be necessary in order
that the Issuer may validly and legally issue fully paid and non-assessable
shares of such Common Stock at such adjusted conversion price.

         Section 2.07 Certain Notices. In case:

                  (i) the Issuer shall authorize the distribution to all holders
         of Common Stock of evidences of its indebtedness or assets (other than
         cash dividends or other cash distributions paid out of surplus); or

                  (ii) The Issuer shall authorize the granting to the holders of
         Common Stock of rights or warrants to subscribe for or purchase any
         shares of capital stock or any class or of any other rights; or

                  (iii) of any reclassification of the capital stock of the
         Issuer (other than a subdivision or combination of its outstanding
         shares of Common Stock), or of any consolidation or merger to which the
         Issuer is a party and for which approval of any stockholders of the
         Issuer is required, or of the sale, lease, or transfer of all or
         substantially all of the property of the Issuer; or




                                       15
<PAGE>   16

                  (iv) of the voluntary or involuntary dissolution, liquidation,
         or winding up of the Issuer;

then, in each case, the Issuer shall provide to the Convertible Lender at least
20 days, but not more than 45 days, prior to the applicable record or effective
date hereinafter specified, a notice stating (x) the date on which a record is
to be taken for the purpose of such dividend, distribution, rights, or warrants,
or, if a record is not to be taken, the date as of which the holders of Common
Stock of record to be entitled to such dividend, distribution, rights, or
warrants are to be determined, or (y) the date on which such reclassification,
consolidation, merger, sale, lease, transfer, dissolution, liquidation, or
winding up is expected to become effective, and the date as of which it is
expected that holders of Common Stock of record shall be entitled to exchange
their shares of Common Stock for securities or other property deliverable upon
such reclassification, consolidation, merger, sale, lease, transfer,
dissolution, liquidation, or winding up.

         Section 2.08 Board of Directors.

                  (a) The Convertible Lender shall have the right to name one
         member of the Board of the Issuer, during such time that the
         Convertible Lender owns 10% or more of the Common Stock of the Issuer.

                  (b) The Convertible Lender shall, as an observer only, have
         the right to send a representative, and such representative shall have
         a right to attend, as an observer only, all Board meetings of the
         Issuer, during such time that the Convertible Lender holds Warrants or
         Convertible Loans convertible into 10% or more of the Common Stock of
         the Issuer, and the Issuer shall give the same prior notice to the
         Convertible Lender of all Board Meetings as is given to the other Board
         members.

                                   ARTICLE III

                                  MISCELLANEOUS

         Section 3.01 Governing Law. This Agreement shall be governed by and
construed in accordance with the laws of the State of Texas.

         Section 3.02 Headings. The headings contained in this Agreement are for
reference purposes only and shall not affect in any way the meaning or
interpretation of this Agreement.

         Section 3.03 No Third Party Beneficiaries. Except as expressly provided
herein nothing in this Agreement shall entitle any person other than the parties
signatory hereto or their respective successors and assigns permitted hereby to
any claim, cause of action, remedy or right of any kind.

         Section 3.04 Successors and Assigns. All of the terms, covenants,
representations, warranties, and conditions of this Agreement shall be binding
on, and inure to the benefit of, and be




                                       16
<PAGE>   17

enforceable by the parties hereto and their respective permitted successors and
assigns. This Agreement and the rights and obligations hereunder shall be
transferred automatically from the Convertible Lender to any Person to whom the
Convertible Note, any Warrants or any Registrable Securities (as such term is
defined in the Registration Rights Agreement) are transferred, provided that (x)
the Issuer is given written notice of the transfer and the name, address,
telephone number and facsimile number of the transferee, (y) the subsequent
transferee agrees in writing to be bound by all the terms of this Agreement and
(z) at the Issuer's option, the Issuer is provided an opinion of counsel,
reasonably acceptable to the Issuer and the fees of which the Issuer shall pay,
that such transfer does not require registration under the Securities Act of
1933, as amended.

         Section 3.05 Entire Agreement. This Agreement, the Registration Rights
Agreement, the Credit Agreement, the Loan Documents and the Warrant Agreement
are intended by the parties hereto to be a complete and exclusive statement of
the agreement and understanding of the parties in respect to the subject matter
contained herein. These agreements supersede all prior agreements or
understandings among the parties with respect to such subject matter.

         Section 3.06 Binding Effect. This Agreement shall be binding upon and
shall inure to the benefit of the parties signatory hereto and their respective
successors and assigns.

         Section 3.07 Counterparts. This Agreement may be executed in any number
of counterparts, no one of which needs to be executed by all the parties, and
this Agreement shall be binding upon all the parties with the same force and
effect as if all the parties had signed the same document, and each such signed
counterpart shall constitute an original of this Agreement.

         Section 3.08 Amendments. This Agreement may be amended and the
observance of any term of this Warrant may be waived only with the written
consent of all the parties hereto.

         Section 3.09 Notice. All notices hereunder shall be in writing and
shall be effective (a) on the day on which delivered if delivered personally or
transmitted by telex or telegram or telecopier with evidence of receipt, (b) one
Business Day after the date on which the same is delivered to a nationally
recognized overnight courier service with evidence of receipt, or (c) five
Business Days after the date on which the same is deposited, postage prepaid, in
the U.S. mail, sent by certified or registered mail, return receipt requested,
and addressed to the party to be notified at the address indicated in the Credit
Agreement for the Issuer, or at the address for the Convertible Lender set forth
in the registry maintained by the Issuer or at such other address and/or
telecopy or telex number and/or to the attention of such other person as the
Issuer or the Convertible Lender may designate by ten-day advance written
notice.




                                       17
<PAGE>   18

         EXECUTED as of the date first written above.

                                                  BRIGHAM EXPLORATION COMPANY


                                                  By:
                                                       -------------------------
                                                  Name:  Curtis F. Harrell
                                                  Title: Chief Financial Officer


                                                  BRIGHAM OIL & GAS L.P.


                                                  By:
                                                       -------------------------
                                                  Name:  Curtis F. Harrell
                                                  Title: Chief Financial Officer


                                                  SHELL CAPITAL INC.


                                                  By:
                                                       -------------------------
                                                  Name:  Robert L. Roberts
                                                  Title: Vice-President




                                       18

<PAGE>   1
                                                                    EXHIBIT 10.7



THIS WARRANT AGREEMENT AND THE SECURITIES ISSUABLE UPON EXERCISE OF THE WARRANTS
HEREIN HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED, OR
THE SECURITIES LAWS OF ANY STATE AND MAY NOT BE TRANSFERRED IN VIOLATION OF SUCH
ACT, THE RULES AND REGULATIONS PROMULGATED THEREUNDER, ANY SUCH STATE SECURITIES
LAWS OR THE PROVISIONS OF THIS WARRANT AGREEMENT.



                                WARRANT AGREEMENT


                                     for the


                            Purchase of Common Stock

                                 By and Between



                           BRIGHAM EXPLORATION COMPANY

                                       and

                               SHELL CAPITAL INC.



                                   Dated as of

                                February 17, 2000





<PAGE>   2




                                TABLE OF CONTENTS

<TABLE>
<CAPTION>
                                                                                                              Page

<S>      <C>                                                                                                  <C>
1.       DEFINITIONS.............................................................................................1

2.       ISSUANCE AND EXERCISE OF WARRANTS.......................................................................6

         2.1      Issuance of Warrants...........................................................................6

         2.2      Manner of Exercise.............................................................................6

         2.3      Payment of Taxes...............................................................................7

         2.4      Fractional Shares..............................................................................7

         2.5      Continued Validity.............................................................................8

         2.6      Conditions to Exercise.........................................................................8

3.       TRANSFERS, DIVISION AND COMBINATION.....................................................................8

         3.1      Transfer.......................................................................................8

         3.2      Division and Combination.......................................................................9

         3.3      Expenses.......................................................................................9

         3.4      Maintenance of Books...........................................................................9

4.       ADJUSTMENTS.............................................................................................9

         4.1      Stock Dividends, Subdivisions and Combinations.................................................9

         4.2      Certain Other Distributions...................................................................10

         4.3      Issuance of Additional Shares of Stock........................................................11

         4.4      Issuance of Warrants or Other Rights..........................................................11

         4.5      Issuance of Convertible Securities............................................................12

         4.6      Superseding Adjustment........................................................................13

         4.7      Other Provisions Applicable to Adjustments Under This Section.................................13

         4.8      Reorganization, Reclassification, Merger, Consolidation or Disposition
                  of Assets.....................................................................................14

5.       NOTICES TO WARRANT HOLDERS.............................................................................15

         5.1      Notice of Adjustments.........................................................................15

         5.2      Notice of Certain Corporate Action............................................................15

6.       REPRESENTATIONS AND WARRANTIES.........................................................................16

7.       CERTAIN COVENANTS......................................................................................17

         7.1      No Impairment.................................................................................17

         7.2      Reservation and Authorization of Common Stock; Registration with, or
                  Approval of, any Governmental Authority.......................................................18
</TABLE>


                                       i

<PAGE>   3

<TABLE>
<S>      <C>                                                                                                  <C>
8.       TAKING OF RECORD; STOCK AND WARRANT TRANSFER BOOKS.....................................................18

9.       RESTRICTIONS ON TRANSFERABILITY........................................................................18

         9.1      Restrictive Legend............................................................................18

         9.2      Notice of Proposed Transfers; Requests for Registration.......................................19

         9.3      Incidental Registration.......................................................................19

         9.4      Registration Procedures.......................................................................20

         9.5      Expenses......................................................................................21

         9.6      Indemnification and Contribution..............................................................21

         9.7      Termination of Restrictions...................................................................24

         9.8      Listing on Securities Exchange................................................................24

10.      SUPPLYING INFORMATION..................................................................................25

11.      LOSS OR MUTILATION.....................................................................................25

12.      OFFICE OF THE ISSUER...................................................................................25

13.      APPRAISAL..............................................................................................25

14.      LIMITATION OF LIABILITY; NO RIGHTS AS STOCKHOLDER......................................................25

15.      MISCELLANEOUS..........................................................................................26

         15.1     Non-waiver and Expenses.......................................................................26

         15.2     Notice Generally..............................................................................26

         15.3     Indemnification...............................................................................27

         15.4     Remedies......................................................................................27

         15.5     Successors and Assigns........................................................................27

         15.6     Complete Agreement; Amendment.................................................................27

         15.7     Severability..................................................................................28

         15.8     Headings......................................................................................28

         15.9     Governing Law; Consent to Jurisdiction and Venue..............................................28

         15.10    Consent to Jurisdiction and Venue.............................................................28

         15.11    Counterparts:.................................................................................29

Exhibits:

Exhibit A  -Form of Warrant Certificate...................................................................Exh. A-1


SCHEDULES:

Schedule A   -Capital Stock of the Issuer, Including Shares Subject to
               Outstanding Warrants, Options, Conversion Rights, Etc........................................Sch. A-1
</TABLE>


                                       ii

<PAGE>   4


THIS WARRANT AGREEMENT AND THE SECURITIES ISSUABLE UPON EXERCISE OF THE WARRANTS
HEREIN HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED, OR
THE SECURITIES LAWS OF ANY STATE AND MAY NOT BE TRANSFERRED IN VIOLATION OF SUCH
ACT, THE RULES AND REGULATIONS PROMULGATED THEREUNDER, ANY SUCH STATE SECURITIES
LAWS OR THE PROVISIONS OF THIS WARRANT AGREEMENT.

                                WARRANT AGREEMENT


THIS WARRANT AGREEMENT, dated as of February 17, 2000 (this "Agreement"), is
entered into by and between Brigham Exploration Company, a Delaware corporation
("Issuer"), and Shell Capital Inc. a Delaware corporation (the "Warrant Holder"
or "SCI").

                              W I T N E S S E T H:


                  WHEREAS, Brigham Oil & Gas, L.P., a limited partnership formed
under the laws of the State of Delaware (the "Borrower"), the financial
institutions party to the Credit Agreement referred to below (each a "Lender"
and collectively, the "Lenders"), and the Bank of Montreal, as agent for Lenders
under the Credit Agreement (in such capacity, the "Agent"), are parties to that
certain Amended and Restated Credit Agreement, of even date herewith (as so
amended and restated, the "Credit Agreement"); and

                  WHEREAS, the Issuer has guaranteed the obligations of the
Borrower to the Lenders and the Agent;

                  WHEREAS, as a consequence of the contractual relationships
between the Borrower and the Lenders, the Issuer has and will continue to
receive substantial benefits from the Lenders;

                  WHEREAS, in order to induce the Lenders to enter into the
Credit Agreement, the Issuer has agreed to execute and deliver this Agreement
and to issue to SCI the warrants herein described;

                  NOW, THEREFORE, in consideration of the premises and mutual
covenants contained herein, the receipt and sufficiency of which is hereby
acknowledged, the parties hereby stipulate and agree as follows:

1.       DEFINITIONS

         Capitalized terms not otherwise defined herein shall have the meaning
         set forth in the Credit Agreement. As used in this Agreement, the
         following terms have the respective meanings set forth below:

         "Additional Shares of Common Stock" shall mean all shares of Common
         Stock issued by the Issuer after the Closing Date, other than Warrant
         Stock or Common Stock issued pursuant to the Equity Conversion
         Agreement.



                                       1
<PAGE>   5

         "Appraised Value" shall mean, in respect of any share of Common Stock
         on any date herein specified, the fair saleable value of such share of
         Common Stock (determined without giving effect to the discount for (i)
         a minority interest or (ii) any lack of liquidity of the Common Stock
         or to the fact that the Issuer may have no class of equity registered
         under the Exchange Act) as of the last day of the most recent fiscal
         month to end prior to such date specified, based on the value of the
         Issuer, as determined by an investment banking firm (approved by SCI
         and the Issuer) in accordance with such firm's customary practices,
         divided by the number of Outstanding shares of Common Stock, after
         giving pro forma effect to the exercise or conversion of all
         exercisable or Convertible Securities (including the Warrants) for
         Common Stock and the payment of the exercise or conversion price
         therefor.

         "Book Value" shall mean, in respect of any share of Common Stock on any
         date herein specified, the consolidated book value of the Issuer as of
         the last day of any month immediately preceding such date, divided by
         the number of Outstanding shares of Common Stock, after giving pro
         forma effect to the exercise or conversion of all exercisable or
         Convertible Securities (including the Warrants) for Common Stock and
         the payment of the exercise or conversion price therefor, as determined
         in accordance with GAAP by any firm of independent certified public
         accountants of recognized national standing selected by the Issuer and
         reasonably acceptable to SCI.

         "Business Day" shall mean each day which is not a day on which banks in
         Houston, Texas are generally authorized or obligated by law or
         executive order to close.

         "Closing Date" shall mean the date hereof.

         "Commission" shall mean the Securities and Exchange Commission, or any
         other federal agency then administering the Securities Act and other
         federal securities laws.

         "Common Stock" shall mean the common stock, $0.01 par value per share,
         of the Issuer, as constituted on the Closing Date, and any capital
         stock into which such Common Stock may thereafter be changed, and shall
         also include (i) capital stock of the Issuer of any other class
         (regardless of how denominated) issued to the holders of shares of
         Common Stock upon any reclassification thereof which is also not
         preferred as to dividends or assets over any other class of stock of
         the Issuer and which is not subject to redemption and (ii) shares of
         common stock of any successor or acquiring corporation (as defined in
         Section 4.8 of this Agreement) received by or distributed to the
         holders of Common Stock of the Issuer in the circumstances contemplated
         by Section 4.8 of this Agreement.

         "Convertible Securities" shall mean evidences of indebtedness, shares
         of stock or other securities which are convertible into or
         exchangeable, with or without payment of additional consideration in
         cash or property, for Additional Shares of Common Stock, either
         immediately or upon the occurrence of a specified date or a specified
         event.

         "Current Market Price" shall mean, in respect of any share of Common
         Stock on any date herein specified, (a) if there shall then be a public
         market for the Common Stock, the average Price per share for the 20
         trading days preceding such date; or (b) at any time



                                       2
<PAGE>   6

         that there is no public market for the Common Stock, the fair market
         value per share of Common Stock on such date as determined reasonably
         and in good faith by the board of directors of the Issuer (determined
         without giving effect to any discount for a minority interest, any
         restrictions on transferability or any lack of liquidity of the Common
         Stock or to the fact that the Issuer has no class of equity registered
         under the Exchange Act), such fair market value to be determined by
         reference to the cash price that would be paid between a fully informed
         buyer and seller under no compulsion to buy or sell, provided that (i)
         if Current Market Price is being determined in connection with an
         issuance of shares of Common Stock, solely to one or more Affiliates of
         the Issuer, then if so requested by the Required Holders, Current
         Market Price shall be the Appraised Value; and (ii) Current Market
         Price shall never be less than Book Value.

         "Current Warrant Price" shall mean, in respect of a share of Common
         Stock at any date herein specified, three dollars ninety cents ($3.90)
         per share as to the Tranche One Warrants, six dollars ($6.00) per share
         as to the Tranche Two Warrants, and eight dollars ($8.00) per share as
         to the Tranche Three Warrants, each subject to adjustment from time to
         time as provided in this Agreement.

         "Demanding Security Holder" shall have the meaning set forth in Section
         9.3.

         "Equity Conversion Agreement" shall mean that certain Equity Conversion
         Agreement of even date herewith among the Issuer, the Borrower and SCI.

         "Exchange Act" shall mean the Securities Exchange Act of 1934, as
         amended, or any similar federal statute, and the rules and regulations
         of the Commission thereunder, all as the same shall be in effect from
         time to time.

         "Exercise Period" shall mean the period during which the Warrants are
         exercisable pursuant to Section 2.2.

         "Expiration Date" shall mean the earlier of December 30, 2003 [364 days
         after final maturity] or two years after the date of full repayment of
         the Note (as such term is defined in the Credit Agreement).

         "GAAP" shall mean generally accepted accounting principles in the
         United States of America, as from time to time in effect.

         "Material Adverse Effect" shall mean, as to the Issuer, any material
         adverse effect on the business, assets, operations, prospects or
         financial or other condition of the Issuer and its Subsidiaries, taken
         as a whole.

         "NASD" shall mean the National Association of Securities Dealers, Inc.,
         or any successor thereto.

         "Other Property" shall have the meaning set forth in Section 4.8.

         "Outstanding" shall mean, when used with reference to Common Stock, at
         any date as of which the number of shares thereof is to be determined,
         all issued shares of Common



                                       3
<PAGE>   7

         Stock, except shares then owned or held by or for the account of the
         Issuer or any Subsidiary, and shall include all shares issuable in
         respect of outstanding scrip or any certificates representing
         fractional interests in shares of Common Stock.

         "Permitted Issuances" shall mean (i) the issuance of shares of Common
         Stock upon exercise of the Warrants or pursuant to the Equity
         Conversion Agreement or the issuance of Warrants pursuant to the Equity
         Conversion Agreement, (ii) the issuance of shares relating to any
         benefit plan, stock option plan or any other compensation plan offered
         solely to the Issuer's officers and/or employees, (iii) the issuance of
         shares of Common Stock as consideration for the purchase of any
         property, stock, business or securities from any Person who is not an
         Affiliate of the Issuer or any Subsidiary immediately prior to such
         transaction whether such shares are issued directly by the Issuer or by
         a Subsidiary of the Issuer in connection with any merger, consolidation
         or other business combination, (iv) if there shall then be a public
         market for the Common Stock, the issuance of shares of Common Stock
         upon receipt by the Issuer of no less than the Current Market Price
         therefor as described in clause (a) of the definition of "Current
         Market Price" and (v) if there shall then be no public market for the
         Common Stock, the issuance of shares of Common Stock, warrants or
         Convertible Securities on terms that are at least as favorable to the
         Issuer as terms that could be obtained in an arm's length transaction
         with third Persons not Affiliates of the Issuer or any Subsidiary and
         for consideration equal to the fair value of such shares as determined
         in good faith by a majority of disinterested members of the board of
         directors of the Issuer.

         "Person(s)" shall mean any individual, sole proprietorship,
         partnership, joint venture, trust, limited liability company,
         incorporated organization, association, corporation, institution,
         public benefit corporation, entity or government (whether federal,
         state, county, city, municipal or otherwise, including, without
         limitation, any instrumentality, division, agency, body or department
         thereof).

         "Price" means the average of the "high" and "low" prices as reported in
         The Wall Street Journal's listing for such day (corrected for obvious
         typographical errors) or if such shares are not reported in such
         listing, the average of the reported "high" and "low" sales prices on
         the largest national securities exchange (based on the aggregate dollar
         value of securities listed) on which such shares are listed or traded,
         or if such shares are not listed or traded on any national securities
         exchange, then the average of the reported "high" and "low" sales
         prices for such shares in the over-the-counter market, as reported on
         the National Association of Securities Dealers Automated Quotations
         System, or, if such prices shall not be reported thereon, the average
         of the closing bid and asked prices so reported, or, if such prices
         shall not be reported, then the average of the closing bid and asked
         prices reported by the National Quotations Bureau Incorporated. The
         "average" Price per share for any period shall be determined by
         dividing the sum of the Prices determined for the individual trading
         days in such period by the number of trading days in such period.

         "Registrable Securities" shall mean, at any particular time and as to
         each Warrant Holder, (i) all shares of common stock issuable upon the
         exercise of such Warrant Holder's Warrants, (ii) all of such Warrant
         Holder's issued and outstanding Warrant Stock, and



                                       4
<PAGE>   8

         (iii) all shares of common stock issuable upon exercise of SCI's rights
         under the Equity Conversion Agreement.

         "Registration Expenses" shall have the meaning set forth in Section 9.5
         of this Agreement.

         "Registration Statement" shall have the meaning set forth in Section
         9.4 of this Agreement.

         "Required Holders" shall mean the Warrant Holders of Warrants
         exercisable for an amount exceeding 50% of the aggregate number of
         shares of Common Stock then purchasable upon exercise of all Warrants,
         whether or not exercisable.

         "Requirement of Law" shall mean, as to any Person, any requirement
         contained in any certificate of incorporation, bylaws, or other
         organizational or governing documents of such Person, and any law,
         treaty, rule or regulation or determination of an arbitrator or a court
         or other governmental authority, in each case applicable to or binding
         such Person or any of the property or to which such Person or any of
         its property is subject.

         "Restricted Common Stock" shall mean shares of Common Stock which are,
         or which upon their issuance on the exercise of a Warrant would be,
         evidenced by a certificate bearing the restrictive legend set forth in
         Section 9.1 of this Agreement.

         "Securities Act" shall mean the Securities Act of 1933, as amended, or
         any similar federal statute, and the rules and regulations of the
         Commission thereunder, all as the same shall be in effect at the time.

         "Subsidiary" of a Person means (i) a corporation, a majority of whose
         stock with voting power, under ordinary circumstances, to elect
         directors is at the time of determination, directly or indirectly,
         owned by such Person or by one or more Subsidiaries of such Person, or
         (ii) any other entity (other than a corporation) in which such Person
         or one or more Subsidiaries of such Person, directly or indirectly, at
         the date of determination thereof has at least a majority ownership
         interest.

         "Tranche One Warrants" shall have the meaning set forth in Section 2.1
         of this Agreement.

         "Tranche Two Warrants" shall have the meaning set forth in Section 2.1
         of this Agreement.

         "Tranche Three Warrants" shall have the meaning set forth in Section
         2.1 of this Agreement.

         "Transfer Notice" shall have the meaning set forth in Section 9.2 of
         this Agreement.

         "Warrant Certificate" shall mean a certificate evidencing one or more
         Warrants, substantially in the form of Exhibit A hereto, with such
         changes therein as may be required to reflect any adjustments made
         pursuant to Section 4 of this Agreement.



                                       5
<PAGE>   9

         "Warrant Holder" shall mean such Person in whose name the Warrants are
         registered on the books of the Issuer maintained for such purpose or
         each Person holding any Warrant Stock. As of the Closing Date, the SCI
         is the Warrant Holder hereof.

         "Warrant Price" shall mean, for any exercise of Warrants pursuant to
         Section 2.2 of this Agreement, an amount equal to (i) the number of
         shares of Common Stock being purchased upon such exercise multiplied by
         (ii) the Current Warrant Price applicable to Tranche One Warrants,
         Tranche Two Warrants or Tranche Three Warrants, as applicable, for each
         share of Common Stock as of the date of such exercise.

         "Warrant Stock" shall mean the shares of Common Stock purchased by the
         Warrant Holders upon the exercise thereof.

         "Warrants" shall mean the Warrants issued pursuant to this Agreement,
         including the Tranche One Warrants, Tranche Two Warrants and Tranche
         Three Warrants, and all Warrants issued upon transfer, division or
         combination of, or in substitution for, such Warrants. All Warrants
         shall at all times be identical as to terms and conditions and date,
         except as to the number of shares of Common Stock for which they may be
         exercised and the Current Warrant Price. A Warrant shall entitle the
         record holder thereof to purchase from the Issuer one share of Common
         Stock (subject to adjustment as provided in Section 4 of this
         Agreement).

2.       ISSUANCE AND EXERCISE OF WARRANTS

2.1      Issuance of Warrants. The Issuer hereby agrees to issue to the Warrant
         Holder on the Closing Date TWO MILLION FIVE HUNDRED SIXTY-FOUR THOUSAND
         ONE HUNDRED TWO (2,564,102) Warrants having a Current Warrant Price of
         three dollars and ninety cents ($3.90) per share of Common Stock (the
         "Tranche One Warrants"), ONE MILLION SIX HUNDRED SIXTY-SIX THOUSAND SIX
         HUNDRED SIXTY-SEVEN (1,666,667) Warrants having a Current Warrant Price
         of six dollars ($6.00) per share of Common Stock (the "Tranche Two
         Warrants"), and ONE MILLION TWO HUNDRED FIFTY THOUSAND (1,250,000)
         Warrants having a Current Price of eight dollars ($8.00) per share
         ("Tranche Three Warrants"). On the Closing Date, the Issuer shall
         deliver to the Warrant Holder Warrant Certificates evidencing the
         Warrants issued to the Warrant Holder.

2.2      Manner of Exercise.

         (a)      The Warrant Holder may, from and after the Closing Date until
                  11:59 p.m., Central Standard Time on the Expiration Date,
                  exercise the Warrants evidenced by a Warrant Certificate, on
                  any Business Day, for all or part of the number of shares of
                  Common Stock purchasable thereunder.

         (b)      In order to exercise the Warrants, in whole or in part, the
                  Warrant Holder shall deliver to the Issuer at its principal
                  office at 6300 Bridge Point Parkway, Building 2, Suite 500,
                  Austin, Texas 78730, Attention: Chief Financial Officer, or at
                  the office or agency designated by the Issuer pursuant to
                  Section 12 of this Agreement (the "Principal Office"), (x) a
                  written notice duly executed by the



                                       6
<PAGE>   10

                  Warrant Holder or its agent or attorney, substantially in the
                  form of the form of election to purchase appearing at the end
                  of the Warrant Certificate as Exhibit A thereto, of such
                  Warrant Holder's election to exercise the Warrants, which
                  notice shall specify the number of shares of Common Stock to
                  be purchased, (y) payment of the Warrant Price in the manner
                  provided below, and (z) the Warrant Certificate or Warrant
                  Certificates evidencing the Warrants. Upon receipt thereof,
                  the Issuer shall, as promptly as practicable, and in any event
                  within three (3) Business Days thereafter, execute or cause to
                  be executed and deliver or cause to be delivered to such
                  Warrant Holder a certificate or certificates representing the
                  aggregate number of full shares of Common Stock issuable upon
                  such exercise, together with cash in lieu of any fraction of a
                  share, as hereinafter provided. The stock certificate or
                  certificates so delivered shall be, to the extent possible, in
                  such denomination or denominations as such Warrant Holder
                  shall request in the notice and shall be registered in the
                  name of the Warrant Holder or, subject to Section 9 of this
                  Agreement, such other name as shall be designated in the
                  notice. The Warrants shall be deemed to have been exercised
                  and such certificate or certificates shall be deemed to have
                  been issued, and such Warrant Holder or any other Person so
                  designated to be named therein shall be deemed to have become
                  a holder of record of such shares for all purposes, as of the
                  date the notice, together with payment of the Warrant Price
                  and the Warrant Certificate or Warrant Certificates, are
                  received by the Issuer as described above and all taxes
                  required to be paid by such Warrant Holder, if any, pursuant
                  to Section 2.3 of this Agreement prior to the issuance of such
                  shares have been paid. If the Warrants evidenced by a Warrant
                  Certificate shall have been exercised, the Issuer shall, at
                  the time of delivery of the certificate or certificates
                  representing the Warrant Stock, deliver to the Warrant Holder
                  a new Warrant Certificate evidencing the rights of the Warrant
                  Holder to purchase the unpurchased shares of Common Stock
                  represented by the old Warrant Certificate, which new Warrant
                  Certificate shall in all other respects be identical to the
                  old Warrant Certificate. Payment of the Warrant Price shall be
                  made in cash in an amount equal to the Warrant Price.

2.3      Payment of Taxes. The Issuer shall pay all expenses in connection with,
         and all transfer taxes and other governmental charges that may be
         imposed with respect to, the issuance or delivery of Warrant Stock. The
         Issuer shall not be required, however, to pay any tax or other charge
         imposed in connection with any transfer involved in the issue of any
         certificate for shares of Warrant Stock issuable upon exercise of
         Warrants in any name other than that of Warrant Holder, and in such
         case the Issuer shall not be required to issue or deliver any stock
         certificate until such tax or other charge has been paid or it has been
         established to the satisfaction of the Issuer that no such tax or other
         charge is due.

2.4      Fractional Shares. The Issuer shall not be required to issue a
         fractional share of Common Stock upon the exercise of Warrants as
         provided in Section 2(b)(i) and (ii). As to any fraction of a share
         which the Warrant Holder would otherwise be entitled to purchase upon
         such exercise, the Issuer shall pay a cash adjustment in respect of
         such fraction in an amount equal to the same fraction of the Current
         Market Price per share of Common Stock on the date of exercise. If the
         determination of Current Market Price for purposes of this Section 2.4
         would otherwise require an appraisal to be made by an investment



                                       7
<PAGE>   11

         banking firm, then Current Market Price for purposes of this Section
         2.4 only shall mean Book Value per share of Common Stock on the date of
         exercise, unless a determination of Appraised Value shall have been
         made within six months prior to such date in which case such Appraised
         Value shall be utilized for the purposes of determining Current Market
         Price.

2.5      Continued Validity.

         A holder of Warrant Stock (other than a holder who acquires such shares
         after the same have been publicly sold pursuant to a Registration
         Statement under the Securities Act) shall continue to be entitled with
         respect to such shares to all rights to which it would have been
         entitled as a holder of Warrant Stock under Sections 9, 10 and 15 of
         this Agreement. The Issuer will, at the time of each exercise of
         Warrants or upon the request of the holder of Warrant Stock issued upon
         the exercise thereof, acknowledge in writing, in form reasonably
         satisfactory to such holder of Warrant Stock, its continuing obligation
         to afford to such holder of Warrant Stock all such rights; provided,
         however, that if such holder of Warrant Stock shall fail to make any
         such request, such failure shall not affect the continuing obligation
         of the Issuer to afford to such holder of Warrant Stock all such
         rights.

2.6      Conditions to Exercise.

         Notwithstanding any other provision of this Agreement, the Warrants
         shall be exercisable only (i) upon any repayment of the SCI Loans,
         whether at Maturity or as a prepayment (whether or not required
         pursuant to Section 2.07 of the Credit Agreement), but only to the
         extent that (A) such repayment reduces the outstanding principal
         balance thereof below the then existing Convertible Amount, and (B) the
         provisions of clauses (ii) and (iii) of Section 2.01(i) of the Equity
         Conversion Agreement are not applicable with respect to such repayment.
         The Warrants shall be exercisable in the following order: the Tranche
         One Warrants shall become exercisable first, as the SCI Loans
         constituting the Tranche One loans are repaid; the Tranche Two Warrants
         shall become exercisable second, as the SCI Loans constituting the
         Tranche Two loans are repaid; and Tranche Three Warrants shall become
         exercisable last, as the SCI Loans constituting the Tranche Three loans
         are repaid. Further, notwithstanding any other provision of this
         Agreement, the number of shares purchasable pursuant to such Warrants
         shall be the quotient of that part of the Convertible Amount of the
         relevant Tranche so repaid divided by the relevant Current Warrant
         Price.

3.       TRANSFERS, DIVISION AND COMBINATION

3.1      Transfer. Subject to compliance with Section 9 of this Agreement,
         transfer of Warrants, in whole or in part, shall be registered on the
         books of the Issuer to be maintained for such purposes, upon surrender
         of the Warrant Certificate representing such Warrants at the principal
         office of the Issuer referred to in Section 2.2 of this Agreement or
         the office or agency designated by the Issuer pursuant to Section 12 of
         this Agreement, together with a written assignment substantially in the
         form of Exhibit B to the Warrant Certificate and a written agreement,
         in form reasonably satisfactory to the Issuer, setting forth the



                                       8
<PAGE>   12

         new Warrant Holder's agreement to be bound by all of the terms of this
         Agreement each duly executed by the Warrant Holder or its agent or
         attorney, and funds sufficient to pay any transfer taxes payable by
         such Warrant Holder upon the making of such transfer. Upon such
         surrender and, if required, such payment, the Issuer shall, subject to
         Section 9 of this Agreement, execute and deliver a new Warrant
         Certificate or Warrant Certificates in the name of the assignee or
         assignees and in the denomination specified in such instrument of
         assignment, and shall issue to the assignor a new Warrant Certificate
         or Warrant Certificates evidencing the portion of the old Warrant
         Certificate not so assigned, and the old Warrant Certificate shall
         promptly be canceled. A Warrant, if properly assigned in compliance
         with Section 9 of this Agreement, may be exercised by a new Warrant
         Holder for the purchase of shares of Warrant Stock without having a new
         Warrant Certificate or new Warrant Certificates issued.

3.2      Division and Combination. Subject to the provisions of Section 9 of
         this Agreement, any Warrant Certificate may be divided or combined with
         other Warrant Certificates upon presentation thereof at the aforesaid
         office or agency of the Issuer, together with a written notice
         specifying the names and denominations in which new Warrant
         Certificates are to be issued, signed by a Warrant Holder or its agent
         or attorney. Subject to compliance with Section 3.1 of this Agreement
         as to any transfer which may be involved in such division or
         combination, the Issuer shall execute and deliver a new Warrant
         Certificate or Warrant Certificates in exchange for the Warrant
         Certificate or Warrant Certificates to be divided or combined in
         accordance with such notice.

3.3      Expenses. The Issuer shall prepare, issue and deliver at its own
         expense (other than transfer taxes) the new Warrant Certificate or
         Warrant Certificates provided for under this Section 3.

3.4      Maintenance of Books. The Issuer agrees to maintain, at its aforesaid
         office or agency, books for the registration of, and the registration
         of transfer of, the Warrants.

4.       ADJUSTMENTS

         The number of shares of Warrant Stock for which Warrants are
         exercisable, and the price at which such shares may be purchased upon
         exercise of Warrants, shall be subject to adjustment from time to time
         as set forth in this Section 4. The Issuer shall give each Warrant
         Holder notice of any event described below which requires an adjustment
         pursuant to this Section 4 within three (3) Business Days after such
         event.

4.1      Stock Dividends, Subdivisions and Combinations. If at any time the
         Issuer shall:

         (a)      take a record of the holders of its Common Stock for the
                  other distribution of, Additional Shares of Common Stock,

         (b)      subdivide its outstanding shares of Common Stock into a larger
                  number of shares of Common Stock, or




                                       9
<PAGE>   13

         (c)      combine its outstanding shares of Common Stock into a smaller
                  number of shares of Common Stock,

                  then (i) the number of shares of Common Stock for which a
                  Warrant is exercisable immediately after the occurrence of any
                  such event shall be adjusted to equal the number of shares of
                  Common Stock which a record holder of the same number of
                  shares of Common Stock for which a Warrant is exercisable
                  immediately prior to the occurrence of such event would own or
                  be entitled to receive after the happening of such event, and
                  (ii) the Current Warrant Price shall be adjusted to equal the
                  Current Warrant Price multiplied by a fraction, the numerator
                  of which shall be the number of shares of Common Stock for
                  which a Warrant is exercisable immediately prior to the
                  adjustment and the denominator of which shall be the number of
                  shares for which a Warrant is exercisable immediately after
                  such adjustment.

4.2      Certain Other Distributions. If at any time the Issuer shall take a
         record of the holders of its Common Stock for the purpose of entitling
         them to receive any dividend or other distribution of:

         (a)      cash;

         (b)      any evidences of its indebtedness (other than Convertible
                  Securities), any shares of its stock (other than Additional
                  Shares of Common Stock or Convertible Securities) or any other
                  securities or property of any nature whatsoever (other than
                  cash); or

         (c)      any warrants or other rights to subscribe for or purchase any
                  evidences of its indebtedness (other than Convertible
                  Securities), any shares of its stock (other than Additional
                  Shares of Common Stock or Convertible Securities) or any other
                  securities or property of any nature whatsoever;

                  then (i) the number of shares of Common Stock for which a
                  Warrant is exercisable shall be adjusted to equal the product
                  obtained by multiplying the number of shares of Common Stock
                  for which a Warrant is exercisable immediately prior to such
                  adjustment by a fraction (A) the numerator of which shall be
                  the Current Market Price per share of Common Stock at the date
                  of taking such record and (B) the denominator of which shall
                  be such Current Market Price per share of Common Stock, minus
                  the amount allocable to one share of Common Stock of any such
                  cash so distributable and of the fair value (as determined
                  reasonably and in good faith by the board of directors of the
                  Issuer) of any and all such evidences of indebtedness, shares
                  of stock, other securities or property or warrants or other
                  subscription or purchase rights so distributable, and (ii) the
                  Current Warrant Price shall be adjusted to equal (A) the
                  Current Warrant Price multiplied by the number of shares of
                  Common Stock for which a Warrant is exercisable immediately
                  prior to the adjustment divided by (B) the number of shares
                  for which a Warrant is exercisable immediately after such
                  adjustment. A reclassification of the Common Stock (other than
                  a change in par value, or from


                                       10
<PAGE>   14

                  par value to no par value or from no par value to par value)
                  into shares of Common Stock and shares of any other class of
                  stock shall be deemed a distribution by the Issuer to the
                  holders of its Common Stock of such shares of such other class
                  of stock within the meaning of this Section 4.2 and, if the
                  Outstanding shares of Common Stock shall be changed into a
                  larger or smaller number of shares of Common Stock as a part
                  of such reclassification, such change shall be deemed a
                  subdivision or combination, as the case may be, of the
                  Outstanding shares of Common Stock within the meaning of
                  Section 4.1 of this Agreement.

4.3      Issuance of Additional Shares of Stock.

         (a)      If at any time the Issuer shall (except as hereinafter
                  provided) issue or sell any Additional Shares of Common Stock,
                  other than Permitted Issuances, for consideration in an amount
                  per Additional Share of Common Stock less than the Current
                  Market Price, then the Current Warrant Price shall be adjusted
                  by multiplying the Current Warrant Price by a fraction, the
                  numerator of which shall be (A) an amount equal to the sum of
                  (X) the number of shares of Common Stock Outstanding
                  immediately prior to such issuance or sale multiplied by the
                  Current Market Price immediately prior to the first to occur
                  of (i) board action by the Issuer authorizing such action or
                  (ii) the public announcement of an intent to take such action,
                  plus (Y) the consideration, if any, received by the Issuer
                  upon such issuance or sale, and the denominator of which shall
                  be (B) the total number of shares of Common Stock Outstanding
                  immediately after such issuance or sale multiplied by the
                  Current Market Price as determined in clause (A) above.

         (b)      The provisions of Section 4.3(a) of this Agreement shall not
                  apply to any issuance of Additional Shares of Common Stock for
                  which an adjustment is provided under Sections 4.1 or 4.2 of
                  this Agreement. No adjustment of the number of shares of
                  Common Stock for which a Warrant shall be exercisable shall be
                  made under Section 4.3(a) of this Agreement upon the issuance
                  of any Additional Shares of Common Stock which are issued
                  pursuant to the exercise of any warrants or other subscription
                  or purchase rights or pursuant to the exercise of any
                  conversion or exchange rights in any Convertible Securities
                  (i) if any such adjustment shall previously have been made
                  upon the issuance of such warrants or other rights or upon the
                  issuance of such Convertible Securities (or upon the issuance
                  of any such warrants or other rights) pursuant to Section 4.4
                  or Section 4.5 of this Agreement, (ii) if no adjustment was
                  required pursuant to such sections upon the issuance of such
                  Convertible Securities, warrants or other rights or (iii) in
                  the event the issuance of such Convertible Securities,
                  warrants or other rights predates or is of the same date as
                  this Agreement, if no adjustment would have been required
                  pursuant to such sections upon such issuance had this
                  Agreement been in effect.

4.4      Issuance of Warrants or Other Rights. If at any time the Issuer shall
         take a record of the holders of its Common Stock for the purpose of
         entitling them to receive a distribution of, or shall in any manner
         (whether directly or by assumption in a merger in which the Issuer



                                       11
<PAGE>   15

         is the surviving corporation) issue or sell, any warrants or other
         rights to subscribe for or purchase any Additional Shares of Common
         Stock or any Convertible Securities, other than Permitted Issuances,
         whether or not the rights to exchange or convert thereunder are
         immediately exercisable, and if the price per share for which Common
         Stock is issuable upon the exercise of such warrants or other rights or
         upon conversion or exchange of such Convertible Securities shall be
         less than the Current Market Price in effect immediately prior to the
         time of such distribution, issue or sale, then the Current Warrant
         Price shall be adjusted as provided in Section 4.3(a) of this Agreement
         on the basis that (A) the maximum number of Additional Shares of Common
         Stock issuable pursuant to all such warrants or other rights or
         necessary to effect the conversion or exchange of all such Convertible
         Securities shall be deemed to be Outstanding immediately following such
         issuance, (B) the price per share for such Additional Shares of Common
         Stock shall be deemed to be the lowest possible price per share in any
         range of prices per share at which such Additional Shares of Common
         Stock are available to such holders, and (C) the Issuer shall be deemed
         to have received all of the consideration payable therefor, if any, as
         of the date of the actual issuance of such warrants or other rights. No
         further adjustments of the Current Warrant Price shall be made upon the
         actual issuance of such Common Stock or of such other rights or upon
         exercise of such warrants or other rights or upon the actual issuance
         of such Common Stock upon such conversion or exchange of such
         Convertible Securities.

4.5      Issuance of Convertible Securities. If at any time the Issuer shall
         take a record of the holders of its Common Stock for the purpose of
         entitling them to receive a distribution of, or shall in any manner
         (whether directly or by assumption in a merger in which the Issuer is
         the surviving corporation) issue or sell, any Convertible Securities,
         other than Permitted Issuances, whether or not the rights to exchange
         or convert thereunder are immediately exercisable, and if the price per
         share for which Common Stock is issuable upon such conversion or
         exchange shall be less than the Current Market Price in effect
         immediately prior to the time of such issue or sale of Convertible
         Securities, then the Current Warrant Price shall be adjusted as
         provided in Section 4.3(a) of this Agreement on the basis that (A) the
         maximum number of Additional Shares of Common Stock necessary to effect
         the conversion or exchange of all such Convertible Securities shall be
         deemed to be Outstanding immediately following such issuance, (B) the
         price per share of such Additional Shares of Common Stock shall be
         deemed to be the lowest possible price in any range of prices at which
         such Additional Shares of Common Stock are available to such holders,
         and (C) the Issuer shall be deemed to have received all of the
         consideration payable therefor, if any, as of the date of actual
         issuance of such Convertible Securities. No adjustment of the Current
         Warrant Price shall be made under this Section 4.5 upon the issuance of
         any Convertible Securities which are issued pursuant to the exercise of
         any warrants or other subscription or purchase rights therefor if any
         such adjustments shall previously have been made upon the issuance of
         such warrants or other rights pursuant to Section 4.4 of this
         Agreement. No further adjustments of the Current Warrant Price shall be
         made upon the actual issue of such Common Stock upon conversion or
         exchange of such Convertible Securities and, if any issue or sale of
         such Convertible Securities is made upon exercise of any warrant or
         other right to purchase any such Convertible Securities for which
         adjustments of the Current Warrant Price have been or are to be made
         pursuant to other provisions of this Section 4,



                                       12
<PAGE>   16

         no further adjustments of the Current Warrant Price shall be made by
         reason of such issue or sale.

4.6      Superseding Adjustment. If, at any time after any adjustment of the
         Current Warrant Price shall have been made pursuant to Section 4.4 or
         Section 4.5 of this Agreement as the result of any issuance of
         warrants, options, rights or Convertible Securities, and such warrants,
         options or rights, or the right of conversion or exchange in such other
         Convertible Securities, shall expire, and all or a portion of such
         warrants, options or rights, or the right of conversion or exchange
         with respect to all or a portion of such other Convertible Securities,
         as the case may be, shall not have been exercised, then such previous
         adjustment shall be rescinded and annulled and, if applicable, the
         Current Warrant Price shall be recalculated as if all such expired and
         unexercised warrants, options, rights or Convertible Securities had
         never been issued.

4.7      Other Provisions Applicable to Adjustments Under This Section. The
         following provisions shall be applicable to the making of adjustments
         of the number of shares of Common Stock for which a Warrant is
         exercisable provided for in this Section 4:

         (a)      Computation of Consideration. To the extent that any
                  Additional Shares of Common Stock shall be issued for cash
                  consideration, the consideration received by the Issuer
                  therefor shall be the amount of the cash received by the
                  Issuer therefor, or, if such Additional Shares of Common Stock
                  are sold to underwriters or dealers for public offering
                  without a subscription offering, the initial public offering
                  price (in any such case subtracting any amounts paid or
                  receivable for accrued interest or accrued dividends, but not
                  subtracting any compensation, discounts or expenses paid or
                  incurred by the Issuer for and in the underwriting of, or
                  otherwise in connection with, the issuance thereof). To the
                  extent that such issuance shall be for a consideration other
                  than cash, then, except as herein otherwise expressly
                  provided, the amount of such consideration shall be deemed to
                  be the fair value of such consideration at the time of such
                  issuance as determined reasonably and in good faith by a
                  majority of the disinterested members of the board of
                  directors of the Issuer.

         (b)      When Adjustments to Be Made. The adjustments required by this
                  Section 4 shall be made whenever and as often as any specified
                  event requiring an adjustment shall occur, except that any
                  adjustment to the number of shares for which the Warrants are
                  exercisable that would otherwise be required may be postponed
                  (except in the case of a subdivision or combination of shares
                  of the Common Stock, as provided for in Section 4.1 of this
                  Agreement) up to, but not beyond, the date and time of
                  exercise of any Warrants if such adjustment either by itself
                  or with other adjustments not previously made adds or
                  subtracts less than 1% to the number of shares of Common Stock
                  for which the Warrants initially issued pursuant to this
                  Agreement are exercisable immediately prior to the making of
                  such adjustment. Any adjustment representing a change of less
                  than such minimum amount (except as aforesaid) which is
                  postponed shall be carried forward and made as soon as such
                  adjustment, together with other adjustments required by this
                  Section 4 and not previously made, would result in a minimum



                                       13
<PAGE>   17

                  adjustment or on the date of exercise. For the purpose of any
                  adjustment, any specified event shall be deemed to have
                  occurred at the close of business on the date of its
                  occurrence.

         (c)      Fractional Interests. In computing adjustments under this
                  Section 4, fractional interests in Common Stock resulting from
                  an issuance of additional Warrants to any Warrant Holder
                  pursuant to this Section 4 shall be taken into account to the
                  nearest 1/10th of a share, subject to Section 2.4 of this
                  Agreement.

         (d)      When Adjustment Not Required. If the Issuer shall take a
                  record of the holders of its Common Stock for the purpose of
                  entitling them to receive a dividend or distribution or
                  subscription or purchase rights and shall, thereafter and
                  before the distribution to stockholders thereof, legally
                  abandon its plan to pay or deliver such dividend,
                  distribution, subscription or purchase rights, no adjustment
                  shall be required by reason of the taking of such record and
                  any such adjustment previously made in respect thereof shall
                  be rescinded and annulled.

         (e)      Escrow of Warrant Stock. If after any property becomes
                  distributable pursuant to this Section 4 by reason of the
                  taking of any record of the holders of Common Stock, but prior
                  to the occurrence of the event for which such record is taken,
                  any Warrant Holder exercises Warrants, any Additional Shares
                  of Common Stock issuable upon exercise of such Warrant by
                  reason of such adjustment shall be held in escrow for a
                  Warrant Holder by the Issuer to be issued to such Warrant
                  Holder upon and to the extent that the event actually takes
                  place, upon payment of the balance, if any, of the Warrant
                  Price for such Warrant at such date (after taking into account
                  any overpayment of the Warrant Price made at any time of the
                  initial Warrant exercise). Notwithstanding any other provision
                  to the contrary herein, if the event for which such record was
                  taken fails to occur or is rescinded, then such escrowed
                  shares shall be canceled by the Issuer and escrowed property
                  returned.

4.8      Reorganization, Reclassification, Merger, Consolidation or Disposition
         of Assets. In the event the Issuer shall reorganize its capital,
         reclassify its capital stock, consolidate or merge with and into
         another corporation or entity (where the Issuer is not the surviving
         corporation or where there is a change in or distribution with respect
         to the Common Stock of the Issuer), or sell, transfer or otherwise
         dispose of all or substantially all its property, assets or business to
         another corporation or entity and, pursuant to the terms of such
         reorganization, reclassification, merger, consolidation or disposition
         of assets, shares of common stock of the successor or acquiring
         corporation or entity, or any cash, shares of stock or other securities
         or property of any nature whatsoever (including warrants or other
         subscription or purchase rights) in addition to or in lieu of common
         stock of the successor or acquiring corporation or entity ("Other
         Property"), are to be received by or distributed to the holders of
         Common Stock of the Issuer, then the Issuer shall, as a condition
         precedent to such transaction, cause effective provisions to be made so
         that each Warrant Holder shall have the right thereafter to receive,
         upon exercise of a warrant, solely the number of shares of "common
         stock of the successor or acquiring corporation" or of the Issuer, if
         it is the surviving corporation, and Other Property receivable upon or
         as a result of such reorganization, reclassification, merger,



                                       14
<PAGE>   18

         consolidation or disposition of assets, by a holder of the number of
         shares of Common Stock for which a Warrant is exercisable immediately
         prior to such event. In case of any such reorganization,
         reclassification, merger, consolidation or disposition of assets, such
         provisions shall include the express assumption by the successor or
         acquiring corporation or entity (if other than the Issuer) of the due
         and punctual observance and performance of each and every covenant and
         condition of this Agreement to be performed and observed by the Issuer
         and all the obligations and liabilities hereunder, subject to such
         modifications as may be deemed appropriate (as determined by resolution
         of the board of directors of the Issuer) to provide for adjustments of
         shares of the Common Stock for which a Warrant is exercisable which
         shall be as nearly equivalent as practicable to the adjustments
         provided for in this Section 4. For purposes of this Section 4.8,
         "common stock of the successor or acquiring corporation" shall include
         stock of such corporation of any class which is not preferred as to
         dividends or assets over any other class of stock or other securities
         of such corporation or entity and which is not subject to redemption
         and shall also include any evidences of indebtedness, shares of stock
         or other securities which are convertible into or exchangeable for any
         such stock or other securities, either immediately or upon the arrival
         of a specified date or the happening of a specified event, and any
         warrants or other rights to subscribe for or purchase any such stock or
         securities. The foregoing provisions of this Section 4.8 shall
         similarly apply to successive reorganizations, reclassifications,
         mergers, consolidations or disposition of assets.

5.       NOTICES TO WARRANT HOLDERS

5.1      Notice of Adjustments. Whenever the number of shares of Common Stock
         for which a Warrant is exercisable, or whenever the price at which a
         share of such Common Stock may be purchased upon exercise of the
         Warrants, shall be adjusted pursuant to Section 4, the Issuer shall
         forthwith prepare a certificate to be executed by the chief financial
         officer of the Issuer setting forth, in reasonable detail, the event
         requiring the adjustment and the method by which such adjustment was
         calculated (including a description of the basis on which the board of
         directors of the Issuer determined the fair value of any evidences of
         indebtedness, shares of stock, other securities or property or warrants
         or other subscription or purchase rights referred to in Section 4 of
         this Agreement), specifying the number of shares of Common Stock for
         which a Warrant is exercisable and (if such adjustment was made
         pursuant to Section 4.8 of this Agreement) describing the number and
         kind of any other shares of stock or Other Property for which a Warrant
         is exercisable, and any change in the purchase price or prices thereof,
         after giving effect to such adjustment or change. The Issuer shall
         promptly cause a signed copy of such certificate to be delivered to
         each Warrant Holder in accordance with Section 15.2 of this Agreement.
         The Issuer shall keep at its office or agency designated pursuant to
         Section 12 of this Agreement copies of all such certificates and cause
         the same to be available for inspection at said office during normal
         business hours by any Warrant Holder or any prospective purchaser of a
         Warrant designated by a Warrant Holder thereof.

5.2      Notice of Certain Corporate Action. Each Warrant Holder shall be
         entitled to the same rights to receive notice of corporate action as
         any holder of Common Stock.




                                       15
<PAGE>   19

6.       REPRESENTATIONS AND WARRANTIES

         The Issuer makes the following representations and warranties, each and
         all of which shall be true and correct as of the date of execution and
         delivery of this Agreement and shall survive the execution and delivery
         of this Agreement:

         (a)      Due Organization; Etc. The Issuer is a corporation duly
                  organized validly existing and in good standing under the laws
                  of the State of Delaware, and has the power and authority to
                  execute and deliver this Agreement and the Warrant
                  Certificates, to issue the Warrants and to perform its
                  obligations under this Agreement and the Warrant Certificates.

         (b)      Due Authorization; No Violation. The execution, delivery and
                  performance by the Issuer of this Agreement and the Warrant
                  Certificates, the issuance of the Warrants and the issuance of
                  the Warrant Stock upon exercise of the Warrants have been duly
                  authorized by all necessary corporate action and do not and
                  will not violate, or result in a breach of, or constitute a
                  default under or require any consent under, or result in the
                  creation of any lien or security interest upon the assets of
                  the Issuer pursuant to, any Requirement of Law or any
                  contractual obligation binding upon the Issuer.

         (c)      Due Execution; Etc. This Agreement has been duly executed and
                  delivered by the Issuer and constitutes a legal, valid and
                  enforceable obligation of the Issuer. When the Warrants and
                  the Warrant Certificates have been issued as contemplated
                  hereby, (i) the Warrants and the Warrant Certificates will
                  constitute legal, valid, binding and enforceable obligations
                  of the Issuer and (ii) the Warrant Stock, when issued upon
                  exercise of the Warrants in accordance with the terms hereof,
                  will be duly authorized, validly issued, fully paid and
                  non-assessable shares of Common Stock with no personal
                  liability attaching to the ownership thereof.

         (d)      Capitalization. The total number of shares of all classes of
                  stock that the Issuer shall on the Closing Date have authority
                  to issue is 40,000,000 shares, consisting of (i) 30,000,000
                  shares of Common Stock, par value $0.01 per share, of which,
                  after giving effect to the transactions contemplated herein
                  and all other issuances of capital stock of the Issuer on or
                  prior to the Closing Date, 14,428,621 shares of Common Stock
                  will be issued and outstanding and 5,480,769 shares of Common
                  Stock will be reserved for future issuance pursuant to this
                  Agreement and (ii) 10,000,000 shares of Preferred Stock, par
                  value $0.01 per share, none of which are presently
                  outstanding. Schedule A sets forth a complete list of the
                  outstanding capital stock of the Issuer, including any
                  options, warrants or rights to purchase the capital stock of
                  the Issuer. The delivery hereunder by the Issuer to the
                  Warrant Holder of the Warrants issued on the Closing Date will
                  transfer and convey to the Warrant Holder good and marketable
                  title to such Warrants and, upon exercise of such Warrants in
                  accordance with this Agreement, good and marketable title to
                  the Common Stock purchased upon such exercise, free and clear
                  of all preemptive rights, liens, charges and encumbrances,
                  except for



                                       16
<PAGE>   20

                  restrictions on transfer referred to in this Agreement, or
                  arising under the Federal and state securities laws. Except as
                  otherwise disclosed on Schedule A, the Issuer does not have
                  outstanding any stock or securities convertible into or
                  exchangeable for any shares of its stock, nor, except as so
                  set forth, does it have outstanding any agreements, rights or
                  options entitling any person to subscribe for or to purchase
                  any capital stock or securities convertible into or
                  exchangeable for any of its shares of stock.

         (e)      Full Disclosure. No information contained in this Agreement,
                  the financial statements referred to in the Credit Agreement
                  or any written statement furnished by or on behalf of the
                  Issuer pursuant to the terms of this Agreement to the Warrant
                  Holder contains any untrue statement of a material fact or
                  omits to state a material fact necessary to make the
                  statements contained herein or therein not misleading in light
                  of the circumstances under which made.

         (f)      Warrant Price. The Issuer has taken all corporate action, and
                  obtained all necessary authorizations or exemptions from any
                  public regulatory body or bodies or governmental entity or
                  entities having jurisdiction thereof, as may be necessary in
                  order that the Issuer may validly and legally issue fully paid
                  and non-assessable shares of Common Stock upon to exercise of
                  the warrants at the Warrant Price, as the same may be adjusted
                  pursuant hereto.

         (g)      Other Representations and Warranties. The Issuer hereby
                  affirms and reaffirms for the express benefit of the Warrant
                  Holders that the representations and warranties made by the
                  Issuer in that certain Guaranty Agreement dated as of January
                  26, 1998, as amended, are true and correct, as if made in
                  favor of the Warrant Holder on the date hereof.

7.       CERTAIN COVENANTS

7.1      No Impairment. The Issuer shall not by any action including, without
         limitation, amending its certificate of incorporation or through any
         reorganization, transfer of assets, consolidation, merger, dissolution,
         issue or sale of securities or any other voluntary action, avoid or
         seek to avoid the observance or performance of any of the terms of this
         Agreement, but will at all times in good faith assist in the carrying
         out of all such terms and in the taking of all such actions as may be
         necessary or appropriate to protect the rights of each Warrant Holder
         against impairment. Without limiting the generality of the foregoing,
         the Issuer will use reasonable good faith efforts to obtain all such
         authorizations, exemptions or consents from any public regulatory body
         having jurisdiction thereof as may be necessary to enable it to perform
         its obligations under this Agreement.

         Upon the request of a Warrant Holder, the Issuer will, at any time
         during the period this Agreement is in effect, acknowledge in writing,
         in form satisfactory to such Warrant Holder, the continuing validity of
         this Agreement and the obligations of the Issuer hereunder.



                                       17
<PAGE>   21

7.2      Reservation and Authorization of Common Stock; Registration with, or
         Approval of, any Governmental Authority. From and after the Closing
         Date, the Issuer shall at all times reserve and keep available for
         issue upon the exercise of Warrants such number of its authorized but
         unissued shares of Common Stock as will be sufficient to permit the
         exercise in full of all outstanding Warrants. All shares of Common
         Stock which shall be so issuable, when issued upon exercise of any
         Warrants and payment therefor in accordance with the terms of this
         Agreement, shall be duly and validly issued and fully paid and
         non-assessable, and not subject to preemptive rights.

         Before taking any action which would result in an adjustment in the
         number of shares of Common Stock for which a Warrant is exercisable or
         in the Current Warrant Price, the Issuer shall obtain all such
         authorizations or exemptions thereof, or consents thereto, as may be
         necessary from any public regulatory body or bodies or governmental
         entity or entities having jurisdiction thereof.

         If any shares of Common Stock required to be reserved for issuance upon
         exercise of Warrants require registration or qualification with any
         governmental authority under any federal or state law (otherwise than
         as provided in Section 9 of this Agreement) before such shares may be
         so issued, the Issuer will in good faith and as expeditiously as
         possible and at its expense endeavor to cause such shares to be duly
         registered.

8.       TAKING OF RECORD; STOCK AND WARRANT TRANSFER BOOKS

         In the case of all dividends or other distributions by the Issuer to
         the holders of its Common Stock with respect to which any provision of
         Section 4 of this Agreement refers to the taking of a record of such
         holders, the Issuer will in each such case take such a record as of the
         close of business on a Business Day. The Issuer will not at any time,
         except upon dissolution, liquidation or winding up of the Issuer, close
         its stock transfer books or Warrant transfer books so as to result in
         preventing or delaying the exercise or transfer of any Warrants.

9.       RESTRICTIONS ON TRANSFERABILITY

         The Warrants and the Warrant Stock shall not be transferred before
         satisfaction of the conditions specified in this Section 9, which
         conditions are intended to ensure compliance with the provisions of the
         Securities Act and applicable state securities laws with respect to the
         transfer of any Warrant or any Warrant Stock. Each Warrant Holder, by
         entering into this Agreement and accepting the Warrants, agrees to be
         bound by the provisions of this Section 9.

9.1      Restrictive Legend. Except as otherwise provided in this Section 9,
         each certificate representing Warrants or Warrant Stock, shall be
         stamped or otherwise imprinted with a legend in substantially the
         following form:

         "THE SECURITIES REPRESENTED BY THIS CERTIFICATE HAVE NOT BEEN
         REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED, OR ANY
         APPLICABLE STATE SECURITIES LAWS, AND MAY NOT BE SOLD OR TRANSFERRED IN
         THE ABSENCE OF SUCH REGISTRATION OR AN



                                       18
<PAGE>   22

         EXEMPTION THEREFROM. SUCH SECURITIES ARE SUBJECT TO THE RESTRICTIONS
         AND PRIVILEGES SPECIFIED IN A WARRANT AGREEMENT, DATED AS OF FEBRUARY
         17, 2000, BETWEEN BRIGHAM EXPLORATION COMPANY AND THE INITIAL HOLDERS
         OF SECURITIES NAMED THEREIN, A COPY OF WHICH IS ON FILE WITH THE
         SECRETARY OF BRIGHAM EXPLORATION COMPANY AND WILL BE FURNISHED WITHOUT
         CHARGE TO THE HOLDER HEREOF UPON WRITTEN REQUEST, AND THE HOLDER OF
         THIS CERTIFICATE AGREES TO BE BOUND THEREBY."

9.2      Notice of Proposed Transfers; Requests for Registration. Prior to any
         transfer of any Warrants or any shares of Restricted Common Stock, the
         Warrant Holder of such Warrants or Restricted Common Stock shall give
         five days prior written notice to the Issuer of such Warrant Holder's
         intention to effect such transfer (a "Transfer Notice"). Each Warrant
         Holder agrees that it will not sell, transfer or otherwise dispose of
         Warrants or any shares of Restricted Common Stock, in whole or in part,
         except pursuant to an effective registration statement under the
         Securities Act or an exemption from registration thereunder. Each
         certificate, if any, evidencing such shares of Restricted Common Stock
         issued upon such transfer shall bear the restrictive legend set forth
         in Section 9.1, and each Warrant Certificate issued upon such transfer
         shall bear the restrictive legend set forth in Section 9.1 of this
         Agreement, unless in the opinion of the transferee's or Warrant
         Holder's counsel delivered to the Issuer in connection with such
         transfer such legend is not required in order to ensure compliance with
         the Securities Act.

         The Warrant Holders of Warrants and Warrant Stock shall have the right
         to request registration of such Warrant Stock pursuant to Section 9.3
         of this Agreement.

9.3      Incidental Registration. If the Issuer at any time proposes to file on
         its behalf and/or on behalf of any of its security holders (the
         "Demanding Security Holders") a Registration Statement under the
         Securities Act on any form (other than a Registration Statement (i)
         filed pursuant to demand under the Company's Registration Rights
         Agreement with Joint Energy Development Investments II Limited
         Partnership, a Delaware limited partnership, and Enron Capital & Trade
         Resources Corp., a Delaware corporation, dated August 20, 1998, as
         amended, or (ii) on Form S-8 or any similar or successor form or any
         other registration statement relating to an offering of securities
         solely to the Issuer's existing security holders or employees) to
         register the offer and sale of its Common Stock for cash, it will give
         written notice to all Warrant Holders of Warrants or Warrant Stock at
         least twenty (20) days before the anticipated date of initial filing
         with the Commission of such Registration Statement, which notice shall
         set forth the Issuer's intention to effect such a registration, the
         class or series and number of equity securities proposed to be
         registered and the intended method of disposition of the securities
         proposed to be registered by the Issuer. The notice shall offer to
         include in such filing all of the Warrant Holder's Registrable
         Securities.

         Each Warrant Holder desiring to have Registrable Securities registered
         under this Section 9.3 shall advise the Issuer in writing within
         fifteen (15) days after the date of receipt of such offer from the
         Issuer, setting forth the amount of such Registrable





                                       19
<PAGE>   23
         Securities for which registration is requested. The Issuer shall
         thereupon include in such filing the number of shares of Registrable
         Securities for which registration is so requested, subject to the next
         sentence, and shall use its best efforts to effect registration under
         the Securities Act of such securities. If the managing underwriter of a
         proposed public offering shall advise the Issuer in writing that, in
         its opinion, the distribution of the Registrable Securities requested
         to be included in the registration concurrently with the securities
         being registered by the Issuer or any Demanding Security Holder would
         materially and adversely affect the distribution of such securities by
         the Issuer or such Demanding Security Holders, then all selling
         security holders (but not the Issuer or the Demanding Security Holders)
         shall reduce the amount of securities each intended to distribute
         through such offering on a pro rata basis to the greatest aggregate
         amount which, in the opinion of such managing underwriter, would not
         materially and adversely affect the distribution of such securities.

         Nothing in this Section 9.3 shall preclude the Issuer from
         discontinuing the registration of its securities being effected on its
         behalf under this Section 9.3 at any time prior to the effective date
         of the registration relating thereto. Notwithstanding any provision
         herein, the rights of the Warrant Holder under this Section 9.3 are
         subject to the express limitations contained in registration rights
         agreements in effect on the date hereof between the Issuer and other
         parties; provided, however, that the Issuer shall not on or after the
         date of this Agreement enter into any registration rights agreement
         with respect to its securities that conflict with the registration
         rights granted to the Warrant Holder herein.

9.4      Registration Procedures. If the Issuer is required by the provisions of
         this Section 9 to use its best efforts to effect the registration of
         any of its securities under the Securities Act, the Issuer will, as
         expeditiously as possible:

         (a)      prepare and file with the Commission a registration statement
                  with respect to such securities (a "Registration Statement")
                  and use its best efforts to cause such Registration Statement
                  to become and remain effective for the period described in
                  paragraph (b) below;

         (b)      prepare and file with the Commission such amendments and
                  supplements to such Registration Statement and the prospectus
                  used in connection therewith as may be necessary to keep such
                  Registration Statement effective and to comply with the
                  provisions of the Securities Act with respect to the sale or
                  other disposition of all securities covered by such
                  Registration Statement until the earlier of such time as all
                  of such securities have been disposed of in a public offering
                  or the expiration of 90 days;

         (c)      furnish to such selling security holders such number of copies
                  of a summary prospectus or other prospectus, including a
                  preliminary prospectus, in conformity with the requirements of
                  the Securities Act, and such other documents, as such selling
                  security holders may reasonably request;



                                       20
<PAGE>   24

         (d)      use its best efforts to register or qualify the securities
                  covered by such Registration Statement under such other
                  securities or blue sky laws of such jurisdictions within the
                  United States as each holder of such securities shall request
                  (provided, however, the Issuer shall not be obligated to
                  qualify as a foreign corporation to do business under the laws
                  of any jurisdiction in which it is not then qualified or to
                  file any general consent to service or process), and do such
                  other reasonable acts and things as may be required of it to
                  enable such holder to consummate the disposition in such
                  jurisdiction of the securities covered by such Registration
                  Statement;

         (e)      enter into customary agreements (including an underwriting
                  agreement in customary form) and take such other actions as
                  are reasonably required in order to expedite or facilitate the
                  disposition of such Registrable Securities; and

         (f)      otherwise use its best efforts to comply with all applicable
                  rules and regulations of the Commission, and make available to
                  its security holders, as soon as reasonably practicable, but
                  not later than 18 months after the effective date of the
                  Registration Statement, an earnings statement covering the
                  period of at least 12 months beginning with the first full
                  month after the effective date of such Registration Statement,
                  which earnings statements shall satisfy the provisions of
                  Section 11(a) of the Securities Act.

                  It shall be a condition precedent to the obligation of the
                  Issuer to take any action pursuant to this Section 9 in
                  respect of the securities which are to be registered at the
                  request of any Warrant Holder of Registrable Securities that
                  such Warrant Holder shall furnish to the Issuer such
                  information regarding the securities held by such Warrant
                  Holder and the intended method of disposition thereof as the
                  Issuer shall reasonably request and as shall be required in
                  connection with the action taken by the Issuer.

9.5      Expenses. All expenses incurred in complying with this Section 9,
         including, without limitation, all registration and filing fees
         (including all expenses incident to filing with the NASD), printing
         expenses, fees and disbursements of counsel for the Issuer, the
         reasonable fees and expenses of one counsel for the selling security
         holders (selected by the Person holding the plurality of the securities
         being registered), expenses of any special audits incident to or
         required by any such registration and expenses of complying with the
         securities or blue sky laws of any jurisdictions pursuant to Section
         9.4(d) of this Agreement (all of such expenses shall be collectively
         referred to herein as "Registration Expenses"), shall be paid by the
         Issuer; provided, however, the Issuer shall not be responsible for any
         discount or commission or cost reimbursement to any underwriter in
         respect of the securities sold by such Warrant Holder of Registrable
         Securities.

9.6      Indemnification and Contribution.

         (a)      In the event of any registration of any of the Registrable
                  Securities under the Securities Act pursuant to this Section
                  9, the Issuer shall indemnify and hold harmless each Warrant
                  Holder of such Registrable Securities, such Warrant



                                       21
<PAGE>   25

                  Holder's directors and officers, each Affiliate of such
                  Warrant Holder, and each other Person (including each
                  underwriter) who participated in the offering of such
                  Registrable Securities and each other Person, if any, who
                  controls such Warrant Holder or such participating Person, if
                  any, who controls such Warrant Holder or such participating
                  Person within the meaning of the Securities Act, against any
                  losses, claims, damages or liabilities, joint or several, to
                  which such Warrant Holder or any such director or officer or
                  participating Person or Affiliate or controlling Person may
                  become subject under the Securities Act or any other statute
                  or at common law, insofar as such losses, claims, damages or
                  liabilities (or actions in respect thereof) arise out of or
                  are based upon (i) any alleged untrue statement of any
                  material fact contained, on the effective date thereof, in any
                  Registration Statement under which such securities were
                  registered under the Securities Act, any preliminary
                  prospectus or final prospectus contained therein, or any
                  amendment or supplement thereto, or (ii) any alleged omission
                  to state therein a material fact required to be stated therein
                  or necessary to make the statements therein, in light of the
                  circumstances under which they were made, not misleading, and
                  shall reimburse such Warrant Holder or such director, officer
                  or participating Person or Affiliate or controlling Person for
                  any legal or any other expenses reasonably incurred by such
                  Warrant Holder or such director, officer or participating
                  Person or Affiliate or controlling Person in connection with
                  investigating or defending any such loss, claim, damage,
                  liability or action; provided, however, that the Issuer shall
                  not be liable in any such case to the extent that any such
                  loss, claim, damage or liability directly arises out of or is
                  directly based upon any alleged untrue statement or alleged
                  omission made in such Registration Statement, preliminary
                  prospectus, prospectus or amendment or supplement in reliance
                  upon and in conformity with written information furnished to
                  the Issuer by such Warrant Holder specifically for use
                  therein. Such indemnity shall remain in full force and effect
                  regardless of any investigation made by or on behalf of such
                  Warrant Holder or such director, officer or participating
                  Person or Affiliate or controlling Person, and shall survive
                  the transfer of such securities by such Warrant Holder.

         (b)      Each Warrant Holder of any Registrable Securities, by
                  acceptance thereof, agrees to indemnify and hold harmless the
                  Issuer, its directors and officers and each other Person, if
                  any, who controls the Issuer within the meaning of the
                  Securities Act against any losses, claims, damages or
                  liabilities, joint or several, to which the Issuer or any such
                  director or officer or any such Person may become subject
                  under the Securities Act or any other statute or at common
                  law, insofar as such losses, claims, damages or liabilities
                  (or actions in respect thereof) directly arise out of or are
                  directly based upon (i) information in writing provided to the
                  Issuer by such Warrant Holder of such Registrable Securities
                  contained, on the effective date thereof, in any Registration
                  Statement under which securities were registered under the
                  Securities Act at the request of such Warrant Holder, any
                  preliminary prospectus or final prospectus contained therein,
                  or any amendment or supplement thereto or (ii) that such
                  Warrant Holder's obligation under this Section 9.6(b) to
                  indemnify and hold harmless the Issuer shall in no event
                  exceed the lesser of (x) the damage attributable solely to the
                  inclusion of such written



                                       22
<PAGE>   26

                  information in such Registration Statement, preliminary
                  prospectus, final prospectus, or amendment or supplement
                  suffered by the Person or Persons whose claims gave rise to
                  such losses, claims, damages or liabilities and (y) the net
                  proceeds received by such Warrant Holder from the sale of
                  Registrable Securities giving rise to such indemnification.

         (c)      If the indemnification provided for in this Section 9 from the
                  indemnifying party is unavailable to an indemnified party
                  hereunder in respect of any losses, claims, damages,
                  liabilities or expenses referred to herein, then the
                  indemnifying party, in lieu of indemnifying such indemnified
                  party, shall contribute to the amount paid or payable by such
                  indemnified party as a result of such losses, claims, damages,
                  liabilities or expenses in such proportion as is appropriate
                  to reflect the relative fault of the indemnifying party and
                  indemnified parties in connection with the actions which
                  resulted in such losses, claims, damages, liabilities or
                  expenses, as well as any other relevant equitable
                  considerations. The relative fault of such indemnifying party
                  and indemnified parties shall be determined by reference to,
                  among other things, whether any action in question, including
                  any untrue or alleged untrue statement of a material fact or
                  omission or alleged omission to state a material fact, has
                  been made by, or related to information supplied by, such
                  indemnifying party or indemnified parties, and the parties'
                  relative intent, knowledge, access to information and
                  opportunity to correct or prevent such action. The amount paid
                  or payable by a party under this Section 9 as a result of the
                  losses, claims, damages, liabilities and expenses referred to
                  above shall be deemed to include any legal or other fees or
                  expenses reasonably incurred by such party in connection with
                  any investigation or proceeding.

                           The parties hereto agree that it would not be just
                  and equitable if contribution pursuant to this Section 9.6(c)
                  were determined by pro rata allocation or by any other method
                  of allocation which does not take account of the equitable
                  considerations referred to in the immediately preceding
                  paragraph. Notwithstanding the provisions of this subsection
                  (c), no Warrant Holder shall be required to contribute any
                  amount in excess of the total amount received by it upon the
                  sale of its securities pursuant to the Registration Statement
                  to which the losses, claims, damages, liabilities and expenses
                  referred to above relate. No Person guilty of fraudulent
                  misrepresentation (within the meaning of Section 11(f) of the
                  Securities Act) shall be entitled to contribution from any
                  Person who was not guilty of such fraudulent
                  misrepresentation. The obligations of each of the Warrant
                  Holders under this subsection (c) to contribute are several
                  and not joint.

         (d)      Conduct of Indemnification Proceedings. Any person or entity
                  entitled to indemnification hereunder shall (i) give prompt
                  written notice to the indemnifying party after the receipt by
                  the indemnified party of a written notice of the commencement
                  of any action, suit, proceeding or investigation or threat
                  thereof made in writing for which such indemnified party will
                  claim indemnification or contribution pursuant to this
                  Agreement; provided, however, that the failure of any
                  indemnified party to give notice as provided herein shall not
                  relieve the indemnifying party of its obligations under
                  Section 9.6 hereof, except to the



                                       23
<PAGE>   27

                  extent that the indemnifying party is actually prejudiced by
                  such failure to give notice, and (ii) unless in such
                  indemnified party's reasonable judgment a conflict of interest
                  may exist between such indemnified and indemnifying parties
                  with respect to such claim, permit such indemnifying party to
                  assume the defense of such claim with counsel reasonably
                  satisfactory to the indemnified party. If the indemnifying
                  party is entitled to, and does, assume the defense of such
                  claim, the indemnified party shall have the right to employ
                  separate counsel and to participate in the defense thereof,
                  but the fees and expenses of such counsel shall be borne by
                  the indemnified party. Whether or not such defense is assumed
                  by the indemnifying party, the indemnifying party shall not be
                  subject to any liability for any settlement made without its
                  consent (but such consent will not be unreasonably withheld).
                  No indemnifying party shall be permitted to consent to the
                  entry of any judgment or to enter into any settlement that
                  does not include as an unconditional term thereof the giving
                  by the claimant or plaintiff to such indemnified party of a
                  release from all liability in respect of such claim or
                  litigation. An indemnifying party who is not entitled to, or
                  elects not to, assume the defense of a claim shall not be
                  obligated to pay the fees and expenses of more than one
                  counsel in any one jurisdiction for all parties indemnified by
                  such indemnifying party with respect to such claim, unless in
                  the reasonable judgment of any indemnified party a conflict of
                  interest may exist between such indemnified party and any
                  other of such indemnified parties with respect to such claim,
                  in which event the indemnifying party shall be obligated to
                  pay the fees and expenses of such additional counsel or
                  counsels.

9.7      Termination of Restrictions. Notwithstanding the foregoing provisions
         of this Section 9, the restrictions imposed by this Section 9 upon the
         transferability of the Warrants, the Warrant Stock and the Restricted
         Common Stock (or Common Stock issuable upon the exercise of the
         Warrants) and the legend requirement of Section 9.1 of this Agreement
         shall terminate as to any particular Warrant or share of Warrant Stock
         or Restricted Common Stock (or Warrant Stock) (i) when and so long as
         such security shall have been registered under the Securities Act and
         disposed of pursuant thereto, or (ii) when the Warrant Holder thereof
         shall have delivered to the Issuer the written opinion of counsel to
         such Warrant Holder, stating that such legend is not required in order
         to ensure compliance with the Securities Act. Whenever the restrictions
         imposed by this Section 9 shall terminate as to any Warrants or any
         Restricted Common Stock, as hereinabove provided, the Warrant Holder
         thereof shall be entitled to receive from the Issuer, at the expense of
         the Issuer, a new Warrant Certificate or a new certificate representing
         such Common Stock, as the case may be, not bearing the restrictive
         legend set forth in Section 9.1 of this Agreement.

9.8      Listing on Securities Exchange. If at any time the Issuer shall list
         any shares of Common Stock on any securities exchange, it will, at its
         expense, use its best efforts to list thereon, maintain and, when
         necessary, increase such listing of, all shares of Common Stock issued
         or, to the extent permissible under the applicable securities exchange
         rules, issuable upon the exercise of the Warrants so long as any shares
         of Common Stock shall be so listed during the Exercise Period.



                                       24
<PAGE>   28

10.      SUPPLYING INFORMATION

         The Issuer shall cooperate with each Warrant Holder of a Warrant and
         each Warrant Holder of Restricted Common Stock in supplying such
         information as may be reasonably necessary for such Warrant Holder to
         complete and file any information reporting forms presently or
         hereafter required by the Commission as a condition to the availability
         of an exemption from the Securities Act for the sale of any Warrant or
         Restricted Common Stock.

11.      LOSS OR MUTILATION

         Upon receipt by the Issuer from any Warrant Holder of evidence
         reasonably satisfactory to it of the ownership of and the loss, theft,
         destruction or mutilation of a certificate representing Warrants or
         Warrant Stock and indemnity reasonably satisfactory to it (it being
         understood that the written agreement of the Warrant Holder or an
         Affiliate thereof shall be sufficient indemnity) and in case of
         mutilation upon surrender and cancellation hereof or thereof, the
         Issuer will execute and deliver in lieu hereof or thereof a new Warrant
         or new stock certificate as the case may be, of like tenor to such
         Warrant Holder; provided, in the case of mutilation, no indemnity shall
         be required if the certificate representing Warrants or Warrant Stock
         in identifiable form is surrendered to the Issuer for cancellation.

12.      OFFICE OF THE ISSUER

         As long as any of the Warrants remain outstanding, the Issuer shall
         maintain an office or agency (which may be the principal executive
         officers of the Issuer) where the Warrants may be presented for
         exercise, registration or transfer, division or combination as provided
         in this Agreement.

13.      APPRAISAL

         The determination of the Appraised Value per share of Common Stock
         shall be made by an investment banking firm of nationally recognized
         standing mutually agreed to by the Issuer and the Required Holders. If
         the investment banking firm selected by the Issuer is not acceptable to
         the Required Holders and the Issuer and the Required Holders cannot
         agree on a mutually acceptable investment banking firm, then the
         Required Holders and the Issuer shall each choose one such investment
         banking firm and the respective chosen firms shall agree on another
         investment banking firm which shall make the determination. The Issuer
         shall retain, at its sole cost, such investment banking firm as may be
         necessary for the determination of Appraised Value required by the
         terms of this Agreement.

14.      LIMITATION OF LIABILITY; NO RIGHTS AS STOCKHOLDER

         No provision hereof, in the absence of affirmative action by any
         Warrant Holder to purchase shares of Common Stock, and no enumeration
         herein of the rights or privileges of any Warrant Holder, shall give
         rise to any liability of such Warrant Holder for the purchase price of
         any Common Stock or as a stockholder of the Issuer, whether such



                                       25
<PAGE>   29

         liability is asserted by the Issuer or by creditors of the Issuer.
         Except as may otherwise be provided by law or by separate agreement
         between a Warrant Holder and the Issuer, no Warrant Holder, as such,
         shall be entitled to vote or be deemed the holder of Common Stock or
         any other securities (other than Warrants) of the Issuer which may at
         any time be issuable on the exercise hereof, nor shall anything
         contained herein be construed to confer upon any Warrant Holder the
         rights of a stockholder of the Issuer or the right to vote for the
         election of directors or upon any matters submitted to stockholders at
         any meeting thereof, or to give or withhold consent to any corporate
         action or to receive notice of meetings or other actions affecting
         stockholders (except as provided herein), or to receive dividends or
         otherwise, until the Warrants shall have been exercised in accordance
         with the terms and conditions hereof.

15.      MISCELLANEOUS

15.1     Non-waiver and Expenses. No course of dealing or any delay or failure
         to exercise any right hereunder on the part of any holder of Warrant
         Stock shall operate as a waiver of such right or otherwise prejudice
         such holder of Warrant Stock's rights, powers or remedies. If the
         Issuer fails to comply with any provision of this Agreement, the Issuer
         shall pay to the applicable holder of Warrant Stock such amounts as
         shall be sufficient to cover any costs and expenses including, but not
         limited to, reasonable attorneys' fees, including those of appellate
         proceedings, incurred by the holder of Warrant Stock in enforcing any
         of its rights, powers or remedies hereunder.

15.2     Notice Generally. Any notice, demand, request, consent, approval,
         declaration, delivery or other communication hereunder to be made
         pursuant to the provisions of this Agreement shall be sufficiently
         given or made if in writing and either delivered in person with receipt
         acknowledged or sent by registered or certified mail, return receipt
         requested, postage prepaid, telex, telecopier or overnight air courier
         guaranteeing next day delivery, addressed as follows:

         (a)      If to SCI, as Warrant Holder, at:

                           Address:       910 Louisiana, Suite 5000
                                          Houston, Texas 77002-4916
                           Attention:     Robert L. Roberts, Vice-President
                           Telecopier No. (713) 241-5222

         (b)      If to the Issuer at:

                           Brigham Exploration Company
                           6300 Bridge Point Parkway
                           Building 2, Suite 500
                           Austin, Texas 78730
                           Attention: President
                           Telecopier No.: (512) 427-3300

                  or at such other address as may be substituted by notice given
                  as herein provided. The giving of any notice required
                  hereunder may be waived in writing by the



                                       26
<PAGE>   30

                  party entitled to receive such notice. Every notice, demand,
                  request, consent, approval, declaration, delivery or other
                  communication hereunder shall be deemed to have been duly
                  given or served on the date on which personally delivered,
                  with receipt acknowledged, or three (3) Business Days after
                  the same shall have been deposited in the United States mail.

15.3     Indemnification. Except to the extent otherwise provided in Section 9.6
         of this Agreement, the Issuer agrees to indemnify and hold harmless
         Warrant Holder and its officers, directors, employees, agents,
         attorneys and Affiliates (each an "Indemnified Party") from and against
         any liabilities, obligations, losses, damages, penalties, actions,
         judgments, suits, claims, costs, attorneys' fees, expenses and
         disbursements of any kind which may be imposed upon, incurred by or
         asserted against such Indemnified Party relating to or arising out of
         (i) such Warrant Holder's exercise of the Warrants and/or ownership of
         any shares of Warrant Stock issued in consequence thereof, or (ii) any
         litigation to which such Warrant Holder is made a party in its capacity
         as a stockholder or Warrant Holder of the Issuer; provided, however,
         that the Issuer will not be liable hereunder to the extent that any
         liabilities, obligations, losses, damages, penalties, actions,
         judgments, suits, claims, costs, attorneys' fees, expenses or
         disbursements (A) arise solely from any violation by such Warrant
         Holder of any law or regulation applicable to it or (B) are found in a
         final non-appealable judgment by a court to have resulted from such
         Warrant Holder's bad faith or willful misconduct or violation of law.
         The procedures to be followed for claims of indemnification under this
         Section 15.3 shall be as set forth in Section 9.6(d) of this Agreement.

15.4     Remedies. Each Warrant Holder of Warrants and Warrant Stock, in
         addition to being entitled to exercise all rights granted by law,
         including recovery of damages, will be entitled to specific performance
         of its rights under Section 9 of this Agreement. The Issuer agrees that
         monetary damages would not be adequate compensation for any loss
         incurred by reason of a breach by it of the provisions of Section 9 of
         this Agreement, and hereby agrees to waive any defense to the contrary
         in any action for specific performance that a remedy at law would be
         adequate.

15.5     Successors and Assigns. Subject to the provisions of Sections 3.1 and 9
         of this Agreement, this Agreement and the rights evidenced hereby shall
         inure to the benefit of and be binding upon the successor of the Issuer
         and the successors and assigns of any Warrant Holder. The provisions of
         this Agreement are intended to be for the benefit of all Warrant
         Holders from time to time of the Warrants and Warrant Stock, and shall
         be enforceable by any such Warrant Holder.

15.6     Complete Agreement; Amendment. This Agreement, the Warrant
         Certificates, the Equity Conversion Agreement, the Credit Agreement and
         the Loan Documents constitute the complete agreement among the parties
         with respect to the subject matter hereof. This Agreement may be
         modified or amended or the provisions hereof waived only with the
         written consent of the Issuer and the Required Holders, provided that
         no Warrant may be modified or amended to reduce the number of shares of
         Common Stock for which such Warrant is exercisable or to increase the
         price at which such shares may be purchased upon exercise of such
         Warrant (before giving effect to any adjustment as provided



                                       27
<PAGE>   31

         herein) or to accelerate the Expiration Date without the prior written
         consent of the Warrant Holder thereof, and any amendment of Section 9
         of this Agreement shall also require the written consent of Warrant
         Holders of Warrants and/or Warrant Stock representing more than 50% of
         the total of (i) all shares of Warrant Stock then subject to purchase
         upon exercise of all Warrants then Outstanding, and (ii) all shares of
         Warrant Stock then Outstanding.

15.7     Severability. Wherever possible, each provision of this Agreement shall
         be interpreted in such manner as to be effective and valid under
         applicable law, but if any provision of this Agreement shall be
         prohibited by or invalid under applicable law, such provision shall be
         ineffective to the extent of such prohibition or invalidity, without
         invalidating the remainder of such provision or the remaining
         provisions of this Agreement.

15.8     Headings. The headings used in this Agreement are for the convenience
         of reference only and shall not, for any purpose, be deemed a part of
         this Agreement.

15.9     Governing Law; Consent to Jurisdiction and Venue. IN ALL RESPECTS,
         INCLUDING ALL MATTERS OF CONSTRUCTION, VALIDITY AND PERFORMANCE, THIS
         AGREEMENT AND THE OBLIGATIONS ARISING HEREUNDER SHALL BE GOVERNED BY,
         AND CONSTRUED AND ENFORCED IN ACCORDANCE WITH, THE LAWS OF THE STATE OF
         TEXAS APPLICABLE TO CONTRACTS MADE AND PERFORMED IN SUCH STATE, WITHOUT
         REGARD TO THE PRINCIPLES THEREOF REGARDING CONFLICT OF LAWS, AND ANY
         APPLICABLE LAWS OF THE UNITED STATES OF AMERICA.

15.10    Consent to Jurisdiction and Venue.

         (a)      THE ISSUER AND EACH WARRANT HOLDER HEREBY EXPRESSLY SUBMITS TO
                  THE JURISDICTION OF THE COURTS OF THE STATE OF TEXAS OR THE
                  UNITED STATES DISTRICT COURT FOR THE SOUTHERN DISTRICT OF
                  TEXAS. FINAL JUDGMENT AGAINST SUCH PARTY IN ANY SUCH SUIT
                  SHALL BE CONCLUSIVE, AND MAY BE ENFORCED IN ANY OTHER
                  JURISDICTIONS BY SUIT ON THE JUDGMENT OR AS OTHERWISE
                  PERMITTED BY APPLICABLE LAW, A CERTIFIED OR TRUE COPY OF WHICH
                  SHALL BE CONCLUSIVE EVIDENCE OF THE FACTS AND OF THE AMOUNT OF
                  ANY INDEBTEDNESS OR LIABILITY OF SUCH PARTY THEREIN DESCRIBED;
                  PROVIDED, HOWEVER, EACH PARTY MAY AT ITS OPTION BRING SUIT, OR
                  INSTITUTE OTHER JUDICIAL PROCEEDINGS AGAINST THE OTHER PARTY
                  OR ANY OF ITS ASSETS, IN THE COURTS OF ANY COUNTRY OR PLACE
                  WHERE SUCH PARTY OR SUCH ASSETS MAY BE FOUND.

         (b)      THE ISSUER AND EACH WARRANT HOLDER HEREBY IRREVOCABLY WAIVES
                  ANY OBJECTION WHICH IT MAY NOW OR HEREAFTER HAVE TO THE LAYING
                  OF VENUE OF ANY SUIT, ACTION OR PROCEEDING BROUGHT IN ANY
                  COURTS OF THE STATE OF TEXAS OR THE UNITED



                                       28
<PAGE>   32

                  STATES DISTRICT COURT FOR THE SOUTHERN DISTRICT OF TEXAS AND
                  HEREBY FURTHER IRREVOCABLY WAIVES ANY CLAIM THAT ANY SUCH
                  SUIT, ACTION OR PROCEEDING BROUGHT IN ANY SUCH COURT HAS BEEN
                  BROUGHT IN AN INCONVENIENT FORUM.

15.11    Counterparts: This Agreement may be executed in two or more
         counterparts, each of which shall be deemed an original, but all of
         which together shall constitute one and the same instrument.



                                       29
<PAGE>   33

         IN WITNESS WHEREOF, the parties hereto have caused this Agreement to be
duly executed as of the date first above written.



                                        BRIGHAM EXPLORATION COMPANY, as Issuer





                                        By:
                                           ------------------------------------
                                        Name:  Curtis F. Harrell
                                        Title: Chief Financial Officer



                                        SHELL CAPITAL INC.,
                                        as Warrant Holder



                                        By:
                                           ------------------------------------
                                        Name:  Robert L. Roberts
                                        Title: Vice President







                                       30
<PAGE>   34

                                                                    EXHIBIT A TO
                                                               Warrant Agreement



                          (FORM OF WARRANT CERTIFICATE)






THE SECURITIES REPRESENTED BY THIS CERTIFICATE HAVE NOT BEEN REGISTERED UNDER
THE SECURITIES ACT OF 1933, AS AMENDED, OR ANY APPLICABLE STATE SECURITIES LAWS,
AND MAY NOT BE SOLD OR TRANSFERRED IN THE ABSENCE OF SUCH REGISTRATION OR AN
EXEMPTION THEREFROM. SUCH SECURITIES ARE SUBJECT TO THE RESTRICTIONS AND
PRIVILEGES SPECIFIED IN THE WARRANT AGREEMENT, DATED AS OF _____________, 2000,
BETWEEN BRIGHAM EXPLORATION COMPANY AND THE INITIAL HOLDER OF SECURITIES NAMED
THEREIN, A COPY OF WHICH IS ON FILE WITH THE SECRETARY OF BRIGHAM EXPLORATION
COMPANY AND WILL BE FURNISHED WITHOUT CHARGE TO THE HOLDER HEREOF UPON WRITTEN
REQUEST, AND THE HOLDER OF THIS CERTIFICATE AGREES TO BE BOUND THEREBY.

No. ___

                               WARRANT CERTIFICATE

This Warrant Certificate certifies that Shell Capital Inc., or registered
assigns thereof, is the holder of ________ warrants (the "Warrants") to purchase
shares of common stock of Brigham Exploration Company, a Delaware corporation
(the "Company"). Each Warrant entitles the holder, but only subject to the
conditions set forth herein and in the Warrant Agreement referred to below, to
purchase from the Company before 11:59 p.m., Central Standard Time, on the
Expiration Date, as such term is defined in the Warrant Agreement, one fully
paid and non-assessable share of common stock of the Company ("Warrant Stock")
at a price (the "Exercise Price") of _______________________ ($______) per share
of Warrant Stock payable as set forth in the Warrant Agreement. The number of
shares of Warrant Stock for which each Warrant is exercisable and the Exercise
Price are each subject to adjustment prior to the Expiration Date upon the
occurrence of certain events as set forth in the Warrant Agreement.

The Company may deem and treat the registered holders of the Warrants evidenced
hereby as the absolute owner thereof (notwithstanding any notation of ownership
or other writing hereon made by anyone), for the purpose of any exercise hereof
and of any distribution to the holders hereof, and for all other purposes.

Warrant Certificates, when surrendered at the office of the Company by the
registered holder hereof in person or by a legal representative duly authorized
in writing, may be exchanged, in the



                                     EXH A-1
<PAGE>   35

manner and subject to the limitations provided in the Warrant Agreement, but
without payment of any service charge, for another Warrant Certificate or
Warrant Certificates of like tenor evidencing in the aggregate a like number of
Warrants.

Upon due presentment for registration of transfer of this Warrant Certificate at
the office of the Company at 6300 Bridge Point Parkway, Building 2, Suite 500,
Austin, Texas 78730, Attention: President, or such other address as the Company
may specify in writing to the registered holder of the Warrants evidenced
hereby, a new Warrant Certificate or Warrant Certificates of like tenor and
evidencing in the aggregate a like number of Warrants shall be issued to the
transferee in exchange for this Warrant Certificate to the transferee(s) and, if
less than all the Warrants evidenced hereby are to be transferred, the
registered holder hereof, subject to the limitations provided in the Warrant
Agreement, without charge except for any tax or other governmental charge
imposed in connection therewith.

The Warrant Certificate is one of the Warrant Certificates referred to in the
Warrant Agreement, dated as of ____________, 2000, between the Company and the
initial holder of Warrants party thereto (the "Warrant Agreement"). Said Warrant
Agreement is hereby incorporated by reference in and made a part of this
instrument and is hereby referred to for a description of the rights, limitation
of rights, obligations, duties and immunities thereunder of the Company and the
holders, and in the event of any conflict between the terms of this Warrant
Certificate and the provisions of the Warrant Agreement, the provisions of the
Warrant Agreement shall control.

IN WITNESS WHEREOF, the Company has caused this Warrant Certificate to be duly
executed and its corporate seal to be impressed hereon and attached by its
secretary.

Dated:                        , 2000.
       -----------------------

                                        BRIGHAM EXPLORATION COMPANY


                                        By:
                                           ------------------------------
                                        Printed Name:
                                                     --------------------
                                        Title:
                                              ---------------------------


(CORPORATE SEAL)

ATTEST:


- --------------------------------------
Secretary


                                    EXH A-2

<PAGE>   36



                                                                    Exhibit A To
                                                             Warrant Certificate


                                SUBSCRIPTION FORM

                 [To be executed only upon exercise of Warrants]


The undersigned registered owner of this Warrant Certificate irrevocably
exercises Warrants for the purchase of shares of Common Stock of [         ] and
herewith makes payment therefor

         $          in cash
          ----

all at the price and on the terms and conditions specified in the Warrant
Certificate and the Warrant Agreement, and requests that certificates for the
shares of Common Stock hereby purchased (and any securities or other property
issuable upon such exercise) be issued in the name of ____________________ and
delivered to _____________________________ whose address is
________________________________ and, if such shares of Common Stock shall not
include all of the shares of Common Stock issuable as provided in the Warrant
Certificate, that a new Warrant Certificate of like tenor and date for the
balance of the shares of Common Stock issuable thereunder be delivered to the
undersigned.



- ----------------------------------------------
(Name of Registered Owner)



- ----------------------------------------------
(Signature of Registered Owner)



- ----------------------------------------------
(Street Address)



- ----------------------------------------------
(City)         (State)         (Zip Code)



                                    EXH A-3

<PAGE>   37


                                                                    Exhibit B To
                                                             Warrant Certificate


                                 ASSIGNMENT FORM


FOR VALUE RECEIVED the undersigned registered owner of the attached Warrant
Certificate hereby sells, assigns and transfers unto the assignee named below
all of the rights of the undersigned under this Warrant Certificate, with
respect to the number of shares of Common Stock set forth below:

Name and Address of Assignee:
                                   -------------------------------

                                            -------------------------

                                            -------------------------

                                            -------------------------

No. of Shares of
Common Stock
             ------

and does hereby irrevocably constitute and appoint_____________________________
attorney-in-fact to register such transfer on the books of [                   ]
maintained for that purpose, with full power of substitution in the premises.

Dated:
              -----------------------------

Name:
        -------------------------------

Signature:
           --------------------------

Witness:
           --------------------------


The assignee named above hereby agrees to purchase and take the attached Warrant
Certificate pursuant to and in accordance with the terms and conditions of the
Warrant Agreement, dated as of ______________, 2000, between [                 ]
and the initial Holder named therein and agrees to be bound thereby.

Dated:
       ------------------------------

Name:
      -------------------------------

Signature:
           --------------------------



                         Exh. B-1 to Warrant Certificate

<PAGE>   38


                                   SCHEDULE A

<TABLE>
<CAPTION>
Shares of
Common                                      Stock Options   Total
Stock                                       Outstanding     Warrants
Outstanding                      Vested     Unvested        Outstanding
As of February 16, 2000

<S>                              <C>        <C>             <C>
14,517,786                       360,671    1,485,390       2,000,000
</TABLE>



                                    SCH. A-1

<PAGE>   1
                                                                   EXHIBIT 10.8




                         REGISTRATION RIGHTS AGREEMENT


         This REGISTRATION RIGHTS AGREEMENT (the "Agreement") is made and
entered into as of February 17, 2000, by and between Brigham Exploration
Company, a Delaware corporation (the "Company"), and Shell Capital Inc., a
Delaware corporation (the "Purchaser").

                                    RECITALS

         WHEREAS, Brigham Oil & Gas, L.P., a Delaware limited partnership
("BOG") and the Purchaser are parties to the Amended and Restated Credit
Agreement of even date herewith (as modified from time to time, the "Credit
Agreement"), governing certain Notes as defined therein (the "Notes"), and such
Notes were issued to the Purchaser.

         WHEREAS, the Company has agreed to issue certain capital stock of the
Company ("Common Stock") in connection with the exercise of certain equity
conversion rights pursuant to that certain Equity Conversion Agreement of even
date herewith among the Company, the Purchaser, and BOG (the "Equity Conversion
Agreement") and in connection with Warrants issued pursuant to that certain
Warrant Agreement of even date herewith between the Company and the Purchaser
(the "Warrants").

         WHEREAS, the Purchaser desires that the Company register the Common
Stock issuable upon conversion of the Notes pursuant to the Equity Conversion
Agreement (the "Conversion Shares") and the Common Stock issuable upon the
exercise of the Warrants (the "Warrant Shares") upon the terms and subject to
the conditions set forth in this Agreement.

         WHEREAS, the execution and delivery of this Agreement is a condition
precedent to the Purchaser's obligations under the Credit Agreement.

         NOW, THEREFORE, the parties hereto, intending legally to be bound,
hereby agree as follows:

1.       DEFINITIONS.

         As used in this Agreement, the following terms shall have the meanings
ascribed to them below:

         "Applicable Rate" shall mean the Base Rate under the Credit Agreement
plus 6% per annum; provided that if the Credit Agreement shall have terminated
then the Base Rate shall be calculated for purposes of this Agreement as if
such Credit Agreement shall not have terminated.

         "BOG" shall have the meaning indicated above.



<PAGE>   2

         "Common Stock" shall have the meaning indicated above.

         "Company" shall have the meaning indicated above.

         "Conversion Shares" shall have the meaning indicated above.

         "Credit Agreement" shall have the meaning indicated above.

         "Equity Conversion Agreement" shall have the meaning indicated above.

         "Holder" shall mean the Purchaser, and any other Person who has become
a Permitted Transferee pursuant to Section 9(c).

         "Notes" shall have the meaning indicated above.

         "Purchaser" shall have the meaning indicated above.

         "Registrable Securities" means (a) the Conversion Shares, (b) the
Warrant Shares, (c) all other shares of Common Stock owned by the Purchaser and
its Affiliates as of the date of filing of the Registration Statement (or which
they shall have the right to purchase or acquire as of such date), and (d) any
securities issued or issuable in respect of or in exchange for any of the
shares of Common Stock referred to in clauses (a) through (c) above by way of a
stock dividend or stock split or in connection with a combination of shares,
recapitalization, reclassification, merger, consolidation, or exchange offer
("Distribution Securities"). For purposes of this Agreement, a Registrable
Security ceases to constitute a Registrable Security hereunder (i) when such
Registrable Security shall have been effectively registered under the
Securities Act and disposed of in a public market transaction pursuant to a
Registration Statement, (ii) when such Registrable Security shall have been
sold pursuant to Rule 144 (or any successor provision) under the Securities
Act, (iii) when such Registrable Security shall have been otherwise transferred
and a new certificate for such Registrable Security not bearing a legend
restricting further transfer shall have been delivered by the Company, (iv)
with respect to a particular Holder, at any time when all of such Holder's
remaining Registrable Securities can be sold in a single transaction in
compliance with Rule 144 under the Securities Act, (v) on the third anniversary
of the original issuance date of such Registrable Security, provided that the
Holder of such Registrable Security is not an Affiliate of the Company as of
such date, and has not been an Affiliate of the Company for a period of three
months preceding such date, or (vi) when such Registrable Security shall have
ceased to be outstanding.

         "Registration Statement" shall have the meaning set forth in Section
2.

         "Registration Termination Date" means, the first date on which all
Conversion Shares and Warrant Shares (and any Distribution Securities with
respect thereto) cease to be Registrable Securities.

         "Securities Act" means the Securities Act of 1933, as amended.

         "Securities Exchange Act" means the Securities Exchange Act of 1934,
         as amended.


                                      -2-


<PAGE>   3


         "SEC" means the United States Securities Exchange Commission, or any
successor agency thereto.

         "Warrant Shares" shall have the meaning indicated above.

         "Warrants" shall have the meaning indicated above.

         Other capitalized terms shall have the meanings ascribed to them in
the other sections of this Agreement or in the Credit Agreement or in the
Equity Conversion Agreement in each case if not defined by the prior agreement
listed.

2.       REGISTRATION UPON CONVERSION.

         (a) Effective Registration. On or before sixty (60) days after the
date that any of the Conversion Shares or Warrant Shares are issued (the
"Filing Deadline"), the Company shall file with the SEC under the Securities
Act a Registration Statement on Form S-3 ("Registration Statement"), or on such
other registration form under the Securities Act as the Company shall deem
appropriate, covering the offer and sale by the Holders on a continuous or
delayed basis pursuant to Rule 415 thereunder (or any similar rule that may be
adopted by the SEC) of the Registrable Securities. The Company shall use its
best efforts to cause each Registration Statement to be declared effective on
or prior to the 120th day following the Filing Deadline and shall thereafter
keep such Registration Statement continuously effective until the Registration
Termination Date.

         (b) Delay in Effectiveness. In the event any Registration Statement is
not declared effective by the SEC within 120 days after the Filing Deadline
(the "Effectiveness Deadline"), or in the event the effectiveness of any
Registration Statement is suspended or terminated at any time after its
Effectiveness Deadline and prior to the Registration Termination Date, in each
case due to any action or inaction of the Company in pursuing, failing to
pursue, securing and maintaining an effective registration, utilizing all
reasonable efforts and good faith, or otherwise primarily for any reason
reasonably within the Company's control, then, at the election of the Holder:
(1) for each month (or portion thereof) such Registration Statement is not so
effective, the Company shall pay to the Holder, as liquidated damages and not
as a penalty, an amount equal to the product of (i) the Applicable Rate and
(ii) the greater of (x) the number of shares of Common Stock that are or could
become, if all Notes were converted and Warrants were exercised, Registrable
Securities multiplied by the closing price of the Common Stock on the first day
of the month as to which liquidated damages are payable as provided below, and
(y) outstanding principal amount of the Notes eligible for conversion to Common
Stock; or (2) the Holder may seek remedies at law or in equity. If there is
more than one Holder, the Company shall pay any damages to each Holder based
upon the proportion of the Registrable Securities owned by such Holder. Such
payments shall be made on the first Business Day of each month following any
month in which such Registration Statement is not effective, with a final
payment within five (5) Business Days after such Registration Statement becomes
effective.

3.       REGISTRATION PROCEDURES.

         (a) Company Procedures. In connection with the Company's registration
obligations pursuant to Section 2, the Company shall keep each Registration
Statement continuously effective for the period of time provided in Section 2,
to permit the sale of Registrable Securities covered by



                                      -3-


<PAGE>   4


such Registration Statement in accordance with the intended method or methods
of distribution thereof specified in such Registration Statement or in the
related prospectus(es), and shall:

                         (i) comply with such provisions of the Securities Act
              as may be necessary to facilitate the disposition of all
              Registrable Securities covered by such Registration Statement
              during the applicable period in accordance with the intended
              method or methods of disposition thereof set forth in such
              Registration Statement or such prospectus or supplement thereto;

                        (ii) notify the Holders, promptly (A) when each
              Registration Statement, prospectus, or supplement thereto or
              further post-effective amendment has been filed, and, with
              respect to each Registration Statement or further post-effective
              amendment, when it has become effective, (B) of any request by
              the SEC for amendments or supplements to any Registration
              Statement or prospectus or for additional information, (C) of the
              issuance by the SEC of any comments with respect to any filing
              and of any stop order suspending the effectiveness of any
              Registration Statement or the initiation of any proceedings for
              that purpose, (D) of the receipt by the Company of any
              notification with respect to the suspension of the qualification
              of any Registrable Securities for sale in any jurisdiction or the
              initiation or threatening of any proceeding for such purpose, (E)
              of the happening of any event that makes any statement made in
              any Registration Statement, prospectus, or any other document
              incorporated therein by reference untrue or that requires the
              making of any changes in such Registration Statement, prospectus,
              or any document incorporated therein by reference in order that
              such documents not contain any untrue statement of a material
              fact or omit to state any material fact required to be stated
              therein or necessary to make the statements therein not
              misleading, and (F) of the Company's determination that a further
              post-effective amendment to such Registration Statement would be
              appropriate;

                       (iii) furnish to each Holder, without charge, as many
              conformed copies as may reasonably be requested by such Holder,
              of each Registration Statement and any further post-effective
              amendments thereto, including financial statements and schedules,
              all documents incorporated therein by reference and all exhibits
              (including those incorporated by reference);

                        (iv) deliver to each Holder, without charge, as many
              copies of the then effective prospectus covering such Registrable
              Securities and any amendments or supplements thereto as such
              Holder may reasonably request;

                         (v) register, qualify, obtain an exemption therefrom,
              or cooperate with the Holders and their counsel in connection
              with the registration or qualification or exemption therefrom of
              such Registrable Securities for offer and sale under the
              securities or blue sky laws of such jurisdictions as may be
              reasonably requested in writing by the Holders and do any and all
              other acts or things necessary or advisable to enable the
              disposition in such jurisdictions of the Registrable Securities
              covered by the then effective Registration Statements; provided,
              however, that the Company shall not be required to (A) qualify as
              a foreign corporation or generally to transact business in any
              jurisdiction where it is not then so qualified, (B) qualify as a
              dealer (or other similar entity) in securities, (C)


                                      -4-


<PAGE>   5






              otherwise subject itself to taxation in connection with such
              activities, or (D) take any action which would subject it to
              general service of process in any jurisdiction where it is not
              then so subject;

                        (vi) upon the occurrence of any event contemplated by
              clauses (E) or (F) of paragraph (ii) above, promptly prepare and
              file, if necessary, a further post-effective amendment to each
              Registration Statement or a supplement to the related
              prospectuses or any document incorporated therein by reference or
              file any other required document so that each Registration
              Statement and the related prospectuses will not thereafter
              contain an untrue statement of a material fact or omit to state
              any material fact necessary to make the statements therein not
              misleading;

                       (vii) in no event later than five (5) Business Days
              before filing any Registration Statement, any further
              post-effective amendment thereto, any prospectus or any amendment
              or supplement thereto (other than any amendment or supplement
              made solely as a result of incorporation by reference of
              documents), furnish to the Holders copies of all such documents
              proposed to be filed;

                      (viii) not file any Registration Statement or amendment
              thereto or any prospectus or any supplement thereto (other than
              any amendment or supplement made solely as a result of
              incorporation by reference of documents) to which the Holders
              holding a majority of the Registrable Securities shall have
              reasonably objected in writing, within three (3) Business Days
              after receipt of such documents, to the effect that such
              Registration Statement or amendment thereto or prospectus or
              supplement thereto does not comply in all material respects with
              the requirements of the Securities Act (including, without
              limitation respect of any information describing the manner in
              which the Holders acquired such Registrable Securities and the
              intended method or methods of distribution of such Registrable
              Securities), (provided that the foregoing shall not limit the
              right of any Holder reasonably to object, within three (3)
              Business Days after receipt of such documents, to any particular
              information relating specifically to such Holder that is to be
              contained in any Registration Statement, prospectus or supplement
              including without limitation, any information describing the
              manner in which such Holder acquired such Registrable Securities
              and the intended method or methods of distribution of such
              Registrable Securities), and if the Company is unable to file any
              such document due to the objections of the Holders, the Company
              shall exert commercially reasonable efforts to cooperate with the
              Holders to prepare, as soon as practicable, a document that is
              responsive in all material respects to the reasonable objections
              of the Holders, provided however, that the Effectiveness Deadline
              (as defined in Section 2(b)) shall be extended by the period
              during which the Company is prevented from filing a Registration
              Statement or amendment thereto by reason of this paragraph
              3(a)(viii);

                        (ix) promptly after the filing of any document that is
              to be incorporated by reference into any Registration Statement
              or prospectus, provide copies of such document to the Holder;

                         (x) cause all Registrable Securities covered by each
              Registration Statement to be listed on the Nasdaq National
              Market, any national securities exchange, an over-the-



                                      -5-

<PAGE>   6




              counter market, or, if the Common Stock securities of the Company
              are not listed thereon, on the primary exchanges, markets, or
              inter-dealer quotations systems (including NASDAQ) if any, on
              which similar securities issued by the Company are then listed,
              prior to the date on which such Registrable Securities were
              issued;

                        (xi) take all actions reasonably required to prevent
              the entry of any stop order by the Securities and Exchange
              Commission or by any state securities regulators or to remove any
              such order if entered; and

                       (xii) file post-effective amendments to any Registration
              Statement or supplement the related prospectus, as required, to
              permit sales of Registrable Securities covered thereby to be made
              by Permitted Transferees of the Holders.

              (b)     Holder Procedures.

                         (i) The Company may require each Holder to furnish to
              the Company such information regarding such Holder and the
              proposed distribution of such Registrable Securities as the
              Company may from time to time reasonably request in writing and
              which is necessary for compliance with applicable law.

                        (ii) Each Holder agrees to cooperate with the Company
              in all reasonable respects in connection with the preparation and
              filing of the Registration Statement, any Amendment, any
              prospectus, and any prospectus supplement.

              (c)     Additional Information Available. So long as any
Registration Statement is effective covering the resale of Registrable
Securities owned by a Holder, the Company will furnish to such Holder(s):

                         (i) as soon as practicable after it becomes available
              (but in the case of the Company's Annual Report to Stockholders,
              within 140 days after the end of each fiscal year of the
              Company), one copy of: (A) its Annual Report to Stockholders
              (which Annual Report shall contain financial statements audited
              in accordance with generally accepted accounting principles by a
              national firm of certified public accountants); (B) its Annual
              Report on Form 10-K; and (C) its Quarterly Reports on Form 10-Q;
              and

                        (ii) upon the reasonable request of a Holder, all
              exhibits to the Annual Report on Form 10-K; and the Company, upon
              the reasonable request of a Holder, will meet with such Holder or
              a representative thereof at the Company's headquarters to discuss
              all information relevant for disclosure in any Registration
              Statement and will otherwise cooperate with any Holder conducting
              an investigation for the purpose of reducing or eliminating such
              Holder's exposure to liability under the Securities Act including
              the reasonable production of information at the Company's
              headquarters.

4.            REGISTRATION EXPENSES.

              All expenses incident to the Company's performance of or
compliance with this Agreement, including without limitation all registration
and filing fees, fees, and expenses of


                                      -6-


<PAGE>   7




compliance with state securities or blue sky laws (including fees and
disbursements of counsel in connection with blue sky qualifications or
registrations (or the obtaining of exemptions therefrom) of the Registrable
Securities), messenger and delivery expenses, internal expenses (including,
without limitation, all salaries and expenses of its officers and employees
performing legal or accounting duties), fees and disbursements of its counsel
and its independent certified public accountants, securities acts liability
insurance (if the Company elects to obtain such insurance), and reasonable fees
and expenses of any special experts retained by the Company in connection with
any registration hereunder (all of such expenses herein referred to as
"Registration Expenses"), shall be borne by the Company; provided, however, the
Registration Expenses shall not include any sales or underwriting discounts,
commissions, or fees attributable to the sale of the Registrable Securities or
the fees and expenses of counsel to the Holders.

5.            INDEMNIFICATION; CONTRIBUTION.

              (a)     Indemnification by the Company. The Company shall
indemnify and hold harmless, to the full extent permitted by law, each Holder,
and such Holder's respective officers, directors, employees, representatives,
agents, and controlling persons (within the meaning of the Securities Act),
against all losses, claims, damages, liabilities, and expenses resulting from
any untrue or alleged untrue statement of a material fact contained in any
Registration Statement, any prospectus, or any amendment or supplement thereto,
or any omission or alleged omission of a material fact required to be stated
therein or necessary to make the statements therein not misleading, except in
each case insofar as the same directly arises out of or is directly based upon
an untrue statement or alleged untrue statement of a material fact or an
omission or alleged omission to state a material fact in such Registration
Statement, prospectus, amendment, or supplement, as the case may be, made or
omitted, as the case may be, in reliance upon and in conformity with
information furnished to the Company in writing by such Holder expressly for
use therein.

              (b)     Indemnification by the Holders. Each Holder shall
indemnify and hold harmless, to the full extent permitted by law, the Company,
its officers, directors, employees, representatives, agents, and controlling
persons (within the meaning of the Securities Act), against all losses, claims,
damages, liabilities, and expenses (including, without limitation, reasonable
costs of investigation and legal expenses) resulting from any untrue or alleged
untrue statement of a material fact contained in any Registration Statement,
any prospectus, or any amendment or supplement thereto, and any omission or
alleged omission of a material fact required to be stated therein or necessary
to make the statements therein not misleading, to the extent the same directly
result from any untrue statement or alleged untrue statement of a material fact
or any omission or alleged omission to state a material fact in such
Registration Statement, prospectus, amendment, or supplement, as the case may
be, made or omitted, as the case may be, in reliance upon and in conformity
with information furnished to the Company in writing by such Holder expressly
for use therein. The liability of each Holder under the indemnity and
contributions provisions of this Section 5 shall be several and not joint and
shall be limited to an amount equal to the gross price of the Registrable
Securities sold by such Holder pursuant to the Registration Statement.

              (c)     Conduct of Indemnification Proceedings. Each party
entitled to indemnification under this Section 5 (the "Indemnified Party")
shall give written notice to the party required to provide indemnification (the
"Indemnifying Party") promptly after such Indemnified Party has actual
knowledge of any claim as to which indemnity may be sought, and shall permit
the Indemnifying Party



                                      -7-



<PAGE>   8





to assume the defense of any such claim or any litigation resulting therefrom;
provided, that counsel for the Indemnifying Party who will conduct the defense
of such claim or litigation, is approved by the Indemnified Party (whose
approval will not be unreasonably withheld or delayed); and provided, further,
that the failure of any Indemnified Party to give notice as provided herein
shall not relieve the Indemnifying Party of its obligations except to the
extent that its defense of the claim or litigation involved is prejudiced by
such failure. The Indemnified Party may participate in such defense at such
party's expense; provided, however, that the Indemnifying Party shall pay such
expense if representation of such Indemnified Party by the counsel retained by
the Indemnifying Party would be inappropriate due to actual or potential
conflicts of interest between the Indemnified Party and any other party
represented by such counsel in such proceeding. No Indemnifying Party, in the
defense of any such claim or litigation, except with the consent of each
Indemnified Party, shall consent to entry of any judgment or enter into any
settlement that does not include as an unconditional term thereof the giving by
the claimant or plaintiff to such Indemnified Party of a release from all
liability in respect of any claim or litigation, and no Indemnified Party will
consent to entry of any judgment or settle any claim or litigation without the
prior written consent of the Indemnifying Party (not to be unreasonably
withheld or delayed). Each Indemnified Party shall furnish such information
regarding himself, herself or itself and the claim in question as the
Indemnifying Party may reasonably request and as shall be reasonably required
in connection with the defense of such claim and litigation resulting
therefrom.

              (d)     Contribution.

                         (i) If for any reason the indemnification provided for
              in this Section 5 from an Indemnifying Party, although otherwise
              applicable by its terms, is unavailable to an Indemnified Party
              hereunder, then the Indemnifying Party, in lieu of indemnifying
              such Indemnified Party, shall contribute to the amount paid or
              payable by the Indemnified Parties as a result of such losses,
              claims, damages, liabilities, or expenses in such proportion as
              is appropriate to reflect the relative fault of such Indemnifying
              Party and the Indemnified Parties in connection with the actions
              that resulted in such losses, claims, damages, liabilities, or
              expenses, as well as any other relevant equitable considerations.
              The relative fault of such Indemnifying Party and the Indemnified
              Parties shall be determined by reference to, among other things,
              whether any action in question, including any untrue or alleged
              untrue statement of a material fact, has been made by, or relates
              to information supplied by, such Indemnifying Party or the
              Indemnified Parties, and the parties' relative intent, knowledge,
              access to information, and opportunity to correct or prevent such
              action. The amount paid or payable by a party as a result of the
              losses, claims, damages, liabilities, and expenses referred to
              above shall be deemed to include, subject to the limitations set
              forth in Section 5(c), any legal or other fees or expenses
              reasonably incurred by such party in connection with any
              investigation or proceeding.

                        (ii) The parties hereto agree that it would not be just
              and equitable if contribution pursuant to this Section 5(d) were
              determined by pro rata allocation or by any other method of
              allocation that does not take account of the equitable
              considerations referred to in the immediately preceding
              paragraph. No person guilty of fraudulent misrepresentation
              (within the meaning of Section 11(f) of the Securities Act) shall
              be entitled to contribution from any Person who was not guilty of
              such fraudulent misrepresentation.




                                      -8-

<PAGE>   9




6.            RULE 144 REQUIREMENTS.

              The Company agrees to:

              (a)     use its best efforts to make and keep public information
available, as those terms are understood and defined in Rule 144 under the
Securities Act;

              (b)     use its best efforts to file with the SEC in a timely
manner all reports and other documents required of the Company under the
Securities Act and the Securities Exchange Act; and

              (c)     furnish to each Holder upon request a written statement by
the Company as to its compliance with the reporting requirements of said Rule
144 and of the Securities Act and the Securities Exchange Act.

7.            INJUNCTIONS.

              Each of the parties hereto acknowledges and agrees that one or
more of the parties would be damaged irreparably in the event the provisions of
this Agreement are not performed in accordance with their specific terms or
otherwise are breached. Accordingly, each of the parties agrees that the other
party shall be entitled to an injunction or injunctions to prevent breaches of
the provisions hereof in any action instituted in any court of the United
States or any state thereof having jurisdiction over the parties in the matter,
in addition to any other remedy to which it may be entitled, at law or in
equity.

8.            TERMINATION.

              This Agreement shall terminate on the Registration Termination
Date; provided, however, that the provisions of Section 5, 6, and 7 shall
survive the termination of this Agreement.

9.            MISCELLANEOUS.

              (a)     Amendments and Waivers. Except as otherwise provided
herein, the provisions of this Agreement may not be amended, supplemented, or
otherwise modified, and waivers or consents to departures from the provisions
hereof may not be given, unless the Company shall have obtained the prior
written consent of the Holders holding more than 80% of the Registrable
Securities at the time of such amendment.

              (b)     Notices. Unless otherwise specified, all notices and other
communications provided for between the Company and the Purchaser in this
Agreement shall be in writing, including telecopy, and delivered or transmitted
to the addresses set forth below, or to such other address as shall be
designated by the Company or the Purchaser in written notice to the other
party. Notice sent by telecopy shall be deemed to be given and received when
receipt of such transmission is acknowledged, and delivered notice shall be
deemed to be given and received when receipted for by, or actually received by,
an authorized officer of the Company or the Purchaser, as the case may be.

                      (i) if to the Purchaser, to such address as is specified
              for the Purchaser under the terms of the Credit Agreement or if
              to another Holder, to the address indicated on the



                                   -9-




<PAGE>   10


              Company's register relating to the Warrants or Registrable
              Securities held by such Holder or at such other address as such
              Holder may have furnished to the Company in writing.

                      (ii)     if to the Company, at:

                                        Brigham Exploration Company
                                        6300 Bridge Point Parkway
                                        Building 2, Suite 500
                                        Austin, TX 78730
                                        Attn: Chief Financial Officer
                                        telephone:        512-427-3300
                                        telecopier:       512-427-3400

              (c)     Successors and Assigns. This Agreement shall be binding
upon and shall inure to the benefit of the Company and each Holder and their
respective successors and assigns. The rights provided by this Agreement shall
be transferred automatically from the Purchaser to any Person to whom any Note,
any Warrants, or any Registrable Securities are transferred, provided that (x)
the Company is given written notice of the transfer and the name, address,
telephone number, and facsimile number of the transferees and (y) the
subsequent transferee agrees in writing to be bound by all of the terms of this
Agreement (any transferee referred to in the foregoing clauses being referred
to herein as a "Permitted Transferee").

              (d)     Counterparts. This Agreement may be executed in any number
of counterparts and by the parties in separate counterparts, each of which when
so executed shall be deemed to be an original and all of which taken together
shall constitute one and the same agreement.

              (e)     Headings; Construction. The Section numbers and headings
in this Agreement are for convenience of reference only and shall not limit or
otherwise affect the meaning hereof. Unless the context otherwise requires, all
references to Sections are to sections of this Agreement, and words in the
singular include the plural and vice versa. In computing any period of time
specified in this Agreement or in any notices, the date of the act or event
from which such period of time is to be measured shall be included, any such
period shall expire at 5:00 p.m., Houston time, on the last day of such period,
and any such period denominated in months shall expire on the date in the last
month of such period that has the same numerical designation as the date of the
act or event from which such period is to be measured; provided, however, that
if there is no date in the last month of such period that has the same
numerical designation as of the date of such act or event, such period shall
expire on the last day of the last month of such period.

              (f)     Governing Law. This Agreement shall be governed by and
construed in accordance with the internal laws of Texas, without regard to the
principles of conflicts of laws thereof which would select any other law.

              (g)     Severability. If one or more of the provisions hereof, or
the application thereof in any circumstance, is held invalid, illegal, or
unenforceable in any respect, for any reason, the validity, legality, and
enforceability of the remaining provisions hereof shall not be in any way
affected or impaired thereby, and the provisions held to be invalid, illegal,
or unenforceable shall be reformed


                                     -10-



<PAGE>   11



to the minimum extent necessary, and in a manner as consistent with the
purposes thereof as is practicable, so as to render it valid, legal, and
enforceable.

              (h)     Entire Agreement. This Agreement, the Credit Agreement,
the Loan Documents, the Equity Conversion Agreement and the Warrant Agreement
are intended by the parties hereto to be a final expression thereof and is
intended to be a complete and exclusive statement of the agreement and
understanding of such parties in respect of the subject matter contained herein
related to the Registrable Securities. These agreements supersede all prior
agreements and understandings among the Company and any of the Holders with
respect to such subject matter.



                                      -11-



<PAGE>   12





              IN WITNESS WHEREOF, the parties hereto have caused this Agreement
to be duly executed as of the day and year first above written.


                            BRIGHAM EXPLORATION COMPANY


                            By:
                                 ----------------------------------------------
                            Name:  Curtis F. Harrell
                            Title: Chief Financial Officer


                            SHELL CAPITAL INC.


                            By:
                                 ----------------------------------------------
                            Name:  Robert L. Roberts
                            Title: Vice-President



[Registration Rights Agreement]

<PAGE>   1
                                                                   EXHIBIT 10.9



                               February 17, 2000


Brigham Oil & Gas, L.P.
6300 Bridge Point Parkway
Building 2, Suite 500
Austin, Texas  78730


         Re:      Certain Fees Pursuant to Credit Agreement Dated as of
                  February 17, 2000, among Brigham Oil & Gas, L.P. (the
                  "Borrower"), Bank of Montreal, as Agent, Shell Capital Inc.
                  ("SCI") and the lenders signatory thereto (the "Credit
                  Agreement")

Ladies/Gentlemen:

         This letter (the "Fee Letter") is written to confirm our mutual
understanding with respect to certain fees in connection with the Credit
Agreement. All capitalized terms not defined herein shall have the meaning
assigned to such terms in the Credit Agreement.

         In further consideration of our agreeing to enter into the facility
evidenced by the Credit Agreement, the Borrower does hereby agree to pay
certain additional fees to SCI for its own account as follows:

         Borrower shall pay the following fees to SCI:

         1.       Engineering  Fee in the amount of $10,000 to be paid on each
                  date of  valuation of RAPRV and each Borrowing Base
                  Redetermination Date.

         2.       If the Target Asset Value of the Borrower, approved by SCI,
                  is less than the amount of outstanding Loans twelve (12)
                  months after the Closing Date, the Borrower shall pay SCI a
                  monthly fee equal to 50 basis points per annum multiplied by
                  the Convertible Amount (as such term is defined in the Equity
                  Conversion Agreement) at that time. Such fee shall accrue
                  beginning twelve (12) months after the Closing Date, shall be
                  payable monthly in arrears, and will cease to accrue upon the
                  Scheduled Asset Valuation Date on which the Target Asset
                  Value, approved by SCI, becomes greater than the amount of
                  outstanding Loans.




<PAGE>   2



Page 2




         3.       If the Target Asset Value of the Borrower, approved by SCI,
                  is less than the amount of outstanding Loans eighteen (18)
                  months after the Closing Date, the Borrower shall pay SCI a
                  monthly fee equal to 100 basis points per annum (in
                  replacement of, but not in addition to, the fee described in
                  item 2 above) multiplied by the Convertible Amount (as such
                  term is defined in the Equity Conversion Agreement) at that
                  time. Such fee shall accrue beginning eighteen (18) months
                  after the Closing Date, shall be payable monthly in arrears,
                  and will cease to accrue upon the Scheduled Asset Valuation
                  Date on which the Target Asset Value, approved by SCI,
                  becomes greater than the amount of outstanding Loans.

         Any breach of the terms of items 1, 2 and 3 above shall be an Event of
Default under the Credit Agreement, subject, however, to a ten (10) Business
Day period of grace.

         This Fee Letter is further written to outline Borrower's
representation of its hedging strategy as follows:

         1.       Within five business days of the Closing Date, the Borrower
                  intends to enter into Hedging Agreements that together
                  provide a floor price covering (i) at least 70% of PDP
                  Reserves for no less than twelve (12) months after the
                  Closing Date, (ii) at least 50% of PDP Reserves for no less
                  than eighteen (18) months after the Closing Date and (iii) at
                  least 30% of PDP Reserves for no less than twenty-four (24)
                  months after the Closing Date.

         2.       Ongoing: The Borrower intends to use its best efforts to
                  maintain floor protection at levels in line with those
                  outlined in item (1) above on an on-going basis.

         As with all significant information provided to SCI, the hedging
         strategy outlined by Borrower was relied upon by SCI in making its
         decision to enter into the Credit Agreement.




<PAGE>   3


Page 3




         Please evidence your acknowledgment and acceptance of the foregoing by
signing in the space provided below.

                                         SHELL CAPITAL INC.

                                         By:
                                             ----------------------------------
                                         Name:    Robert L. Roberts
                                         Title:   Vice President



ACKNOWLEDGED AND AGREED
this 17 day of February, 2000

BRIGHAM OIL & GAS, L.P.

By:      Brigham, Inc., its General Partner

         By:
             ------------------------------
         Name: Curtis F. Harrell
         Title:   Chief Financial Officer


<PAGE>   1
                                                                   EXHIBIT 10.10

                                                                  EXECUTION COPY


                               SECOND AMENDMENT TO
                    INTERCREDITOR AND SUBORDINATION AGREEMENT


                  This Second Amendment to Intercreditor and Subordination
Agreement (this "Amendment") is dated as of February 17, 2000 by and among ECT
Merchant Investments Corp., a Delaware corporation ("ECT Merchant"), Joint
Energy Development Investments II Limited Partnership, a Delaware limited
partnership ("JEDI-II," and, together with ECT Merchant, the "Subordinated
Lender"), and JEDI-II, as agent for the Subordinated Lender (in such capacity,
the "Subordinated Agent"), and Bank of Montreal, as agent (in such capacity, and
together with any successor in such capacity, the "Senior Agent") for each of
the lenders that is a signatory to, or which becomes a signatory to, the Senior
Credit Agreement (as defined below) and/or the Restated Senior Credit Agreement
(as defined below) (collectively, the "Senior Lender"), for the benefit of the
Senior Agent and the Senior Lender.

                                    RECITALS

                  A. Brigham Oil & Gas, L.P., a Delaware limited partnership
(the "Borrower"), the Senior Agent and the Senior Lender previously entered into
that certain Credit Agreement dated as of January 26, 1998, as amended by First
Amendment to Credit Agreement dated August 20, 1998, Second Amendment to Credit
Agreement dated as of March 26, 1999, Third Amendment to Credit Agreement dated
as of July 19, 1999 and Fourth Amendment to Credit Agreement dated as of October
7, 1999 (as so amended, the "Senior Credit Agreement"), pursuant to which the
Senior Lender agreed to make certain loans and extensions of credit to the
Borrower.

                  B. On even date herewith, Borrower, Senior Agent, and Bank of
Montreal, Societe Generale, Southwest Agency ("Soc-Gen") and Shell Capital Inc.
("SCI"), each a Senior Lender are executing that certain Amended and Restated
Credit Agreement (such agreement as may from time to time be amended or
modified, called the "Restated Senior Credit Agreement"), which amends and
restates the Senior Credit Agreement in its entirety.

                  C. Brigham Exploration Company, a Delaware corporation (the
"Parent") has executed an Indenture dated August 20, 1998, with Chase Bank of
Texas, National Association, Trustee, as amended by First Amendment to Indenture
dated March 26, 1999 and by Second Amendment to Indenture dated as of February
17, 2000 (as so amended, the "Indenture"), pursuant to which the Parent has
issued its Senior Subordinated Secured Notes due 2003, in the aggregate
principal amount of $50,000,000 (the "Subordinated Notes").

                  D. JEDI-II and ECT Merchant, as the Subordinated Lender, own
100% of the Subordinated Notes currently outstanding under the Indenture.


<PAGE>   2

                  E. The Parent owns indirectly 100% of the general and limited
partnership interests in the Borrower, and the Parent and Borrower are members
of the same consolidated group of companies and are engaged in related
businesses, and the Parent has derived and will derive direct and indirect
economic benefit from the Restated Senior Credit Agreement.

                  F. Pursuant to the terms and conditions stated in the
Indenture, the Senior Credit Agreement and the Restated Senior Credit Agreement,
the Subordinated Lender, the Subordinated Agent, the Senior Agent, the Borrower,
the Parent and certain of the Parent's Subsidiaries entered into the
Intercreditor and Subordination Agreement (the "Subordination Agreement") dated
as of August 20, 1998.

                  G. The Subordinated Lender, the Subordinated Agent and the
Senior Agent now desire to amend certain provisions of the Subordination
Agreement.

                  NOW, THEREFORE, in consideration of the mutual covenants and
agreements herein contained, the Subordinated Lender, the Subordinated Agent and
the Senior Agent hereby agree that the Subordination Agreement shall be amended
as follows:

Section 1. Certain Definitions. As used in this Amendment, the terms "Senior
Agent", "Amendment", "Subordinated Agent", "Borrower", "SCI", "Soc-Gen",
"Subordination Agreement", "Senior Credit Agreement", "Restated Senior Credit
Agreement", "Parent", "Senior Lender," "Subordinated Notes", "ECT Merchant",
"JEDI-II", and "Subordinated Lender" shall have the meanings indicated above;
and unless otherwise defined herein, all terms beginning with a capital letter
which are defined in the Subordination Agreement shall have the same meanings
herein as therein unless the context hereof otherwise requires.

                  Section 2. Amendments to Subordination Agreement.

                  2.1 Section 1.2 of the Subordination Agreement is amended
hereby:

                      (i)    by inserting the following definitions where
                             alphabetically appropriate:

                           "Affiliate" of any Person shall mean (i) any Person
                      directly or indirectly controlled by, controlling or under
                      common control with such first Person, (ii) any director
                      or officer of such first Person or of any Person referred
                      to in clause (i) above and (iii) if any Person in clause
                      (i) above is an individual, any member of the immediate
                      family (including parents, spouse and children) of such
                      individual and any trust whose principal beneficiary is
                      such individual or one or more members of such immediate
                      family and any Person who is controlled by any such member
                      or trust. For purposes of this definition, any Person
                      which owns directly or


                                       2
<PAGE>   3


                      indirectly 20% or more of the securities having
                      ordinary voting power for the election of directors or
                      other governing body of a corporation or 20% or more of
                      the partnership or other ownership interests of any other
                      Person (other than as a limited partner of such other
                      Person) will be deemed to "control" (including, with its
                      correlative meanings, "controlled by" and "under common
                      control with") such corporation or other Person.

                           "Term ORRI" shall heave the meaning attributed to
                      such term under the Indenture.

                           "Term ORRI Conveyance" shall have the meaning
                      attributed to such term under the Indenture.

                      (ii) by deleting the definition of the term "Hedging
                           Agreement" in its entirety and substituting the
                           following therefor:

                           "Hedging Agreement" shall mean any commodity,
                      interest rate or currency swap, cap, floor, collar,
                      forward agreement or other exchange or protection
                      agreements or any option with respect to any such
                      transaction in existence as of the date hereof or
                      hereafter arising between (i) Borrower and Bank of
                      Montreal and its successors or assigns (a "BMO Hedge
                      Party") and Soc-Gen and its successors or assigns (a
                      "Soc-Gen Hedge Party") entered into while such BMO Hedge
                      Party or such Soc-Gen Hedge Party is a Lender; and (ii)
                      Borrower and SCI and its successors or assigns (with Loans
                      or Commitments of $20 million or more) or any Affiliate of
                      SCI (SCI and any Affiliate of SCI a "SCI Hedge Party")
                      entered into while such SCI Hedge Party or Fathom Energy
                      Capital I, L.L.C, is a Lender.

                      (iii) by deleting the reference "Hedging Agreement" in the
                            definition of "Senior Indebtedness" and substituting
                            therefor the reference "Hedging Agreements."

                      (iv) by amending the Recital H of the Subordination
                            Agreement by inserting the words "as any of such
                            documents or instruments may be amended,
                            supplemented or replaced from time to time" after
                            the words "attached hereto" in the last line
                            thereof.

                  2.2 Section 2.6(a)(i) of the Subordination Agreement is
amended by inserting, after the phrase "modify the interest payment schedule"
the additional phrase: "so as to require earlier payments of interest".


                                       3
<PAGE>   4

                  2.3 Section 2.6 of the Subordination Agreement is amended by
inserting the following phrase at the beginning of subsections (b) and (d):

                  "Subject to the Term ORRI Conveyances,"

                  2.4 The following new Section 2.9 to the Subordination
Agreement is inserted after Section 2.8:

                  "Section 2.9. Notwithstanding anything in this Agreement or
                  any other Senior Loan Document to the contrary, (a) no Term
                  ORRI Conveyance shall be considered a Subordinated Loan
                  Document for the purposes of this Agreement, (b) no
                  obligations or liabilities under any Term ORRI Conveyance
                  shall be Subordinated Indebtedness, and (c) reductions of the
                  Subordinated Indebtedness pursuant to the terms of the Term
                  ORRI Conveyances shall not be prohibited under the terms of
                  this Agreement and any other Senior Indebtedness Document.
                  Upon any payment or distribution of property or securities to
                  the creditors of the Parent, BOG, or any other grantor under
                  any Term ORRI Conveyance in a liquidation, dissolution,
                  insolvency or reorganization of such person or property or in
                  an assignment for the benefit of creditors or any marshaling
                  of its assets and liabilities, the grantee under any Term ORRI
                  Conveyance shall be entitled to receive payment in full of all
                  amounts not paid when due pursuant to Section 4.2 of the Term
                  ORRI Conveyances without any limitation under this Agreement
                  or any Senior Loan Document. In the event the Senior Agent or
                  any Senior Lender shall receive any amounts owed to the
                  grantee under any Term ORRI Conveyance (but only such amounts
                  owed pursuant to such Term ORRI Conveyance), the Senior Agent
                  or such Senior Lender will hold any amount so received in
                  trust for such grantee and will forthwith turn over such
                  payment to grantee in the form received by it (together with
                  any necessary endorsement)."

                  2.5 Section 3.3(d) of the Subordination Agreement is amended
to hereafter read in its entirety as follows:

                  "(c) not amend, supplement or otherwise modify the terms of
                  the Subordinated Indebtedness (including, without limitation,
                  the Subordinated Loan Documents) without the express written
                  consent of the Senior Agent, which consent will not be
                  unreasonably withheld, which has the effect of (i) increasing
                  the principal amount of the Subordinated Indebtedness,
                  provided that the foregoing shall not affect the Parent's
                  right to make payment in kind of accrued interest or the
                  Subordinated Lender's ability to accept payment in kind as
                  provided in the Subordinated Loan Documents, thereby
                  increasing the principal amount of the Subordinated
                  Indebtedness, (ii) increasing the rate of interest or any fees
                  charged on the Subordinated Indebtedness (provided that the
                  foregoing shall not prohibit any fees or changes in the rate
                  of interest contemplated by the terms of the


                                       4
<PAGE>   5

                  Securities Purchase Agreement), (iii) amending or modifying
                  the terms of the Term ORRI Conveyance or (iv) amending or
                  modifying the terms of the Indenture which relate to the Term
                  ORRI."

                  2.6 All references to the "Senior Credit Agreement" in the
Subordination Agreement shall henceforth refer to the Restated Senior Credit
Agreement as defined in this Amendment, as such Restated Senior Credit Agreement
is from time to time further amended, supplemented or restated.

                  Section 3. Representations and Warranties. The Subordinated
Lender and the Subordinated Agent hereby reaffirm that as of the effective date
of this Amendment, the representations and warranties made by the Subordinated
Lender and the Subordinated Agent in Article III of the Subordination Agreement
will be true and correct as though made on and as of the effective date of this
Amendment. The Senior Agent hereby reaffirms that as of the effective date of
this Amendment, the representations and warranties made by the Senior Agent in
Article III of the Subordination Agreement will be true and correct as though
made on and as of the effective date of this Amendment.

                  Section 4. Consents.

                  (a) Notwithstanding any provisions of Section 2.6 of the
Subordination Agreement, the Subordinated Lender and the Subordinated Agent of
their own free will hereby consent in all respects to and acknowledge the Senior
Credit Agreement, as amended as provided in Recital A above (a copy of which is
attached hereto as Schedule I), and the Restated Senior Credit Agreement, as
restated and amended as provided in Recital B above (a copy of which is attached
hereto as Schedule II) and to the transactions contemplated thereby and confirm
that they remain bound by the subordination provisions of Article II of the
Subordination Agreement. The Senior Lenders and the Senior Agent hereby consent
to the amendment of the Indenture pursuant to the Second Amendment to Indenture
and to the transactions contemplated therein, including the execution of the
Term ORRI Conveyances.

                  (b) The Senior Agent and the Senior Lender covenant and agree
not to contest or dispute, whether in any proceeding or otherwise, the validity,
enforceability, attachment, priority or perfected status of (i) any Lien granted
in favor of the Subordinate Agent or any Subordinate Lender or (ii) any Term
ORRI Conveyance or, with respect to the Term ORRI Conveyance, take any steps or
actions, including the institution of any proceedings, to enjoin or restrain the
grantee under any Term ORRI Conveyance from the exercise of the remedies
afforded them under any Term ORRI Conveyance.

                  Section 5. Ratification. The Subordinated Lender, the
Subordinated Agent and the Senior Agent hereby expressly ratify and affirm their
respective obligations under the Subordination Agreement (as amended hereby) and
agree that the Subordination Agreement remains in full force and effect.


                                       5
<PAGE>   6

                  Section 6. Descriptive Headings, etc. The headings,
descriptive or otherwise, of this Amendment and the several Sections of this
Amendment are inserted for convenience only and shall not be deemed to affect
the meaning or construction of any of the provisions hereof.

                  Section 7. Counterparts. This Amendment may be executed in any
number of counterparts and by different parties on separate counterparts and all
of such counterparts shall together constitute one and the same instrument.

                           [SIGNATURES ON NEXT PAGE.]


                                       6
<PAGE>   7

                  IN WITNESS WHEREOF, the parties hereto have caused this
Amendment to be duly executed and delivered and effective as of the date first
above written.

                                       SENIOR AGENT:

                                       BANK OF MONTREAL



                                       By:
                                            ---------------------------------
                                       Name:  Thomas McGraw
                                       Title:    Director

                                       SUBORDINATED LENDER:

                                       ECT MERCHANT INVESTMENTS CORP.


                                       By:
                                            ---------------------------------
                                       Name:
                                             --------------------------------
                                       Title:
                                              -------------------------------

                                       JOINT ENERGY DEVELOPMENT INVESTMENTS II
                                       LIMITED PARTNERSHIP

                                       By: Enron Capital Management II Limited
                                       Partnership, its General Partner

                                       By: Enron Capital II Corp., its General
                                       Partner

                                       By:
                                            ---------------------------------
                                       Name:
                                             --------------------------------
                                       Title:
                                              -------------------------------


                                       S
<PAGE>   8



                                       SUBORDINATED AGENT:

                                       JOINT ENERGY DEVELOPMENT INVESTMENTS II
                                       LIMITED PARTNERSHIP, as a Subordinated
                                       Lender and Subordinated Agent

                                       By: Enron Capital Management II Limited
                                       Partnership, its General Partner

                                       By: Enron Capital II Corp., its General
                                       Partner

                                       By:
                                            ---------------------------------
                                       Name:
                                             --------------------------------
                                       Title:
                                              -------------------------------


                                       S

<PAGE>   9

ACKNOWLEDGED AND CONSENTED TO:

Brigham Exploration Company

By:
    ---------------------------
         Karen E. Lynch
         Vice President

Brigham Oil & Gas, L.P.

By:      Brigham, Inc., its
         General Partner

By:
    ---------------------------
         Karen E. Lynch
         Vice President

Brigham, Inc.

By:
    ---------------------------
         Karen E. Lynch
         Vice President

Brigham Holdings I, LLC,
a Nevada limited liability company

By:
    ---------------------------
Name:
      -------------------------
Title:
      -------------------------

Brigham Holdings II LLC,
a Nevada limited liability company

By:
    ---------------------------
Name:
      -------------------------
Title:
      -------------------------


                                        S

<PAGE>   1
                                                                   EXHIBIT 10.11

                          SECOND AMENDMENT TO INDENTURE


         This SECOND AMENDMENT TO INDENTURE, dated as of February 17, 2000
("this Amendment"), is among BRIGHAM EXPLORATION COMPANY, a corporation duly
organized and existing under the laws of the State of Delaware (the "Borrower"),
and CHASE BANK OF TEXAS, NATIONAL ASSOCIATION, a national banking association
existing under the laws of the United States, as trustee (the "Trustee").

                              PRELIMINARY STATEMENT

         All covenants and agreement made by the Borrower herein are for the
benefit and security of the holders of the Borrower's Senior Subordinated
Secured Notes due 2003.

                                    RECITALS

         The Borrower and the Trustee are parties to that certain Indenture
dated as of August 20, 1998, as amended by the First Amendment to Indenture
dated as of March 26, 1999 (as amended, the "Indenture"). Capitalized terms used
and not otherwise defined herein are used with the meanings ascribed thereto in
the Indenture.

         The Borrower has advised the Noteholders and the Trustee that it
desires to amend certain provisions of the Indenture, and the Borrower has
requested that the Trustee and the Noteholders agree to various amendments to
certain provisions of the Indenture.

         The Trustee, upon the consent and authorization of the Noteholders, has
agreed to so amend certain provisions of the Indenture upon the terms and
subject to the conditions and limitations of this Amendment.

         NOW, THEREFORE, in consideration of the premises, covenants and
agreements contained herein, the parties hereto agrees as follows:

         Section 1. Definitions. The following capitalized terms shall have the
following respective meanings when used herein:


               1.1 "RELEASED CLAIMS" SHALL MEAN ANY AND ALL CLAIMS (INCLUDING
         WITHOUT LIMITATION ANY LIABILITIES, DAMAGES, DEMANDS AND CAUSES OF
         ACTION ARISING THEREFROM), WHETHER (A) AT LAW OR IN EQUITY, (B) ON THE
         ALLEGED COMMISSION OF A TORT, (C) ON THE ALLEGED BREACH (OR
         ANTICIPATORY BREACH OR REPUDIATION) OF ANY CONTRACT, DUTY, OR WARRANTY
         (WHETHER


<PAGE>   2


         ORAL OR WRITTEN, EXPRESS OR IMPLIED), (D) ON THE ALLEGED VIOLATION OF
         ANY STATUTE, TARIFF, OR REGULATION (WHETHER PROMULGATED BY THE UNITED
         STATES, ANY STATE THEREOF, ANY FOREIGN STATE OR COUNTRY, OR ANY OTHER
         GOVERNMENTAL AGENCY OR ENTITY, WHEREVER LOCATED), OR (E) ON ANY OTHER
         FACTUAL, LEGAL OR EQUITABLE THEORY, INCLUDING, WITHOUT LIMITATION, ANY
         CLAIM FOR DAMAGES OF ANY TYPE OR NATURE, FOR INJUNCTIVE OR OTHER
         RELIEF, FOR ATTORNEYS' FEES, INTEREST OR ANY OTHER LIABILITY WHATSOEVER
         ON ANY THEORY, INCLUDING WITHOUT LIMITATION ANY LOSS, COST OR DAMAGE IN
         CONNECTION WITH OR BASED UPON "LENDER LIABILITY", UNFAIR DEALING,
         DURESS, COERCION, CONTROL OR UNDUE INFLUENCE, EXTORTION OR COMMERCIAL
         BRIBERY, BREACH OF AN IMPLIED COVENANT OR DUTY OF GOOD FAITH AND FAIR
         DEALING, MATERIAL MISREPRESENTATION OR OMISSION, OVERREACHING,
         UNCONSCIONABILITY, CONFLICT OF INTEREST, BAD FAITH, MALPRACTICE,
         DISPARATE BARGAINING POSITION, DETRIMENTAL RELIANCE, PROMISSORY
         ESTOPPEL, ESTOPPEL BY DEED, WAIVER, LACHES, OR ANY OTHER EQUITABLE
         THEORY, EQUITABLE SUBORDINATION, BREACH OF FIDUCIARY DUTY OR ANY OTHER
         DUTY, OR TORTIOUS INDUCEMENT TO COMMIT SUCH BREACH, TORTIOUS
         INTERFERENCE WITH CONTRACT OR PROSPECTIVE BUSINESS RELATIONS, NEGLIGENT
         PERFORMANCE OF CONTRACTUAL OBLIGATIONS, OR OTHER THEORIES OF
         NEGLIGENCE, NEGLIGENT OR INTENTIONAL INFLICTION OF EMOTIONAL DISTRESS,
         SLANDER, LIBEL, OTHER DEFAMATION, FRAUDULENT TRANSFER, CONVERSION,
         TRESPASS TO (OR CLOUDING THE TITLE OF) PROPERTY, USURY, VIOLATIONS OF
         THE RACKETEER INFLUENCED AND CORRUPT ORGANIZATIONS ACT, DECEPTIVE TRADE
         PRACTICES, CONSPIRACY, OR ANY THEORY OF LIABILITY AS PARTNERS OR JOINT
         VENTURERS, THAT ANY RELEASING PARTY MAY HAVE AS OF THE DATE HEREOF
         AGAINST ANY RELEASED PARTY WITH RESPECT TO THE LENDING RELATIONSHIP.

               1.2 "Released Party" shall mean each of the Trustee, the
         Noteholders and their respective predecessors, successors, assigns,
         directors, officers, partners, employees, agents, attorneys, principals
         and Affiliates and all other Persons liable or who might be claimed to
         be liable on their behalf (collectively, the "Released Parties").

               1.3 "Releasing Party" shall mean each of the Borrower and the
         Guarantors and their respective predecessors, successors, assigns,
         directors, officers, partners, employees, agents, attorneys,
         principals, Affiliates and all other Persons who might have a claim
         against any Released Party (collectively, the "Releasing Parties").


                                      -2-
<PAGE>   3


         Section 2. Amendments to Indenture. The Indenture is amended as
follows:

               2.1     Section 1.01. Section 1.01 is amended as follows:

               2.1.1   The definition of "Consolidated Net Income" is amended as
         follows:

               2.1.1.1 By deleting all of subsection (iv) and replacing with the
         following:

                       "(iv) any extraordinary gains or losses;"

               2.1.1.2 By inserting after the end of subsection (iv) a new
         subsection (v) as follows:

                       "(v) any gains or losses attributable to Property sales
                       not in the ordinary course of business or attributable to
                       sales of Hydrocarbon Interests other than sales of
                       Hydrocarbon production in the ordinary course of
                       business: and"

               2.1.1.3 By relettering the existing subsection (v) as subsection
         (vi).

               2.1.1.4 By adding to the end of such definition the following:

                       "Any amounts paid on account of the Term ORRI shall be
                       added to Consolidated Net Income, regardless of the
                       accounting treatment afforded the Term ORRI."

               2.1.2   By adding to the end of the definition of "ECT", the
         words "and its successors and assigns".

               2.1.3   By deleting the definition of the term "First Borrowing
         Base Determination Date" in its entirety and substituting the following
         therefor:

                       "First Borrowing Base Determination Date" shall have the
                       meaning assigned to it in the Senior Credit Agreement."

               2.1.4   By deleting the definition of the term "Interest Expense"
         in its entirety and substituting the following therefor:

                       "Interest Expense" means, for each applicable period for
                       which EBITDA is to be calculated, the sum of all required
                       payments of interest (whether paid in cash or in kind,
                       but excluding any payments made on account of the Term
                       ORRI) during such period on borrowed money."


                                      -3-
<PAGE>   4


               2.1.5   By deleting the definition of the term "Adjusted
         Consolidated Net Tangible Assets" in its entirety.

               2.1.6   By deleting subsection (a) of the definition of the term
         "Permitted Debt" in its entirety and substituting the following
         therefor:

                       "(a) The Senior Loan, up to the lesser of (i) $75,000,000
                       or (ii) the Borrowing Base; provided that upon the
                       payment of any portion of the principal of the Senior
                       Loan, the maximum principal balance permitted under the
                       Senior Loan Documents shall be reduced by the amount of
                       the payment unless, until and to the extent reborrowing
                       such amount would be supported by an industry standard
                       "borrowing base" as reasonably determined by the Senior
                       Lenders constituting Majority Lenders under the Senior
                       Loan Documents, whether as part of a formal Borrowing
                       Base determination or in determination of the Target
                       Asset Value (as defined in the Senior Credit Agreement)
                       under the Senior Credit Agreement;"

               2.1.7   By adding the phrase "(other than the Senior Loan)"
         following the words "Financial Statements" in subsection (c) of the
         definition of "Permitted Debt".

               2.1.8   By adding to the end of the definition of "Registration
         Rights Agreement", the words ", as it may be amended, supplemented or
         restated from time to time".

               2.1.9   By inserting the following new definitions:

                       "Accrued PIK Amount" means, as of any particular day, the
                       aggregate dollar amount of all accrued interest on the
                       Notes that has been paid in kind (and not in cash) as of
                       such day in accordance with this Indenture, as reduced by
                       any amounts paid on or prior to such day under any Term
                       ORRI Conveyances or otherwise paid in cash as reduced
                       pursuant to Section 9.01. The Accrued PIK Amount as of
                       February 20, 2000 shall be $6,936,456.

                       "Applied Payments" has the meaning assigned to it in
                       Section 2.5.

                       "Non-Proved Reserves" means any reserves, other than
                       Proved Reserves.

                       "PDNP Reserves" shall mean proved, developed,
                       non-producing oil and gas reserves, as determined in
                       conformity with the guidelines in effect from time to
                       time as promulgated by the Society of Petroleum Engineers
                       or its successor association.


                                      -4-
<PAGE>   5


                       "PDP Reserves" shall mean proved, developed, producing
                       oil and gas reserves, as determined in conformity with
                       the guidelines in effect from time to time as promulgated
                       by the Society of Petroleum Engineers or its successor
                       association.

                       "Proved Reserves" means PDP Reserves, PDNP Reserves and
                       PUD Reserves.

                       "PUD Reserves" shall mean proved, undeveloped oil and gas
                       reserves, as determined in conformity with the guidelines
                       in effect from time to time as promulgated by the Society
                       of Petroleum Engineers or its successor association.

                       "Second Amendment" means the Second Amendment to
                       Indenture among the Borrower and the Trustee dated
                       February 17, 2000.

                       "Subject Reserves" means (a) any PDP Reserves and PDNP
                       Reserves identified by BOG or Borrower (or any Subsidiary
                       thereof) as of the date hereof as being produced or
                       producible in paying quantities out of wells now located
                       on the Hydrocarbon Interests owned by any of them as of
                       the date hereof including those listed on the attached
                       Exhibit I or (b) any PDP Reserves and PDNP Reserves
                       identified by BOG or Borrower (or any Subsidiary thereof)
                       following the date hereof and on or before December 31,
                       2000, as being produced or producible in paying
                       quantities out of any well spudded or acquired by BOG or
                       Borrower (or any Subsidiary thereof) on or before
                       December 31, 2000, (c) in the event only that Borrower's
                       Consolidated Interest Coverage Ratio calculated as of
                       September 30, 2000 (in accordance with the Indenture), is
                       less than 1.1 to 1.0, any PDP Reserves and PDNP Reserves
                       identified by BOG or Borrower (or any Subsidiary thereof)
                       following December 31, 2000 and on or before December 31,
                       2001, as being produced or producible in paying
                       quantities out of any well spudded or acquired after
                       December 31, 2000 but on or before December 31, 2001, and
                       (d) in the cases of (a), (b) and (c), above, a sufficient
                       interest in the Hydrocarbon Interests and Oil and Gas
                       Properties to afford BOG or the Borrower as applicable
                       the right, prior to giving effect to any Term ORRI
                       Conveyance, to secure the maximum authorized share of
                       production that is allocable to PDP Reserves and, when
                       applicable, PDNP Reserves found in each Subject Well.
                       Under no circumstances, and notwithstanding any provision
                       hereof to the contrary, shall the term "Subject Reserves"
                       include (1) any PUD Reserves or any Non-Proved Reserves
                       or (2) any PDP Reserves and/or PDNP Reserves beneficially
                       or legally owned


                                      -5-
<PAGE>   6


                       (whether in a vested or contingent manner) by a third
                       party (which is not an Affiliate of the Borrower) under
                       or pursuant to any agreement or other matter disclosed in
                       Exhibit H hereto, or (3) any PDP Reserves or PDNP
                       Reserves identified by Borrower or BOG as a result of the
                       deepening or sidetracking of a Subject Well after
                       December 31, 2000 (in the event item (c) of the
                       definition of Subject Reserves is not triggered) and
                       after December 31, 2001, (in the event item (c) of the
                       definition of Subject Reserves is triggered). Under no
                       circumstances shall the term "Subject Reserves" include
                       reserves that are not either producing or capable of
                       producing (or being made in the case of PDNP Reserves to
                       produce or capable of producing) in "paying quantities,"
                       as such term is defined under the Texas common law
                       (regardless of the jurisdiction in which the subject Oil
                       and Gas Properties are located).

                       "Subject Wells" means wells in which Subject Reserves are
                       now or hereafter identified and which are covered by a
                       Term ORRI Conveyance.

                       "Term ORRI" means any present or future right and
                       interest in the Oil and Gas Properties owned or hereafter
                       acquired by the Borrower, BOG or any other Affiliate of
                       the Borrower, to be conveyed by the Borrower and/or its
                       Subsidiaries, as applicable, to the Noteholders in
                       accordance with this Indenture, entitling the holders
                       thereof to 4% of the net proceeds (reducing to 3% of the
                       net proceeds) received by the Borrower or its Subsidiary
                       on account of production from the Subject Reserves. Each
                       Term ORRI shall be conveyed pursuant to a Term ORRI
                       Conveyance.

                       "Term ORRI Conveyance" means a conveyance of a Term ORRI
                       by the Borrower and/or its Subsidiaries, pursuant to
                       which the Borrower (or the applicable Subsidiary) conveys
                       to the Noteholders, a Term ORRI in the Oil and Gas
                       Properties owned or hereafter acquired by the Borrower,
                       BOG or any other Affiliate of the Borrower, in the form
                       attached hereto as Exhibit I.

               2.2 Section 1.02. Section 1.02 is amended by deleting the phrase
         "(including the ACNTA calculations)".

               2.3 Section 4.01. Section 4.01 is amended by adding the phrase
         "the ORRI and" following the words "subordinate in priority only to",
         in the introductory paragraph.

               2.4 Section 7.01. Section 7.01 of the Indenture is amended as
         follows:


                                      -6-
<PAGE>   7


               2.4.1 By deleting the reference "60" from the first sentence of
         subsection (b) and inserting the reference "45".

               2.4.2 By deleting subparagraph (g) in its entirety and
         substituting the following therefor:

                         "(g) Notices Under Other Loan Agreements. Concurrently
                         with the furnishing thereof to any Senior Lender or the
                         Senior Loan Agent, copies of any statement (including
                         financial statements), report or notice so furnished to
                         any Senior Lender or the Senior Loan Agent pursuant to
                         the terms of the Senior Loan Documents and not
                         previously furnished to the Agent or the Trustee
                         pursuant to any other provision of this Section 7.01."

               2.4.3 By amending subparagraph (j) to add a new sentence to the
         end as follows:

                         "Until the earliest date (i) on which there is a
                         payment in full of the Accrued PIK Amount and all other
                         Obligations, (ii) on or after November 21, 2000, on
                         which there is a payment in full of the Accrued PIK
                         Amount, or (iii) after November 21, 2000, on which the
                         Noteholders have received payment in full of the
                         Accrued PIK Amount through payment of the Term ORRI,
                         each monthly operating report shall identify all Oil
                         and Gas Properties that constitute Subject Reserves,
                         the date at which the well attributable to the Subject
                         Reserves was spudded and any additions to Subject
                         Reserves from the previous month's operating report."

               2.4.4 By deleting the final paragraph of Section 7.01 and
         substituting the following therefor:

                         "The Borrower will furnish to the Agent, at the time it
                         furnishes each set of financial statements pursuant to
                         paragraph (a) or (b) above, a certificate substantially
                         in the form of Exhibit J attached hereto executed by a
                         Responsible Officer (i) certifying as to the matters
                         set forth therein and stating that no Default has
                         occurred and is continuing (or, if any Default has
                         occurred and is continuing, describing the same in
                         reasonable detail), (ii) for the year 2000, setting
                         forth in reasonable detail an aged accounts payable and
                         accounts receivable listing, (iii) setting forth in
                         reasonable detail the computations necessary to
                         determine whether the Borrower is in compliance with
                         the financial covenants in Sections 8.16 and 8.17 as of
                         the end of the applicable reporting period(s) and,
                         together with pro forma calculations for each of such
                         financial covenants as of the end of the next fiscal
                         quarter, and (iv) certifying that said financial
                         statements fairly present the consolidated and
                         consolidating financial


                                      -7-
<PAGE>   8


                         condition and consolidated results of operations in
                         accordance with GAAP, as at the end of, and for, such
                         period (subject to normal year-end audit adjustments)."

               2.5 Section 7.07. Section 7.07 is amended by deleting subsection
         (b) in its entirety and substituting the following therefor:

                         "(b) Not less than 15 days prior to each of the First
                         Borrowing Base Determination Date and any Scheduled
                         Redetermination Date, the Borrower shall furnish to the
                         Agent a Reserve Report. The Reserve Report furnished
                         for the First Asset Valuation Date (as defined in the
                         Senior Credit Agreement) shall be prepared as of July
                         31, 2000, and the Reserve Report furnished for the
                         First Borrowing Base Determination Date shall be
                         prepared as of December 31, 2001. The Reserve Report
                         furnished for the Scheduled Redetermination Date to
                         occur in March of each year shall be prepared as of the
                         preceding December 31, and the Reserve Report furnished
                         for the Scheduled Redetermination Date to occur in
                         September of each year other than such First Asset
                         Valuation Date, shall be prepared as of the preceding
                         June 30. The Reserve Report to be furnished in March of
                         each year shall be prepared by certified independent
                         petroleum engineers or other independent petroleum
                         consultant(s) acceptable to the Agent and the Reserve
                         Reports to be furnished in September of each year shall
                         be prepared by or under the supervision of the chief
                         engineer or Vice President of Operations of the
                         Borrower who shall certify such Reserve Report to have
                         been prepared in accordance with the procedures used in
                         the immediately preceding March Reserve Report. At
                         Borrower's option, the Reserve Report to be furnished
                         in September of each year may instead consist of a
                         report from the independent petroleum engineers
                         referred to above on any new wells and a roll-forward
                         by Borrower on any wells previously reported in the
                         Reserve Report described in the immediately preceding
                         March."

               2.6 Section 7.12. A new Section 7.12 is added to the Indenture as
         follows:

                   "Section 7.12 Term ORRI. (a) Contemporaneously with the
                   execution of the Second Amendment, the Borrower has executed
                   and delivered, or caused its Subsidiaries to execute and
                   deliver, to the Noteholders, in their respective
                   Participations, a Term ORRI Conveyance to the Noteholders
                   covering all Hydrocarbon Interests owned by the Borrower and
                   its Subsidiaries. On the last Business Day of each calendar
                   month following the date of the Second Amendment, beginning
                   March 31, 2000, the Borrower shall execute and deliver, or
                   cause its Subsidiaries to execute and deliver, to the
                   Noteholders, in their respective Participations, (i) a Term
                   ORRI Conveyance covering all Hydrocarbon Interests owned by
                   the Borrower and its Subsidiaries identified


                                      -8-
<PAGE>   9


                   or acquired during the prior calendar month on or before
                   December 31, 2000, and (ii) in the event the Borrower's
                   Consolidated Interest Coverage Ratio calculated as of
                   September 30, 2000, is less than 1.1 to 1.0, a Term ORRI
                   Conveyance covering all Hydrocarbon Interests owned by the
                   Borrower and its Subsidiaries identified or acquired during
                   the prior calendar month on or before December 31, 2001.

                   (b) Any and all payments made on account of any Term ORRI or
                   otherwise pursuant to any Term ORRI Conveyance (the "Applied
                   Payments"), including payments made on account of the sale of
                   ORRI Hydrocarbons and payments made on account of a
                   piggy-back sale, farm-out, exchange or other transfer of a
                   Term ORRI pursuant to Section 3.2(a) of any Term ORRI
                   Conveyance, shall reduce the Accrued PIK Amount by the dollar
                   amount of such payment(s).

                   (c) Notwithstanding any provision hereof to the contrary, an
                   actual payment obligation on account of the Term ORRI shall
                   only be triggered by (i) the actual production, sale and
                   collection of proceeds on account of PDP Reserves from
                   Subject Reserves or (ii) a piggy-back sale, farm-out,
                   exchange or other transfer of any Term ORRI, or any portion
                   thereof, pursuant to Section 3.2 of any Term ORRI Conveyance,
                   and the mere identification by Borrower or BOG of PDP
                   Reserves and/or PDNP Reserves in any particular Subject Well
                   shall not trigger such an actual payment obligation or
                   otherwise constitute a representation, warranty or other
                   assurance that any such reserves (at any level) actually
                   exist and/or are producible in paying quantities.

                   (d) Notwithstanding any provision of this Amendment or any
                   Term ORRI Conveyance to the contrary, Agent shall serve as
                   agent and attorney-in-fact on behalf of the Noteholders for
                   purposes of (A) receiving Applied Payments under the Term
                   ORRI Conveyances, (B) receiving notices and other
                   communications under the Term ORRI Conveyances and (C)
                   executing instruments necessary or appropriate, in the
                   reasonable discretion of Borrower, to give effect to Section
                   2.4 or the last sentence of Section 3.2 of each Term ORRI
                   Conveyance.

                   (e) Notwithstanding any provision of any Term ORRI Conveyance
                   to the contrary, (i) all of the rights and interests of any
                   particular Noteholder under all, but not less than all, of
                   the Term ORRI Conveyances may be assigned by such Noteholder
                   to an Affiliate of such Noteholder, (ii) all or an undivided
                   portion of the rights and interests of any particular
                   Noteholder under all, but not less than all, of the Term ORRI
                   Conveyances may be assigned to a successor or assign of all
                   or a portion of such Noteholder's interest in the Loan
                   Documents, in proportion to the interest so transferred, or
                   (iii) all or an undivided portion of the rights and interests
                   of any particular Noteholder under all, but not less than
                   all, of the Term ORRI Conveyances may be assigned to a
                   successor or assign of all or a portion of such Noteholder's


                                      -9-
<PAGE>   10


                   interest in Accrued PIK Amounts subject to payment by virtue
                   of any Term ORRI. Upon any transfer of a Noteholder's
                   interest in the Term ORRI's and under the Term ORRI
                   Conveyances pursuant to this subsection (e), the Agent shall
                   serve as agent and attorney-in-fact on behalf of the
                   transferee for purposes of (A) receiving Applied Payments
                   under the Term ORRI Conveyances, (B) receiving notices and
                   other communications under the Term ORRI Conveyances and (C)
                   executing instruments necessary or appropriate, in the
                   reasonable discretion of Borrower, to give effect to Section
                   2.4 or the last sentence of Section 3.2 of each Term ORRI
                   Conveyance.

                   (f) The Term ORRI shall not apply to any Subject Reserves as
                   are, as of the date hereof, subject to the rights and
                   interests of third parties that are not Affiliates of the
                   Borrower under any agreement or other matter described in
                   Exhibit H hereto.

                   (g) Unless and until there is an Event of Default that is
                   continuing (and no longer subject to a cure period), BOG
                   under each Term ORRI Conveyance shall, notwithstanding any
                   provision of Section 4.2 of any Term ORRI Conveyance to the
                   contrary, have the absolute right to receive all payments for
                   (or on account of) ORRI Hydrocarbons as defined in the Term
                   ORRI Conveyance, and to net out Permissible Charges as
                   defined in the Term ORRI Conveyance and make distributions to
                   Agent, on behalf of Noteholders. In the event Agent or
                   Noteholders begin to receive payments on account of the Term
                   ORRI after and during the continuance of an Event of Default,
                   on or before the last day of each month, Agent shall provide
                   Borrower with an accounting of payments received (and a copy
                   of any invoices delivered to Agent in connection therewith)
                   during the previous calendar month on account of the Term
                   ORRI.

                   (h) Neither the Borrower nor any Subsidiary shall have any
                   obligation under any Term ORRI Conveyance, express or
                   implied, to maintain any Oil and Gas Property in force and
                   effect (whether by drilling, production, payment of delay
                   rentals, exercise of an option or otherwise), such
                   maintenance and all decisions with respect thereto to be in
                   the sole and absolute discretion of Borrower and BOG.

                   (i) In the event that Borrower's Consolidated Interest
                   Coverage Ratio calculated as of September 30, 2000 (in
                   accordance with the Indenture) is 1.1 to 1.0 or greater, the
                   Noteholders or Agent, on behalf of Noteholders, shall, on or
                   before January 30, 2001, release and reconvey to BOG, under a
                   form reasonably satisfactory to both Borrower and Noteholders
                   and free of all liens, claims and encumbrances created by,
                   through or under Noteholders, all rights, titles and
                   interests described in or covered by any Term ORRI
                   Conveyance, other than those carved out of Oil and Gas
                   Properties constituting Subject Reserves. In the event that
                   Borrower's Consolidated Interest Coverage Ratio calculated as
                   of September 30, 2000 (in accordance with the Indenture) is
                   1.1 to 1.0 or greater, Noteholders or Agent, on behalf of
                   Noteholders, shall, on or before January 30, 2002, release
                   and reconvey to BOG, under a form


                                      -10-
<PAGE>   11


                   reasonably satisfactory to both Borrower and Noteholders and
                   free of all liens, claims and encumbrances created by,
                   through or under Noteholders, all rights, titles and
                   interests described in or covered by any Term ORRI
                   Conveyance, other than those carved out of Oil and Gas
                   Properties constituting Subject Reserves. Upon termination of
                   the Term ORRIs, the Noteholders shall execute such documents
                   as the Borrower may reasonably request to evidence such
                   termination."

               2.7 Section 8.01. Section 8.01 of the Indenture is amended as
         follows:

               2.7.1 By deleting subsection (a) in its entirety and substituting
         the following therefor:

                   "(a) Incur, create or assume any Debt other than Permitted
                   Debt."

               2.7.2 By deleting the last paragraph of Section 8.01 in its
         entirety.

               2.8 Section 8.07. Section 8.07 of the Indenture is amended hereby
         by deleting clause (ii) in its entirety and substituting the following
         therefor:

                   "(ii) after giving effect to such merger or consolidation,
                   the Borrower or the applicable Subsidiary shall be the
                   surviving entity, and"

               2.9 Section 8.16. Section 8.16 of the Indenture is amended by
         deleting the section in its entirety and substituting the following
         therefor:

                   "Section 8.16 Consolidated Interest Coverage Ratio. As of the
                   last day of each fiscal quarter, beginning September 30,
                   2000, the Borrower will not permit the Consolidated Interest
                   Coverage Ratio to be less than (i) 1.05 to 1.0 as of
                   September 30, 2000, (ii) 1.2 to 1.0 as of December 31, 2000,
                   (iii) 1.4 to 1.0 as of March 31, 2001, (iv) 1.6 to 1.0 as of
                   June 30, 2001, (v) 1.8 to 1.0 as of September 30, 2001, and
                   (vi) 2.0 to 1.0 as of December 31, 2001 and the end of each
                   fiscal quarter thereafter."

               2.10 Article VIII. Article VIII of the Indenture is amended by
         inserting the following new Section 8.18 at the end of Article VIII:

                   "Section 8.18 Prepayments. During the continuation of any
                   Default, BOG shall not make any optional prepayment of the
                   Senior Loans pursuant to Section 2.01(i) of the Equity
                   Conversion Agreement (as defined in the Senior Credit
                   Agreement)."


               2.11 Section 9.01. Section 9.01 of the Indenture is amended by
         inserting the following at the end of Section 9.01:


                                      -11-
<PAGE>   12


                   "In addition, any payments received by the Agent or the
                   Noteholders (or otherwise owing to the Noteholders in
                   instances where the Noteholders have elected to be paid
                   directly on account of the Term ORRI pursuant to Section 4.2
                   of any Term ORRI Conveyance) which payments are (a)
                   attributable to any Term ORRI or (b) otherwise received
                   pursuant to Section 3.2(a) of any Term ORRI Conveyance
                   (collectively, the "Applied Payments") shall constitute a
                   prepayment on the Notes of that portion of the principal
                   balance which has been added to the Notes as a result of the
                   Borrower's election to pay accrued interest in kind in
                   accordance with the provisions of Section 9.02(b).
                   Notwithstanding the foregoing, to the extent that any Applied
                   Payment received by any Noteholder due to any Term ORRI is
                   subsequently invalidated, declared to be fraudulent or
                   preferential, set aside or required to be repaid by the Agent
                   or any Noteholder to the Borrower, any Subsidiary, trustee,
                   debtor in possession, receiver or other Person under any
                   bankruptcy law, common law or equitable cause, then to such
                   extent and further only to the extent Agent or Noteholder has
                   actually repaid the affected Applied Payment, the obligations
                   hereunder with respect to the Notes satisfied by payment of
                   the Term ORRI in the form of the affected Applied Payment
                   shall be revived and continue as if such payment or proceeds
                   had not been received and the Agent's and the Noteholder's
                   Liens, interests, rights, powers and remedies under this
                   Indenture and the Loan Documents shall continue in full force
                   and effect."

               2.12 Section 9.02. Section 9.02 of the Indenture is amended as
         follows:

               2.12.1 By deleting the last two sentences of subsection (a)
         beginning with "Notwithstanding".

               2.12.2 By deleting subsection (b) in its entirety and
         substituting the following therefor:

                   "(b) The Borrower shall have the option to pay accrued
                   interest on the Notes in kind on each of the seven (7)
                   consecutive Interest Payment Dates commencing with and
                   following February 20, 1999, as provided in this Section
                   9.02(b). In addition, the Borrower shall have the option to
                   pay accrued interest on the Notes in kind on November 20,
                   2000, in the event one of the following events has occurred
                   following the date of the Second Amendment and on or before
                   August 31, 2000: (i) Borrower sells common or preferred
                   equity securities resulting in net proceeds received by
                   Borrower (after deducting all costs and expenses incurred in
                   such sale) of at least $10,000,000; or (ii) BOG and/or
                   Borrower acquires in exchange for common or preferred equity
                   securities, Oil and Gas Properties containing PDP Reserves
                   and PDNP Reserves with a collective net


                                      -12-
<PAGE>   13


                   present value, discounted at 10% per annum, of at least
                   $10,000,000 (in the reasonable judgement of Majority
                   Noteholders); or (iii) through a combination of (i) and (ii)
                   above, Borrower receives net proceeds and newly acquired Oil
                   and Gas Properties, which (as valued above), total at least
                   $10,000,000 in net present value. In the event Borrower pays
                   interest in kind, at any time, the accrued interest due on
                   the applicable Interest Payment Date shall be calculated at
                   the rates set forth in this Section 9.02(b) and the interest
                   due (calculated at the rates set forth in this Section
                   9.02(b)) shall be deemed an advance of principal on the Notes
                   and, as of the applicable Interest Payment Date, shall be
                   added to the outstanding principal balance of the Notes
                   (notwithstanding the outstanding principal balance may
                   exceed, in the aggregate, the face amount of the Notes). In
                   order to not exercise its option under the first sentence of
                   this Section 9.02(b), the Borrower must, on or before the
                   applicable Interest Payment Date, deliver written notice to
                   the Agent executed by a Responsible Officer notifying Agent
                   of its election to not pay interest in kind. Should Borrower
                   fail to deliver such written notice in a timely fashion,
                   Borrower shall be deemed to have irrevocably elected to make
                   payment of accrued interest in kind on the next applicable
                   Interest Payment Date. Should Borrower deliver such notice in
                   a timely fashion, Borrower shall be deemed to have
                   irrevocably elected to make payment of accrued interest in
                   cash and any subsequent failure to do so in a timely fashion
                   (subject to the five (5) day grace period provided in Section
                   10.01(a)) shall constitute an Event of Default hereunder. In
                   order to exercise its option under the second sentence of
                   this Section 9.02(b), the Borrower must, on or before
                   September 7, 2000, deliver written notice to the Agent
                   executed by a Responsible Officer certifying to Agent that
                   Borrower has satisfied the conditions set forth in the second
                   sentence of this Section 9.02(b), together with reasonable
                   supporting evidence, and notifying Agent of its election to
                   pay interest in kind on the November 20, 2000 Interest
                   Payment Date. Should Borrower fail to deliver such written
                   notice in a timely fashion, Borrower shall be deemed to have
                   irrevocably elected not to make payment of accrued interest
                   in kind on the November 20, 2000 Interest Payment Date.
                   Should Borrower deliver such notice in a timely fashion,
                   Borrower shall be deemed to have irrevocably elected to make
                   payment of accrued interest in cash and any subsequent
                   failure to do so in a timely fashion (subject to the five (5)
                   day grace period provided in Section 10.01(a)) shall
                   constitute an Event of Default hereunder. In the event the
                   Borrower elects to pay interest in kind, such interest to be
                   paid shall be calculated at 13% per


                                      -13-
<PAGE>   14


                   annum commencing on the immediately preceding Interest
                   Payment Date."

               2.13 Section 10.01. Section 10.01 of the Indenture is amended as
         follows:

               2.13.1 By deleting subsection (a) in its entirety and
         substituting the following therefore:

                   "(a) the Borrower shall default in the payment or prepayment
                   when due of any Obligation, and such default, other than a
                   default of a payment or prepayment of principal (which shall
                   have no cure period), shall continue unremedied for a period
                   of five (5) days after such Obligation becomes due, in the
                   case of interest, or thirty (30) days after the Borrower
                   receives notice from the Agent that such Obligation is due,
                   in the case of Obligations other than principal or interest;
                   or"

               2.13.2 By deleting clause (ii) of subsection (b) in its entirety
         and substituting the following therefor:

                   "(ii) as to the Senior Loan, there shall have (x) occurred a
                   default thereunder in the payment of any principal or
                   interest due on the Senior Loan beyond any cure period
                   contained in the Senior Loan Documents as of the date of the
                   Second Amendment, whether or not the Senior Lenders have
                   waived such default or modified the Senior Loan Documents to
                   extend the due date thereof or any cure period or (y)
                   occurred a default thereunder and the holders of the Senior
                   Loan shall have elected to accelerate the payment of the
                   Senior Loan (or it shall be accelerated automatically or
                   otherwise be due and payable in full); or"

               2.13.3 By deleting the "." at the end of subsection (m) and
         substituting "; or"

               2.13.4 By adding the following new subsection (n) at the end of
         Section 10.01:

                   "(n) BOG, Borrower or any Subsidiary of Borrower, shall
                   default in the performance of its obligations under any Term
                   ORRI Conveyance and such default shall continue unremedied
                   for a period of thirty days after the earlier of (A) the date
                   notice thereof to the Borrower by the Agent or (B) the
                   Borrower's knowledge thereof; provided that the foregoing 30
                   day cure period shall be reduced to five days for any payment
                   default. As used in this Section 10.01(n), "Borrower's
                   knowledge" shall be limited to the actual knowledge of any of
                   the officers of the Borrower or BOG."


                                      -14-
<PAGE>   15


               2.14 Exhibits.

               2.14.1 A new Exhibit "H" is added to the Indenture in the form of
         Exhibit "H" to this Second Amendment.

               2.14.2 A new Exhibit "I" is added to the Indenture in the form of
         Exhibit "I" to this Second Amendment.

               2.14.3 A new Exhibit "J" is added to the Indenture in the form of
         Exhibit "J" to this Second Amendment.

         Section 3. Conditions Precedent. This Amendment shall become binding
only upon receipt by the Agent of the following documents and satisfaction of
the other conditions provided in this Section 3 (the "Closing Date"), each of
which must be satisfactory to the Agent in form and substance:

               3.1 The Second Amendment. Counterparts of this Amendment executed
         by the Borrower and the Trustee.

               3.2 New Mortgage. The Borrower shall have satisfied all of its
         obligations under Section 7.09(a) of the Indenture, including the (i)
         delivery to the Agent of all Mortgages required thereby and (ii)
         evidence that the New Mortgage and the related UCC-1 financing
         statements delivered have been filed in all jurisdictions necessary to
         perfect and protect the security interests, assignments and Liens
         created thereby.

               3.3 Registration Rights. Counterparts of the Second Amendment to
         Registration Rights Agreement executed by the Borrower, JEDI-II and ECT
         Merchant.

               3.4 Financial Statements. All past due financial statements
         through the month of November 1999 described in Section 7.01 of the
         Indenture.

               3.5 Officer's Certificates. All past due officer's certificates
         through the month of November 1999 described in Sections 7.01 and 7.07
         of the Indenture.

               3.6 Accounts Payable. An aged accounts payable and accounts
         receivable listing as of December 31, 1999.

               3.7 Secretary's Certificate. Certificates of the Secretary or an
         Assistant Secretary of the Borrower and each of the Guarantors setting
         forth for each of them (i) the resolutions of its board of directors or
         managers (or if such Guarantor is a partnership, resolutions of the
         general partner of such partnership), as applicable, with respect to
         the authorization to execute and deliver this Amendment and the
         consummation of the transactions contemplated


                                      -15-
<PAGE>   16


         hereby; (ii) the Responsible Officer of such entity authorized to sign
         this Amendment, and (iii) the signature of such authorized Responsible
         Officer of such entity.

               3.8 Term ORRI Conveyance. A Term ORRI Conveyance in the form
         attached hereto as Exhibit I conveying a Term ORRI in all Oil and Gas
         Properties owned by the Borrower, BOG or any other Affiliate of the
         Borrower.

               3.9 Consent by Guarantors. A Consent and Acknowledgment executed
         by BOG and Brigham, Inc.

               3.10 Warrants. Duly executed revised warrants in the form
         attached hereto as Exhibit A, issued by the Borrower to the Noteholders
         in their respective Participations, in substitution for the current
         Warrants issued pursuant to Section 2.03 of the Securities Purchase
         Agreement (and any Warrants issued in substitution therefor), for the
         purchase of an aggregate of 1,000,000 shares of Common Stock, and which
         warrants shall constitute the "Warrants" under the Indenture and the
         Securities Purchase Agreement for all purposes.

               3.11 Opinion of Counsel. An opinion of Thompson & Knight, LLP in
         form satisfactory to the Noteholders.

               3.12 Fees and Expenses. Payment of the expenses of the Agent and
         the Noteholders in accordance with Section 6 hereof.

               3.13 Senior Lenders Consent. A consent executed by each of the
         Senior Lenders and the Senior Loan Agent, consenting to the terms of
         this Amendment and subordinating all of the liens securing the Senior
         Loan to each Term ORRI.

               3.14 Letter. A letter from Borrower in the form attached hereto
         as Exhibit B.

               3.15 Subordination Agreement. An amendment to the Subordination
         Agreement satisfactory to the Noteholders, the Senior Lenders, the
         Agent and the Senior Loan Agent.

               3.16 Closing of Amended Senior Credit Agreement.
         Contemporaneously with the Closing Date, the Borrower and/or its
         Subsidiaries, the Senior Loan Agent and the Senior Lenders shall have
         executed the amended Senior Credit Agreement (in such form as is
         satisfactory to the Noteholders) and all other Senior Loan Documents
         (in such form as is satisfactory to the Noteholders).

               3.17 Other Documents. Such other documents as Agent or its
         counsel may reasonably request.


                                      -16-
<PAGE>   17



         Section 4. Post Closing. Within 30 days as of the Closing Date hereof,
Brigham Holdings I, LLC and Brigham Holdings II, LLC will execute a Consent and
Acknowledgment.

         Section 5. Representations and Warranties.

               5.1 Reaffirmation. The Borrower hereby reaffirms that, as of the
         date of this Amendment, the representations and warranties made by the
         Borrower in the Securities Purchase Agreement and each of the Loan
         Documents are true and correct as though made on and as of the date
         hereof, subject only to the revisions to the schedules to the
         Securities Purchase Agreement and Indenture as are reflected in the
         schedules attached hereto and further, the Borrower represents that,

               5.1.1 As of the date hereof, no Default or Material Adverse
         Effect has occurred and is continuing except as previously disclosed to
         the Agent in writing.

               5.1.2 The execution, delivery and performance by the Borrower or
         the Guarantors of this Amendment and the other Loan Documents and all
         instruments and documents to be delivered by the Borrower or the
         Guarantors, to the extent a party thereto, hereunder and thereunder and
         the creation of all Liens provided for herein and therein: (i) are
         within the Borrower's or such Guarantor's corporate power; (ii) have
         been duly authorized by all necessary or proper corporate action,
         including the consent of stockholders, members and/or partners therein
         or thereof; (c) are not in contravention of any provision of the
         Borrower's or such Guarantor's certificate of incorporation, bylaws or
         similar organizational and/or governing documents; (d) will not violate
         (1) any law or regulation or (2) any order or decree of any court or
         governmental instrumentality; (e) will not conflict with or result in
         the breach or termination of, constitute a default under or accelerate
         any performance required by, any indenture, mortgage, deed of trust,
         lease, agreement or other instrument to which the Borrower or any of
         the Guarantors is a party or by which the Borrower or any of the
         Guarantors or any of their respective property is bound; (f) will not
         result in the creation or imposition of any Lien upon any of the
         property of the Borrower or the Guarantors other than those in favor of
         the Agent pursuant to the terms of this Amendment and the other Loan
         Documents to be delivered in connection herewith; and (g) do not
         require the consent or approval of any governmental body, agency,
         authority or any other Person that has not been duly obtained, made or
         complied with prior to the date hereof. At or prior to the date hereof,
         each of this Amendment and the other Loan Documents to be delivered in
         connection herewith shall have been duly executed and delivered for the
         benefit of or on behalf of the Borrower or the Guarantors, in each case
         to the extent a party thereto, and each shall then constitute a legal,
         valid and binding obligation of the Borrower or such Guarantor,
         enforceable against it in accordance with its terms.


                                      -17-
<PAGE>   18


               5.2 Independent Counsel. Each of the Borrower and the Guarantors
         further represents and warrants, for itself only that it (i) is
         executing this Amendment, and the documents executed in connection
         herewith to which it is a party, after consultation with counsel of its
         own choosing, (ii) has read and understands the release granted by
         Section 5 hereof, (iii) desires to execute this Amendment and such
         documents to which it is a party and (iv) has the requisite authority
         to enter into and be bound by this Amendment and such documents to
         which it is a party, including the release granted by Section 5 hereof.

         Section 6. Release.

               6.1 EACH OF THE RELEASING PARTIES DESIRES AND INTENDS FULLY TO
         COMPROMISE, RELEASE AND SETTLE ANY AND ALL OF THE RELEASED CLAIMS; AND
         EACH OF THE RELEASING PARTIES HEREBY COVENANTS, WARRANTS AND REPRESENTS
         UNTO EACH OF THE RELEASED PARTIES THAT SUCH RELEASING PARTY DOES HEREBY
         FOREVER RELEASE, ACQUIT, WAIVE AND DISCHARGE EACH OF THE RELEASED
         PARTIES OF AND FROM THE RELEASED CLAIMS AND EACH OF THE RELEASING
         PARTIES HEREBY DECLARES THE SAME FOREVER RELEASED, ACQUITTED, WAIVED,
         SETTLED AND DISCHARGED. THIS RELEASE IS EFFECTIVE WITHOUT REGARD TO
         WHETHER (I) SUCH RELEASED CLAIMS ARE KNOWN OR UNKNOWN, (II) DAMAGES
         ARISING OUT OF SUCH RELEASED CLAIMS HAVE YET ACCRUED, (III) SUCH
         RELEASED CLAIMS AROSE COLLATERALLY, DIRECTLY, DERIVATIVELY, OR
         OTHERWISE BETWEEN THE PARTIES HERETO OR (IV) AN ORDINARY PERSON IN THE
         SAME OR SIMILAR CIRCUMSTANCES WOULD OR WOULD NOT, THROUGH THE EXERCISE
         OF DUE CARE, HAVE DISCOVERED SUCH CLAIMS BY THE DATE OF THIS AMENDMENT.
         IN CONNECTION WITH THE FOREGOING RELEASE:

               6.2 Borrower and each of the Guarantors represents and warrants
         that it has the full power and authority to perform the release granted
         in this Section 6 and that it has not in any manner made any assignment
         of any Released Claim to any third party.

               6.3 The release granted in this Section 6 will be effective upon
         execution of this Amendment by all of the parties hereto.

               6.4 Each party executing this Amendment understands and agrees
         that the release granted in this Section 6 is a full, final and
         complete release of the Released Claims and that such release may be
         pleaded as an absolute and final bar to any or all suits which may
         hereafter be filed or prosecuted by any one or more of the Releasing
         Parties or anyone claiming by, through or under any one or more of the
         Releasing Parties in respect of any of the matters released hereby, and
         that no recovery on account of the Released Claims may hereafter be had
         from any of the Released Parties; and that the consideration given for
         such release is not an


                                      -18-
<PAGE>   19


         admission of liability or fault on the part of any of the Released
         Parties (it being the express intent of the parties hereto to obtain
         peace of mind and avoid the expense and uncertainty of potential
         litigation), and that none of the Releasing Parties or those claiming
         by, through or under any of them will ever claim that it is.

               6.5 The parties hereto acknowledge that the release granted by
         this Section 6 does not have any effect with respect to relationships
         between the Borrower and each of the Guarantors and the Noteholders and
         the Agent other than in connection with the Lending Relationship.

         Section 7. Payment of Fees and Expenses; Form of Payment.

               7.1 The Borrower agrees, whether or not the transactions
         contemplated hereby are consummated, to pay all reasonable expenses of
         the Agent and the Noteholders (including, without limitation, all
         reasonable fees and disbursements of counsel and other outside
         consultants for the Agent and/or the Noteholders) in connection with
         the negotiation, investigation, preparation, execution and delivery of,
         recording and filing of, preservation of rights under and enforcement
         of this Amendment and the other Loan Documents to be delivered in
         connection herewith.

               7.2 All payments to be made by the Borrower under this Amendment
         shall be made in Dollars, in immediately available funds, to the Agent
         at such account as the Agent shall specify.

         Section 8. Limitations. The amendments set forth herein are limited
precisely as written and shall not be deemed to (a) be a consent to, or waiver
or modification of, any other term or condition of the Securities Purchase
Agreement or the Indenture or any of the other Loan Documents, or (b) prejudice
any right or rights which the Noteholders or the Agent may now have or may have
in the future under or in connection with the Securities Purchase Agreement or
the Indenture or any of the other Loan Documents. Except as expressly
supplemented, amended or modified hereby, the terms and provisions of the
Securities Purchase Agreement or the Indenture or any other Loan Documents are
and shall remain in full force and effect. In the event of a conflict between
this Amendment and any of the foregoing documents, the terms of this Amendment
shall be controlling.

         Section 9. Governing Law. This Amendment and the rights and obligations
of the parties hereunder and under the Indenture shall be construed in
accordance with and be governed by the laws of the State of Texas and the United
States of America.


                                      -19-
<PAGE>   20


         Section 10. Descriptive Headings, etc. The descriptive headings of the
several Sections of this Amendment are inserted for convenience only and shall
not be deemed to affect the meaning or construction of any of the provisions
hereof.

         Section 11. Counterparts. This Amendment may be executed  in any number
of counterparts and by different parties on separate counterparts and all of
such counterparts shall together constitute one and the same instrument.


                                      -20-
<PAGE>   21


         IN WITNESS WHEREOF, the parties hereto have caused this Amendment to be
executed as of the date first written above.

             NOTICE PURSUANT TO TEX. BUS. & COMM. CODE SECTION 26.02

THIS AMENDMENT AND OTHER LOAN DOCUMENTS EXECUTED BY ANY OF THE PARTIES BEFORE OR
SUBSTANTIALLY CONTEMPORANEOUSLY WITH THE EXECUTION HEREOF TOGETHER CONSTITUTE A
WRITTEN LOAN AGREEMENT AND REPRESENT THE FINAL AGREEMENT BETWEEN THE PARTIES AND
MAY NOT BE CONTRADICTED BY EVIDENCE OF PRIOR, CONTEMPORANEOUS OR SUBSEQUENT ORAL
AGREEMENTS OF THE PARTIES. THERE ARE NO UNWRITTEN ORAL AGREEMENT BETWEEN THE
PARTIES.


BORROWER:                 BRIGHAM EXPLORATION COMPANY


                          By:
                             ----------------------------------------------
                               Curtis F. Harrell
                               Chief Financial Officer



TRUSTEE:                  CHASE BANK OF TEXAS, NATIONAL ASSOCIATION,
                          as Trustee


                          By:
                             ----------------------------------------------
                                 Mauri J. Cowen
                                 Vice President and Trust Officer






<PAGE>   22


The Noteholders have joined herein solely for the purpose of evidencing their
(i) consent to the foregoing, and (ii) authorization to the Trustee to execute
this Amendment:

                            JOINT ENERGY DEVELOPMENT INVESTMENTS
                            II LIMITED PARTNERSHIP, a Delaware limited
                            partnership, as Purchaser

                            By:  Enron Capital Management II Limited
                                 Partnership, its General Partner

                                 By:  Enron Capital II Corp., its
                                      General Partner


                                      By:
                                         --------------------------------------
                                            Mark Warner
                                            Agent and Attorney-in-Fact


                            ECT MERCHANT INVESTMENTS
                            CORP., a Delaware corporation


                            By:
                               ----------------------------------------------
                                   Mark Warner
                                   Agent and Attorney-in-Fact


<PAGE>   23


                                    EXHIBIT A

                                 Form of Warrant


<PAGE>   24


                                    EXHIBIT B

                                 Form of Letter



                                February 28, 2000



Mr. John S. Hopley
Enron North America Corp.
1400 Smith Street
Houston, Texas 77002-7361


Dear John:

         Brigham Exploration Company ("BEXP") agrees to engage within thirty
days from the date hereof of a reputable investment banking firm mutually
acceptable to Enron North America Corp. and BEXP and to secure from such
investment banking firm advice concerning financial, capitalization, strategic,
sale, merger and restructure options available to BEXP within thirty days after
such engagement. BEXP agrees to present such advice to its board of directors
and to analyze and consider any such advice offered, but shall in no way be
obligated to act on such advice.



                                   Sincerely,




                                   Curtis F. Harrell

CFH/ldl


<PAGE>   25



                                    EXHIBIT H

                                  TITLES, ETC.

(a) The rights and interests afforded Gasco Limited Partnership ("Gasco") and
its successors and assigns under the terms of (i) that certain Expense
Allocation and Participation Agreement dated as of April 1, 1996, by and between
Gasco and BOG, as heretofore and/or hereafter amended, expanded, supplemented,
renewed and/or extended, and (ii) that certain Expense Allocation and
Participation Agreement II dated as of April 1, 1997, by and between Gasco and
BOG, as heretofore and/or hereafter amended, expanded, supplemented, renewed
and/or extended, and (iii) that certain Expense Allocation and Participation
Agreement III dated as of March 1, 1998, by and between Gasco and BOG, as
heretofore amended, expanded, supplemented, renewed and/or extended.

(b) The rights and interests afforded Middle Bay Oil Company ("Middle Bay") and
its successors and assigns under the terms of that certain Expense Allocation
and Participation Agreement dated as of April 1, 1996, by and between Middle Bay
and BOG, as heretofore amended, modified, expanded, supplemented, renewed and/or
extended.

(c) The rights and interests afforded Stephens Production Company ("Stephens")
and its successors and assigns under the terms of that certain Anadarko Basin
Joint Participation Agreement dated as of May 1, 1996, by and between BOG and
Stephens, as heretofore amended, modified, expanded, supplemented, renewed
and/or extended.

(d) The rights and interests afforded Vintage Petroleum, Inc. ("Vintage") and
its successors and assigns under the terms of that certain Anadarko Basin Joint
Participation Agreement dated as of May 1, 1996, by and between BOG and Vintage,
as heretofore amended, modified, expanded, supplemented, renewed and/or
extended.

(e) The rights and interests afforded Brigham-Duke (Delaware) LLC ("Duke") and
its successors and assigns under the terms of that certain Joint Development
Agreement dated as of February 17, 1999, by and between Duke and BOG, as
heretofore amended.

(f) The rights and interests, whether real or equitable, vested or contingent,
afforded third parties under the terms of various farmout, exploration, joint
participation and/or operating agreements, in existence as of the date hereof,
under or in relation to which BOG, Borrower or any Subsidiary agrees to farm-out
to one or more third party(ies) one or more Oil and Gas Property and/or
undertakes with one or more third party(ies) the joint exploration and/or
development of one or more Oil and Gas Properties (which rights and interests
may include, without limitation, rights under Area of Mutual Interests
agreements and rights in respect of forfeiture of all or a portion of Borrower's
interests in an Oil and Gas Property, or part thereof or interest therein, that
is triggered by an election not to participate in a proposed operation; and


<PAGE>   26



(g) consulting agreements in existence as of the date hereof, as same may have
heretofore been amended, expanded, supplemented, renewed and/or extended, with
third party geologists, landmen or other oil and gas industry participants who
agree to perform services in return, in whole or in part, for an overriding
royalty interest or other interest in or relating to any Oil and Gas Properties.




<PAGE>   27



                                    EXHIBIT I

                              Term ORRI Conveyance


<PAGE>   28



                                    EXHIBIT I

                              Hydrocarbon Interests



<PAGE>   29



                                    EXHIBIT J

                        FORM OF CERTIFICATE ACCOMPANYING

                               FINANCIAL STATEMENT




<PAGE>   1
                                                                   EXHIBIT 10.12

                            CONVEYANCE OF ADJUSTABLE
                        TERM OVERRIDING ROYALTY INTEREST

         This Conveyance of Adjustable Term Overriding Royalty Interest (this
"Conveyance"), is by and between Brigham Oil & Gas, L.P., a Delaware limited
partnership (the "Grantor"), and ECT Merchant Investments Corp., a Delaware
corporation ("ECT Merchant") and Joint Energy Development Investments II
Limited Partnership, a Delaware limited partnership ("JEDI-II and, together
with ECT Merchant, the "Grantee").

                                   RECITALS:

         1. Brigham Exploration Company ("Brigham Parent") and Chase Bank of
Texas, National Association, as Trustee, have entered into an Indenture dated
as of August 20, 1998, as amended by a First Amendment to Indenture dated as of
March 26, 1999, and a Second Amendment to Indenture dated as of even date
herewith (as amended, the "Indenture"), pursuant to which Brigham Parent issued
certain Notes (as defined in the Indenture).

         2. In accordance with the terms of the Indenture, Brigham Parent
agreed to convey, and to cause its Subsidiaries to convey, to the Noteholders
(as defined in the Indenture), Term ORRI's (as defined below), as an absolute
assignment, and not as collateral, such conveyance to be made pursuant to one
or more Term ORRI Conveyances (as defined in the Indenture).

         3. This Conveyance constitutes one of the Term ORRI Conveyances
contemplated by the Indenture.

                                   ARTICLE I.

                                 DEFINED TERMS

         Section 1. Defined Terms and References. Reference is hereby made to
the Indenture for all purposes. Unless otherwise defined herein, all
capitalized terms used herein shall have the meaning attributed to such term in
the Indenture. In addition, as used in this Conveyance, the following
capitalized terms shall have the following meanings:

         "Accrued PIK Amount" means, as of any particular day, the aggregate
dollar amount of all accrued interest on the Notes, that has been paid in kind
(and not in cash) as of such day in accordance with the Indenture.

         "Applicable Percentage" shall mean, with respect to any Subject
Reserves, Grantor's actual net revenue interest (expressed as a percentage) in
the production of oil, gas and/or other minerals in, under and/or that may be
produced from any Subject Reserves, (including without limitation any
net revenue interest attributable to an overriding royalty interest or acquired
by virtue of a third party



<PAGE>   2







nonconsent election in any drilling, completion or other operation), subject to
the agreements and other matters set out in Exhibit B hereto, and the rights
afforded third parties (which are not affiliates or Subsidiaries of Brigham
Parent) thereunder.

         "Brigham Parent" is defined in the Recitals.

         "Effective Date" shall mean 7:00 a.m. local time on February 17, 2000.

         "Hydrocarbon Interests" means all rights, titles and estates of
Grantor in and to the oil and gas leases, oil, gas and mineral leases, or other
liquid or gaseous hydrocarbon leases, mineral fee interests, overriding royalty
and royalty interests, net profit interests and production payment interests
identified on Exhibit A attached hereto or otherwise owned by Grantor,
including any reserved or residual interest of whatever nature.

         "Indenture" is defined in the Recitals.

         "Marketing Terms and Conditions" shall have the meaning assigned to it
in Section 4.1.

         "Non-Proved Reserves" means any category of oil and gas reserves other
than Proved Reserves.

         "ORRI Hydrocarbons" shall have the meaning assigned to it in Section
4.1.

         "ORRI Percentage" shall be defined as follows:

                  (a)      Until the occurrence of the Recalculation Event, the
                           ORRI Percentage shall be four percent (4%).

                  (b)      Under circumstances more particularly described in
                           Section 2.3, effective from and after the occurrence
                           of the Recalculation Event, the ORRI Percentage
                           shall be adjusted downward to three percent (3%).

         "ORRI Term" means the period from the Effective Date to a date that is
the earliest to occur of (a) the date on which there is a payment in full of
the Accrued PIK Amount and all other Obligations under the Indenture or (b) the
date on or after November 21, 2000, on which there is a payment in full of the
Accrued PIK Amount.

         "Overproduced Position" shall mean a position that arises as a result
of a party (and/or its predecessors in title) taking more production from a
property than its ownership interest in such property would, but for a gas
balancing or similar agreement, entitle it to take.

         "Permissible Charges" shall mean (i) all production, severance, ad
valorem or similar taxes assessed against or measured by production and
severance of ORRI Hydrocarbons or the value and (ii) with respect to each well
not operated by the Grantor or any Affiliate thereof, the Term ORRI's allocable
share of any reasonable post production expenses, costs, charges, and fees
incurred in



                                      -2-



<PAGE>   3





transporting, processing, gathering, treating, separating, dehydrating and
marketing the Subject Reserves allocable to such well.

         "PDNP Reserves" shall mean proved, developed, non-producing oil and
gas reserves, as determined in conformity with the guidelines in effect from
time to time as promulgated by the Society of Petroleum Engineers or its
successor association.

         "PDP Reserves" shall mean proved, developed, producing oil and gas
reserves, as determined in conformity with the guidelines in effect from time
to time as promulgated by the Society of Petroleum Engineers or its successor
association.

         "Proved Reserves" means PDP Reserves, PDNP Reserves and PUD Reserves.

         "PUD Reserves" shall mean proved, undeveloped oil and gas reserves, as
determined in conformity with the guidelines in effect from time to time as
promulgated by the Society of Petroleum Engineers or its successor association.

         "Recalculation Event" shall have the meaning assigned to it in Section
2.3.

         "Subject Reserves" means (a) any PDP Reserves and PDNP Reserves
identified by Grantor or Brigham Parent (or any Subsidiary thereof) as of the
date hereof as being produced or producible in paying quantities out of wells
now located on the Hydrocarbon Interests as of the date hereof including those
listed on the attached Exhibit A or (b) any PDP Reserves and PDNP Reserves
identified by Grantor or Brigham Parent (or any Subsidiary thereof) following
the date hereof and on or before December 31, 2000, as being produced or
producible in paying quantities out of any well spudded or acquired by Grantor
or Brigham Parent (or any Subsidiary thereof) on or before December 31, 2000,
(c) in the event only that Brigham Parent's Consolidated Interest Coverage
Ratio calculated as of September 30, 2000 (in accordance with the Indenture),
is less than 1.1 to 1.0, any PDP Reserves and PDNP Reserves identified by
Grantor or Brigham Parent (or any Subsidiary thereof) following December 31,
2000 and on or before December 31, 2001, as being produced or producible in
paying quantities out of any well spudded or acquired after December 31, 2000
but on or before December 31, 2001, and (d) in the cases of (a), (b) and (c),
above, a sufficient interest in the Hydrocarbon Interests to afford Grantor or
the Brigham Parent as applicable the right, prior to giving effect hereto or to
any Term ORRI Conveyance, to secure the maximum authorized share of production
that is allocable to PDP Reserves and, when applicable, PDNP Reserves found in
each Subject Well. Under no circumstances, and notwithstanding any provision
hereof to the contrary, shall the term "Subject Reserves" include (1) any PUD
Reserves or any Non-Proved Reserves or (2) any PDP Reserves and/or PDNP
Reserves beneficially or legally owned (whether in a vested or contingent
manner) by a third party (which is not an Affiliate of the Brigham Parent)
under or pursuant to any agreement or other matter disclosed in Exhibit B
hereto, or (3) any PDP Reserves or PDNP Reserves identified by Brigham Parent
or Grantor as a result of the deepening or sidetracking of a Subject Well after
December 31, 2000 (in the event item (c) of the definition of Subject Reserves
is not triggered) and after December 31, 2001, (in the event item (c) of the
definition of Subject Reserves is triggered). Under no circumstances shall the
term "Subject Reserves" include reserves that are not either producing or
capable of producing (or being made in



                                      -3-



<PAGE>   4




the case of PDNP Reserves to produce or capable of producing) in "paying
quantities," as such term is defined under the Texas common law (regardless of
the jurisdiction in which the subject Oil and Gas Properties are located).

         "Term ORRI" shall have the meaning assigned to it in Section 2.1.

         "Underproduced Position" shall mean a position that arises as a result
of a party (and/or its predecessors in title) taking less production from a
property than its ownership interest in such property would, but for a gas
balancing or similar agreement, entitle it to take.

                                  ARTICLE II.

                              GRANTING PROVISIONS

         Section  2.1      Granting Clause. For a good and valuable
                           consideration, the receipt and sufficiency of which
                           is hereby acknowledged, Grantor does hereby GRANT,
                           BARGAIN, SELL, TRANSFER, ASSIGN, CONVEY, WARRANT and
                           DELIVER, for and during the ORRI Term only, to each
                           Grantee according to their Participations, an
                           overriding royalty interest (collectively, the "Term
                           ORRI") equal to the ORRI Percentage of the
                           Applicable Percentage of each of the Subject
                           Reserves.

         Section  2.2      Adjustment of the Term ORRI; Further Assurances.
                           Upon the occurrence of the Recalculation Event,
                           Grantor and Grantee agree, at Grantor's expense, to
                           execute (or cause to be executed) any such
                           instruments as may be necessary or appropriate in
                           order to evidence of record in the appropriate
                           filing jurisdictions that the ORRI Percentage has
                           been adjusted.

         Section 2.3       Adjustment of ORRI Percentage. The ORRI Percentage
                           shall be automatically decreased from four (4%) to
                           three (3%) on the first to occur of the following
                           (the "Recalculation Event"):

               (a)  Brigham Parent sells common or preferred equity securities
                    of Brigham Parent resulting in net proceeds received by
                    Brigham Parent (after deducting all costs and expenses
                    incurred in such sale) of at least $10,000,000;

               (b)  Grantor and/or Brigham Parent acquires, in exchange for
                    common or preferred equity securities of Brigham Parent,
                    Oil and Gas Properties containing PDP Reserves and/or PDNP
                    Reserves with a net present value, discounted at 10% per
                    annum, of at least $10,000,000 (in Grantees' reasonable
                    judgement); or



                                      -4-

<PAGE>   5




               (c)  through a combination of (a) and (b) above, Brigham Parent
                    and/or Grantor receives net proceeds and newly acquired Oil
                    and Gas Properties, which (as valued above), total at least
                    $10,000,000 in net present value;

provided that, on or before August 31, 2000, the Recalculation Event shall have
closed and (a) Brigham Parent shall have received the $10,000,000 of cash
and/or properties as provided above, and (b) either the Chief Financial Officer
or President of Brigham Parent shall have delivered a certificate to Grantor to
that effect.

         Section 2.4       Term. The Term ORRI shall automatically terminate at
                           the end of the ORRI Term. Upon such event, Grantee
                           shall execute such instruments as Grantor shall
                           reasonably request to evidence such termination,
                           and/or reassigning such Term ORRI, free and clear of
                           all liens, encumbrances and other burdens created
                           by, through or under Grantee.

         Section 2.5       Permissible Charges. The Term ORRI shall be free of
                           any expense for exploration, drilling, development,
                           operating, marketing and other costs incident to the
                           production and sale of oil and gas other than
                           Permissible Charges. Notwithstanding any provision
                           hereof to the contrary, the Term ORRI shall not
                           apply to (a) any oil, gas and/or other minerals as
                           are (i) unavoidably lost in operations on or
                           relating to the Subject Reserves or in marketing of
                           oil, gas and/or other minerals from or attributable
                           to the Subject Reserves, or (ii) consumed or
                           utilized (e.g., as part of a re-injection program)
                           in prudent operations conducted on the Subject
                           Reserves with a reasonable expectation of increasing
                           ultimate recovery of oil, gas and/or other minerals
                           from the Subject Reserves; provided that, to the
                           extent any oil, gas and/or other minerals utilized
                           in operations conducted on the Subject Reserves are
                           subsequently re-produced, the Term ORRI shall apply
                           to such re-produced volumes.

         Section 2.6       Pooling Issues. Prior to the date hereof, certain of
                           the Hydrocarbon Interests may have been pooled or
                           unitized for the production of oil, gas and/or
                           minerals and without the joinder of Grantee with
                           respect to the Term ORRI, Grantor shall, from and
                           after the date hereof, have the right and power to
                           unitize, communitize or pool any portion or portions
                           of the Term ORRI. If pursuant to any law, rule,
                           regulation or order of any governmental body or
                           official, any portion of the Hydrocarbon Interests
                           is automatically or involuntarily pooled,
                           communitized or unitized in any manner, the Term
                           ORRI, insofar as it affects such Hydrocarbon
                           Interests, shall also be pooled, communitized and
                           unitized. With respect to each existing pool or
                           unit, and with respect to each pool or unit in which
                           the Term ORRI is hereafter included in accordance
                           with the


                                      -5-


<PAGE>   6



                           foregoing, the Term ORRI in each portion of the
                           Hydrocarbon Interests included in such pool or unit
                           shall apply to the portion of production from such
                           pool or unit which is attributable to such portion
                           of the Hydrocarbon Interests under and by virtue of
                           the applicable pooling, communitization and
                           unitization agreements, designations and/or orders.
                           Nothing in this Section 2.6 shall be construed to
                           afford Grantee rights in PDP Reserves or PDNP
                           Reserves identified in wells that are not now
                           located on the Hydrocarbon Interests.


         Section 2.7       Renewals and Extensions. The Term ORRI shall apply
                           to all renewals and extensions of any oil, gas
                           and/or mineral lease, deed or any other interest
                           included, in part or in whole, in the Subject
                           Reserves.

         Section 2.8       Gas Imbalances. It is hereby recognized that certain
                           of the Subject Reserves are or may be subject to
                           Underproduced Positions. It is hereby further
                           recognized and stipulated that the Term ORRI does
                           and shall apply to the volumes of oil, gas or other
                           hydrocarbons taken by Grantor in reducing or making
                           up an Underproduced Position (which volumes and any
                           make-up rights relating thereto shall for all
                           purposes hereof be included within the Subject
                           Reserves), whether the subject Underproduced
                           Position arose before, or arises after, the
                           Effective Date hereof.

         Section 2.9       Fee, Royalty and Similar Interests. It is hereby
                           recognized that certain of the Hydrocarbon Interests
                           may constitute or include (a) unleased mineral fee
                           interests and unleased mineral rights or servitudes
                           (the "Unleased Mineral Interests"), (b) mineral fee
                           interests and mineral rights or servitudes that are
                           owned by Grantor but subject to an existing oil, gas
                           and/or mineral lease or similar agreement in favor
                           of a third party or parties, which oil, gas and/or
                           mineral lease or similar agreement entitles Grantor
                           to be paid a royalty, either in kind or in money
                           (the "Leased Mineral Interests"), and (c) perpetual
                           or term royalty or overriding royalty interests
                           carved out of and burdening a mineral fee, right,
                           servitude or lease owned by a third party or third
                           parties (the "Royalty Interests") (the Unleased
                           Mineral Interests, the Leased Mineral Interests and
                           the Royalty Interests are herein collectively called
                           the "Non-Working Interest Properties"). It is hereby
                           recognized and stipulated that the Term ORRI is
                           payable out of and shall burden the Non-Working
                           Interest Properties, to the extent they constitute
                           Subject Reserves, just as it is payable out of and
                           burdens the balance of the Hydrocarbon Interests. By
                           way of example (and not by way of limitation):



                                      -6-

<PAGE>   7


                  (i)      If Grantor owns an Unleased Mineral Interest that
                           constitutes a 50% undivided mineral fee interest in
                           a particular tract of land, the Term ORRI payable
                           relative to such tract of land would, until the
                           occurrence of the Recalculation Event, be equal to
                           and measured by an undivided 4% of 50% of the oil,
                           gas and/or other minerals in, under and/or that may
                           be produced from the subject tract of land;

                  (ii)     If Grantor owns a Leased Mineral Interest that
                           constitutes an undivided 50% mineral fee interest in
                           a particular tract of land that is subject to a
                           lease entitling Grantor to a 20% royalty interest,
                           proportionately reduced, the Term ORRI payable
                           relative to such tract of land would, until the
                           occurrence of the Recalculation Event, be equal to
                           and measured by an undivided 4% of 10% of the oil,
                           gas and/or other minerals in, under and/or that may
                           be produced from the subject tract of land; and

                  (iii)    If Grantor owns a Royalty Interest that constitutes
                           a 1/32nd nonparticipating royalty interest in a
                           particular tract of land, the Term ORRI payable
                           relative to such tract of land would, until the
                           occurrence of the Recalculation Event, be equal to
                           and measured by an undivided 4% of 1/32nd of the
                           oil, gas and/or other minerals in, under and/or that
                           may be produced from the subject tract of land.

         Section 2.10      Habendum Clause and Subrogation. TO HAVE AND TO HOLD
                           the Term ORRI unto Grantee, its successors and
                           assigns, during the ORRI Term. This Conveyance is
                           made with full substitution and subrogation of
                           Grantee in and to all covenants and warranties by
                           others heretofore given or made.

                                  ARTICLE III.

                           ASSIGNMENTS AND TRANSFERS

         Section 3.1       Assignment and Transfer by Grantee. Subject to
                           Section 7.12(e) of the Indenture, nothing herein
                           contained shall in any way limit or restrict the
                           right of Grantee to sell, convey, assign, mortgage
                           or otherwise dispose of the Term ORRI (including its
                           rights, titles, interests, estates, remedies, powers
                           and privileges appurtenant or incident to the Term
                           ORRI under this Conveyance), in whole or in part.

         Section 3.2       Assignment and Transfer by Grantor.


                                      -7-


<PAGE>   8

         (A) In the event any of the Subject Reserves are sold, farmed out or
otherwise transferred by the Grantor in a bona fide transaction with a
third-party that is not an Affiliate of Grantor, the Term ORRI conveyed herein
in the Subject Reserves so sold, farmed out or otherwise transferred shall
automatically terminate and merge into the interest so sold, farmed-out or
otherwise transferred upon the final closing of such transaction; provided that
the Grantor pays or otherwise affords to Grantee, in accordance with their
Participations, (a) the ORRI Percentage of all net cash proceeds or other
consideration received (or credited) to Grantor as a result of such
transaction, to the extent only such net cash proceeds are allocable to the
Subject Reserves out of which the subject Term ORRI is carved and (b) the ORRI
Percentage of the Applicable Percentage secured by (in a contemporaneous
exchange of properties) or reserved to (e.g., in the form of an override or
back-in) Grantor as a result of such transaction, to the extent only the
properties exchanged or the interests reserved are allocable to the Subject
Reserves out of which the subject Term ORRI is carved. Where requested by the
purchaser, farmee, exchange counterparty or transferee, Grantee shall join in
any instrument of sale, farm-out, exchange or transfer.

         (B) In the event any of the Hydrocarbon Interests not constituting
Subject Reserves at the time of sale, farm-out or other transfer (the
"NonSubject Reserves") are sold, farmed out, or otherwise transferred by the
Grantor in a bona fide transaction with a third party that is not an affiliate
of Grantor, the Term ORRI conveyed herein in the NonSubject Reserves so sold,
farmed-out or otherwise transferred shall automatically terminate and merge
into the interest so sold, farmed-out or otherwise transferred upon the final
closing of such transaction; and the Grantee shall not be entitled to any of
the cash proceeds or other consideration received by Grantor on account of the
sale, farm-out or other transfer (either as an Applied Payment or otherwise).
When requested by the purchaser, farmee or transferee on NonSubject Reserves,
Grantee shall join in any instrument of sale, farm-out exchange or transfer.


                                  ARTICLE IV.

          MARKETING OF ORRI HYDROCARBONS AND DISTRIBUTION OF PROCEEDS

         Section 4.1       Nature of Marketing Arrangements. Grantor shall have
                           the obligation to market, or cause to be marketed,
                           the oil, gas and other minerals attributable to the
                           Term ORRI (the "ORRI Hydrocarbons") on behalf of and
                           for the account of Grantee in arm's-length
                           transactions with purchasers who are not Affiliates,
                           on the same terms upon which Grantor markets its own
                           Subject Reserves from the same Subject Well. Grantor
                           shall have no express or implied obligation to sell
                           or otherwise to market or render marketable or more
                           valuable the ORRI Hydrocarbons on any terms better
                           or otherwise different than those pursuant to which
                           it sells, markets or renders marketable or more
                           valuable its own Subject Reserves from the same
                           Subject Well. As to any third parties, all acts of
                           Grantor in marketing the ORRI Hydrocarbons and all
                           sales or other marketing agreements executed by
                           Grantor in accordance herewith shall be binding on
                           Grantee and the Term ORRI; it being understood that
                           the right and obligation to



                                      -8-

<PAGE>   9



                           market the ORRI Hydrocarbons is at all times vested
                           in Grantor, and Grantee does not have any such right
                           or obligation or any possessory interest in all or
                           part of the ORRI Hydrocarbons. Accordingly, it shall
                           not be necessary for Grantee to join in any
                           production sales or marketing agreements or any
                           amendments to existing production sales or marketing
                           agreements.

         Section 4.2       Distribution of Funds. Until notified by Grantee to
                           the contrary, Grantor shall receive all payments for
                           (or on account of) ORRI Hydrocarbons and shall, on
                           or before the last day of each calendar month,
                           distribute any such payments received during the
                           previous calendar month, net only of Permissible
                           Charges, to Agent, on behalf of and for further
                           distribution to Grantee, by wire transfer to such
                           account(s) or location(s) as Agent may direct from
                           time to time in writing. Any monies received by
                           Agent for or on account of ORRI Hydrocarbons shall
                           constitute trust funds in Agent's hands. Except as
                           provided otherwise in the Indenture, Grantee shall
                           have the right at all times, upon thirty (30) days'
                           written notice sent to Grantor, to begin receiving
                           payment for (or on account of) all ORRI Hydrocarbons
                           directly from the purchasers thereof or from any
                           other parties obligated to make payment therefor. In
                           the event Grantee exercises its right to receive
                           payment for (or on account of) ORRI Hydrocarbons
                           directly, Grantor shall immediately cause to be
                           prepared and executed such division orders, transfer
                           orders, or instructions in lieu thereof, as Grantee
                           (or any third party) may reasonably require from
                           time to time to cause payments to be made directly
                           to Grantee; in the event that, for any reason,
                           Grantee cannot (or does not) receive such payments
                           directly, the same shall be collected by Grantor and
                           shall constitute trust funds in Grantor's hands, to
                           be immediately paid over to Grantee by wire transfer
                           to such account or location as Grantee may direct
                           from time to time in writing (or by such other form
                           of transfer reasonably specified by Grantee).

         Section 4.3       Notification to Production Purchasers. ANY AND ALL
                           PURCHASERS OF ORRI HYDROCARBONS SHALL HAVE THE RIGHT
                           TO ASSUME THAT THE TERM ORRI IS STILL VALID AND
                           EXISTING - CALCULATED UTILIZING AN ORRI PERCENTAGE
                           OF 4% UNTIL THE OCCURRENCE OF THE RECALCULATION
                           EVENT - UNTIL SUCH TIME AS SUCH PURCHASER IS
                           NOTIFIED IN WRITING BY GRANTEE TO BEGIN MAKING
                           PAYMENTS ON SOME OTHER BASIS. UNTIL RECEIVING SUCH
                           WRITTEN NOTIFICATION, ALL PURCHASERS OF PRODUCTION
                           SHALL CONTINUE MAKING PAYMENTS IN ACCORDANCE WITH
                           THE FOREGOING ASSUMPTIONS (AND OTHERWISE IN
                           ACCORDANCE WITH




                                      -9-



<PAGE>   10



                           THE DIRECTIVES SET OUT IN SECTION 4.2 HEREOF), AND
                           SHALL NOT PLACE THE FUNDS IN SUSPENSE.

         Section 4.4       Ad Valorem and Severance Taxes. For so long as
                           Grantor is receiving payments and making
                           distributions on account of ORRI Hydrocarbons to
                           Grantee under Section 4.2 hereof, Grantor shall, as
                           an administrative convenience to Grantee and to the
                           extent only that funds are on hand on account of
                           sales of ORRI Hydrocarbons, timely pay and discharge
                           (a) all ad valorem taxes assessed against the
                           Subject Reserves (or the Hydrocarbon Interests
                           directly allocable thereto, including the Term ORRI)
                           or any part thereof, and (b) all production,
                           severance, excise and other taxes assessed against,
                           or measured by, the ORRI Hydrocarbons or the value,
                           or proceeds, of the ORRI Hydrocarbons (the "Taxes").
                           Grantor shall have the right to net Taxes payable
                           under this and any other Term ORRI Conveyance on
                           account of the Term ORRI and the ORRI Hydrocarbons
                           hereunder and thereunder against amounts otherwise
                           distributable on account of the sale of ORRI
                           Hydrocarbons under this and any other Term ORRI
                           Conveyance. Nothing contained in this Section 4.4
                           shall, however, create a personal obligation on the
                           part of Grantor to pay any Taxes on behalf of
                           Grantee to the extent amounts in the possession of
                           Grantee on account of the ORRI Hydrocarbons are
                           insufficient to cover the payment of Taxes on
                           account of the Term ORRI and/or the ORRI
                           Hydrocarbons. Without limitation of the generality
                           of the foregoing, in the event that, in Grantor's
                           reasonable discretion, distributions owing to
                           Grantee will be insufficient to fully cover any ad
                           valorem or similar Taxes allocable to the Term ORRI,
                           Grantee agrees to pay the difference to the
                           appropriate taxing authority within twenty (20) days
                           after receipt from Grantor of the applicable ad
                           valorem or similar Tax assessment. Grantor shall
                           have the right to offset against any distributions
                           owing or to become owing to Grantee the full amount
                           of any Taxes so paid on behalf of Grantee. In the
                           event Grantee elects pursuant to Section 4.2 hereof
                           to receive payment on account of ORRI Hydrocarbons
                           directly, it shall be responsible to pay all Taxes
                           allocable to the Term ORRI directly, for its own
                           account.


                                   ARTICLE V.

                              COVENANTS OF GRANTOR

         Grantor hereby covenants for the benefit of Grantee that Neither
Brigham Parent or Grantor, will allow any Subsidiary to transfer any assets to
Quest Resources LLC or Venture Acquisitions, L.P.



                                     -10-

<PAGE>   11



                                  ARTICLE VI.

                            MISCELLANEOUS PROVISIONS

         Section 6.1       Further Assurances. Grantor agrees to execute and
                           deliver to Grantee, and, to the extent it is
                           reasonably within Grantor's power to do so, to cause
                           any third parties to execute and deliver to Grantee,
                           all such other and additional instruments and to do
                           all such further acts and things as may be necessary
                           or appropriate to more fully vest in and assure to
                           Grantee all of the rights, titles, interests,
                           remedies, powers and privileges herein granted or
                           intended so to be, Grantee agrees to execute and
                           deliver to Grantor all such other and additional
                           instruments and to do all such further acts and
                           things as may be necessary or appropriate to more
                           fully vest in and assure to Grantor all of the
                           rights, titles, interests, remedies, powers and
                           privileges herein granted or intended so to be.

         Section 6.2       Termination. Upon Grantor's request, Grantee will
                           confirm to Grantor in writing reasonably acceptable
                           to Grantor the occurrence of the Recalculation Event
                           and the termination of the Term ORRI (as to all or
                           any one or more Hydrocarbon Interests).

         Section 6.3       No Waiver. The failure of any party to insist upon
                           strict performance of a covenant hereunder or of any
                           obligation hereunder, irrespective of the length of
                           time for which such failure continues, shall not be
                           a waiver of such party's right to demand strict
                           compliance in the future. No consent or waiver,
                           express or implied, to or of any breach or default
                           in the performance of any obligation hereunder shall
                           constitute a consent or waiver to or of any other
                           breach or default in the performance of the same or
                           any other obligation hereunder.

         Section 6.4       Applicable Law. THIS CONVEYANCE AND THE RIGHTS AND
                           OBLIGATIONS OF THE PARTIES HEREUNDER SHALL, WITHOUT
                           REGARD TO PRINCIPLES OF CONFLICTS OF LAWS, BE
                           GOVERNED BY AND INTERPRETED, CONSTRUED AND ENFORCED
                           IN ACCORDANCE WITH THE LAWS OF THE STATE OF TEXAS,
                           EXCEPT TO THE EXTENT THE LAWS OF ANY STATE IN WHICH
                           ANY PART OF THE HYDROCARBON INTERESTS IS LOCATED
                           NECESSARILY, GOVERNS WITH RESPECT TO SUCH PART OF
                           THE HYDROCARBON INTERESTS LOCATED IN SUCH STATE.


                                     -11-


<PAGE>   12




         Section 6.5       Severability. Every provision in this Conveyance is
                           intended to be severable. If any term or provision
                           hereof is determined to be invalid, illegal or
                           unenforceable for any reason whatsoever, such
                           invalidity, illegality or unenforceability shall not
                           affect the validity, legality and enforceability of
                           the remainder of this Conveyance.

         Section 6.6       No Personal Liability of Grantee/Indemnities.
                           NOTWITHSTANDING ANYTHING TO THE CONTRARY CONTAINED
                           IN THIS CONVEYANCE, GRANTEE SHALL NEVER PERSONALLY
                           BE RESPONSIBLE FOR PAYMENT OF ANY PART OF THE COSTS,
                           EXPENSES OR LIABILITIES INCURRED IN CONNECTION WITH
                           THE EXPLORING, DEVELOPING, OPERATING, OWNING AND/OR
                           MAINTAINING OF THE HYDROCARBON INTERESTS. GRANTOR
                           AGREES TO INDEMNIFY AND HOLD GRANTEE AND ITS
                           DIRECTORS, OFFICERS, EMPLOYEES, REPRESENTATIVES,
                           AGENTS AND AFFILIATES, HAS FROM AND AGAINST ALL SUCH
                           COSTS, EXPENSES AND LIABILITIES (WITH SUCH INDEMNITY
                           TO ALSO COVER ALL COSTS AND EXPENSES OF GRANTEE,
                           INCLUDING REASONABLE LEGAL FEES AND EXPENSES, WHICH
                           ARE INCURRED INCIDENT TO THE MATTERS INDEMNIFIED
                           AGAINST); PROVIDED, HOWEVER; THAT PERMISSIBLE
                           CHARGES SHALL, TO THE EXTENT THE SAME RELATE TO
                           PERIODS AFTER THE EFFECTIVE DATE, NEVERTHELESS BE
                           CHARGEABLE AGAINST THE TERM ORRI OR OTHERWISE
                           PAYABLE AND/OR BORNE DIRECTLY BY GRANTEE UNDER
                           CIRCUMSTANCES DESCRIBED HEREIN, AS AND TO THE EXTENT
                           HEREIN PERMITTED. EXPRESSLY WITHOUT LIMITATION OF
                           THE GENERALITY OF THE FOREGOING, GRANTOR HEREBY
                           AGREES TO INDEMNIFY AND HOLD GRANTEE AND ITS
                           DIRECTORS, OFFICERS, EMPLOYEES, REPRESENTATIVES,
                           AGENTS AND AFFILIATES, HARMLESS FROM AND AGAINST ALL
                           CLAIMS, DEMANDS, LIABILITIES, LOSSES, DAMAGES, COSTS
                           AND EXPENSES (A) ARISING FROM ANY FAILURE OF GRANTOR
                           TO PERFORM OR COMPLY WITH ANY OF THE PROVISIONS OF
                           THIS CONVEYANCE, (B) ARISING OUT OF THE CONDITION OF
                           THE HYDROCARBON INTERESTS (WHETHER KNOWN OR UNKNOWN,
                           LATENT OR PATENT) ON, BEFORE OR AFTER THE DATE
                           HEREOF, AND/OR (C) ARISING UNDER ANY ENVIRONMENTAL
                           LAWS, WHETHER NOW IN EXISTENCE OR HEREINAFTER



                                     -12-

<PAGE>   13




                           ENACTED. THE INDEMNITIES AND HOLD HARMLESS
                           PROVISIONS CONTAINED IN THIS SECTION 7.6 SHALL APPLY
                           WHETHER OR NOT THE INDEMNIFIED PARTY WAS WHOLLY OR
                           PARTIALLY NEGLIGENT (OTHER THAN GROSSLY NEGLIGENT).

         Section 6.7       Counterparts. This Conveyance is being executed in
                           several counterparts, all of which are identical,
                           except that, to facilitate recordation, in certain
                           counterparts hereof only that portion of Exhibit A
                           which contains specific descriptions of the
                           Hydrocarbon Interests located in the recording
                           jurisdiction in which the counterpart is to be
                           recorded shall be included, and all other portions
                           of Exhibit A shall be included by reference only.
                           All of such counterparts together shall constitute
                           one and the same instrument. Complete copies of this
                           Conveyance, containing the entire Exhibit A, have
                           been retained by Grantor and Grantee.



                                     -13-


<PAGE>   14


         THIS CONVEYANCE IS EXECUTED this 17th day of February, 2000, and made
effective as of the Effective Date.

                                       BRIGHAM OIL & GAS, L.P.

                                       By:  Brigham, Inc. a Nevada corporation,
                                            its General Partner

                                            By:
                                                -------------------------------
                                                Karen E. Lynch
                                                Vice President


ADDRESS OF GRANTOR:                         ADDRESS OF GRANTEE:
6300 Bridge Point Parkway                   1400 Smith Street
Austin, Texas 78730                         Houston, Texas 77002


This instrument prepared by:
Gray H. Muzzy
Bracewell & Patterson, L.L.P.
711 Louisiana
Houston, Texas 77002
(713) 221-1406

<PAGE>   15

                                 ACKNOWLEDGMENT


STATE OF TEXAS                    )
                                  )
COUNTY OF HARRIS                  )

                                     KANSAS

         The foregoing instrument was acknowledged before me on February 17,
2000, by Karen Lynch, Vice President of Brigham, Inc., a Nevada corporation, as
general partner of Brigham Oil & Gas, L.P., a Delaware limited partnership, on
behalf of the corporation, as general partner of the limited partnership.

                                   LOUISIANA

         This instrument was acknowledged by me on February 17, 2000 by Karen
Lynch, Vice President of Brigham, Inc., a Nevada corporation, as general
partner of Brigham Oil & Gas, L.P., a Delaware limited partnership, on behalf
of the corporation, as general partner of the limited partnership.

                                    MONTANA

         The foregoing instrument was acknowledged before me on February 17,
2000, by Karen Lynch, Vice President of Brigham, Inc., a Nevada corporation, as
general partner of Brigham Oil & Gas, L.P., a Delaware limited partnership, on
behalf of the corporation, as general partner of the limited partnership.

                                   NEW MEXICO

         The foregoing instrument was acknowledged before me on February 17,
2000, by Karen Lynch, Vice President of Brigham, Inc., a Nevada corporation, as
general partner of Brigham Oil & Gas, L.P., a Delaware limited partnership, on
behalf of the corporation, as general partner of the limited partnership.

                                    OKLAHOMA

         Before me, a Notary Public in and for said county and state, on this
17th day of February, 2000, personally appeared Karen Lynch, to me know to be
the identical person who subscribed the name of the maker thereof to the
foregoing instrument as Vice President of BRIGHAM, INC., as general partner of
BRIGHAM OIL & GAS, L.P., a Delaware limited partnership, and acknowledged to me
that she executed the same as her free and voluntary act and deed, and as the
free and voluntary act and deed of such corporation for the uses and purposes
therein set forth.




<PAGE>   16

                                     TEXAS

         This instrument was acknowledged before me on February 17, 2000 by
Karen E. Lynch, Vice President of BRIGHAM, INC., a Nevada corporation, as
general partner of BRIGHAM OIL & GAS, L.P., a Delaware limited partnership, on
behalf of such corporation, as general partner of the limited partnership.


                                       ----------------------------------------
                                       NOTARY PUBLIC IN AND FOR
                                       THE STATE OF TEXAS

                                       Notarial Seal:



<PAGE>   17




                                   EXHIBIT A


            [Describe leases and wells - to be provided by Brigham]






<PAGE>   18

                                   EXHIBIT B

                                  TITLES, ETC.

 (a) The rights and interests afforded Gasco Limited Partnership ("Gasco") and
its successors and assigns under the terms of (i) that certain Expense
Allocation and Participation Agreement dated as of April 1, 1996, by and
between Gasco and Grantor, as heretofore and/or hereafter amended, expanded,
supplemented, renewed and/or extended, and (ii) that certain Expense Allocation
and Participation Agreement II dated as of April 1, 1997, by and between Gasco
and Grantor, as heretofore and/or hereafter amended, expanded, supplemented,
renewed and/or extended, and (iii) that certain Expense Allocation and
Participation Agreement III dated as of March 1, 1998, by and between Gasco and
Grantor, as heretofore amended, expanded, supplemented, renewed and/or
extended.

(b) The rights and interests afforded Middle Bay Oil Company ("Middle Bay") and
its successors and assigns under the terms of that certain Expense Allocation
and Participation Agreement dated as of April 1, 1996, by and between Middle
Bay and Grantor, as heretofore amended, modified, expanded, supplemented,
renewed and/or extended.

(c) The rights and interests afforded Stephens Production Company ("Stephens")
and its successors and assigns under the terms of that certain Anadarko Basin
Joint Participation Agreement dated as of May 1, 1996, by and between Grantor
and Stephens, as heretofore amended, modified, expanded, supplemented, renewed
and/or extended.

(d) The rights and interests afforded Vintage Petroleum, Inc. ("Vintage") and
its successors and assigns under the terms of that certain Anadarko Basin Joint
Participation Agreement dated as of May 1, 1996, by and between Grantor and
Vintage, as heretofore amended, modified, expanded, supplemented, renewed
and/or extended.

(e) The rights and interests afforded Brigham-Duke (Delaware) LLC ("Duke") and
its successors and assigns under the terms of that certain Joint Development
Agreement dated as of February 17, 1999, by and between Duke and Grantor, as
heretofore amended.

(f) The rights and interests, whether real or equitable, vested or contingent,
afforded third parties under the terms of various farmout, exploration, joint
participation and/or operating agreements, in existence as of the date hereof,
under or in relation to which Grantor, Brigham Parent or any Subsidiary agrees
to farm-out to one or more third party(ies) one or more Oil and Gas Property
and/or undertakes with one or more third party(ies) the joint exploration
and/or development of one or more Oil and Gas Properties (which rights and
interests may include, without limitation, rights under Area of Mutual
Interests agreements and rights in respect of forfeiture of all or a portion of
Brigham Parent's interests in an Oil and Gas Property, or part thereof or
interest therein, that is triggered by an election not to participate in a
proposed operation; and



<PAGE>   19



(g) consulting agreements in existence as of the date hereof, as same may have
heretofore been amended, expanded, supplemented, renewed and/or extended, with
third party geologists, landmen or other oil and gas industry participants who
agree to perform services in return, in whole or in part, for an overriding
royalty interest or other interest in or relating to any Oil and Gas
Properties.




<PAGE>   1
                                                                  EXHIBIT 10.13


                               WARRANT CERTIFICATE


Number of Warrants: 750,000                                 Warrant No.  A-6

         This warrant certificate ("Warrant Certificate") certifies that, for
value received,

         JOINT ENERGY DEVELOPMENT INVESTMENTS II LIMITED PARTNERSHIP

is the registered holder of the number of warrants (the "Warrants") set forth
above. Each Warrant entitles the holder thereof, at any time or from time to
time during the Exercise Period, to purchase from the Company one fully paid and
nonassessable share of Common Stock at the Exercise Price, subject to adjustment
as provided herein. The Warrants constitute, as of February 17, 2000, 3.1015% of
the outstanding Common Stock on a fully diluted basis including, for purposes of
such calculation, the Acquired Shares and the Warrant Shares. Initially
capitalized terms used but not defined herein shall have the meanings ascribed
to them in the Securities Purchase Agreement. This Warrant Certificate amends
and restates Warrant No. A-4 issued to Joint Energy Development Investments II
Limited Partnership as of March 26, 1999, which in turn had amended and restated
Warrant No. A-2 issued to Joint Energy Development Investments II Limited
Partnership on August 20, 1998.

         "Acquired Shares" means the shares of Common Stock acquired by Enron
North America Corp. and Joint Energy Development Investments II Limited
Partnership pursuant to Section 2.01 of the Securities Purchase Agreement.

         "Appraiser" has the meaning set forth in Section 13.

         "Appreciation Amount" has the meaning set forth in Section 1(b).

         "Common Stock" means the common stock, $.01 par value per share, of the
Company and such other class of securities as shall then represent the common
equity of the Company.

         "Company" means Brigham Exploration Company, a Delaware corporation.

         "Exercise Period" means the period of time between the Funding Date, as
defined in the Securities Purchase Agreement and 5:00 p.m. (New York City time)
on the Expiration Date.

         "Exercise Price" subject in all circumstances to adjustment in
accordance with Section 2, means $______, which represents the average volume
weighted Price during the twenty (20) calendar day period that begins February
22, 2000 and ends March 12, 2000.

         "Expiration Date" means August 22, 2008.




<PAGE>   2



         "Dissenting Notice" has the meaning set forth in Section 13.

         "Fair Market Value" has the meaning set forth in Section 13.

         "Funding Date" is defined in the Securities Purchase Agreement.

         "IPO" shall mean the initial public offering of securities of the
Company consummated on May 24, 1997, pursuant to a registration statement filed
under the Securities Act of 1933, as amended, and the rules and regulations
promulgated thereunder.

         "Issuance Date" means August 20, 1998.

         "Notes" means the Senior Subordinated Secured Notes issued pursuant to
the Securities Purchase Agreement.

         "Person" means any individual, corporation, company, partnership, joint
venture, trust, limited liability company, unincorporated organization or
government or any agency, instrumentality or political subdivision thereof, or
any other form of entity.

         "Price" means the average of the "high" and "low" prices as reported in
The Wall Street Journal's listing for such day (corrected for obvious
typographical errors) or if such shares are not reported in such listing, the
average of the reported "high" and "low" sales prices on the largest national
securities exchange (based on the aggregate dollar value of securities listed)
on which such shares are listed or traded, or if such shares are not listed or
traded on any national securities exchange, then the average of the reported
"high" and "low" sales prices for such shares in the over- the-counter market,
as reported on the National Association of Securities Dealers Automated
Quotations System, or, if such prices shall not be reported thereon, the average
of the closing bid and asked prices so reported, or, if such prices shall not be
reported, then the average of the closing bid and asked prices reported by the
National Quotations Bureau Incorporated, or, in all other cases, the Fair Market
Value as determined in accordance with Section 13 below. The "average" Price per
share for any period shall be determined by dividing the sum of the Prices
determined for the individual trading days in such period by the number of
trading days in such period.

         "Publicly Traded" means, with respect to the Common Stock, that such
securities are listed for trading on the New York Stock Exchange, Inc., the
American Stock Exchange, Inc. or the NASDAQ National Market. The Common Stock
shall also be deemed to be Publicly Traded if the Common Stock is included in
the NASDAQ SmallCap Market.

         "Securities Purchase Agreement" means the Securities Purchase
Agreement, dated as of August 20, 1998, among the Company, Enron North America
Corp. (formerly named Enron Capital





                                      -2-
<PAGE>   3


& Trade Resources Corp.), and Joint Energy Development Investments II Limited
Partnership, individually and as agent, as amended from time to time.

         "Warrant Shares" means the shares of Common Stock and other securities
receivable upon exercise of the Warrants.

         "Warrants" means the Warrants issued by the Company to Enron North
America Corp. and Joint Energy Development Investments II Limited Partnership
pursuant to the Securities Purchase Agreement and any Warrants issued upon the
transfer thereof or in substitution therefor.

         1. EXERCISE OF WARRANTS. (a) The Warrants may be exercised in whole or
in part, at any time or from time to time, during the Exercise Period, by
presentation and surrender to the Company at its address set forth in Section 9
of (i) this Warrant Certificate with the Election To Exercise, attached hereto
as Exhibit A-1, duly completed and executed, and (ii) payment of the Exercise
Price for the number of Warrants being exercised. At the option of the holder
hereof, payment of the Exercise Price shall be made (w) by wire transfer of
funds, (x) by check payable to the order of the Company, (y) by application of
any Warrant Shares or credit against any Notes, as provided below, or (z) by any
combination of such methods.

If the holder of this Warrant Certificate at any time exercises less than all
the Warrants, the Company shall issue to such holder a warrant certificate
identical in form to this Warrant Certificate, but evidencing a number of
Warrants equal to the number of Warrants originally represented by this Warrant
Certificate less the number of Warrants previously exercised. Likewise, upon the
presentation and surrender of this Warrant Certificate to the Company at its
address set forth in Section 9 and at the request of the holder, the Company
will, without expense, at the option of the holder, issue to the holder in
substitution for this Warrant Certificate one or more warrant certificates in
identical form and for an aggregate number of Warrants equal to the number of
Warrants evidenced by this Warrant Certificate.

              (b) In lieu of exercise in accordance with paragraph (a) above,
the Warrants represented hereby may be exercised, in whole or in part, by
presentation and surrender at the office of the Company specified herein of this
Warrant Certificate with the "Alternative Election to Exercise", attached hereto
as Exhibit A-2, duly completed and executed. Upon such exercise, the holder
shall be entitled to receive from the Company, for each share of Common Stock
issuable upon exercise of each Warrant being exercised, shares of Common Stock
with a value equal to the amount by which either the Price or, in the event that
the Common Stock is not Publicly Traded, the Fair Market Value of one share of
Common Stock on the date of exercise exceeds the Exercise Price (the
"Appreciation Amount"). If the Common Stock is Publicly Traded on the date




                                      -3-
<PAGE>   4


of exercise of Warrants pursuant to this Section 1(b), the Company shall deliver
(or cause its transfer agent to deliver) certificates representing shares of
Common Stock issuable upon such exercise within five business days following the
date of exercise. If the Common Stock is not Publicly Traded on the date of
exercise of Warrants pursuant to this Section 1(b), such election may be
withdrawn by the holder at any time prior to the third business day following
the date on which the holder receives notice of the final determination of Fair
Market Value pursuant to Section 15. Unless the holder timely withdraws its
exercise, the Company shall deliver (or cause its transfer agent to deliver)
certificates representing Common Stock so issuable within 10 business days
following the date of determination of the Fair Market Value. In lieu of any
fractional shares otherwise issuable upon exercise pursuant hereto, the Company
shall pay to the holder cash in an amount equal to the Price, or in the event
the Company is not Publicly Traded, the Fair Market Value of such fractional
share.

              (c) Upon the exercise of this Warrant in whole or in part by the
holder of any Notes, such holder may, at its option, deliver written notice to
the Company that the holder has elected to apply some or all of the Exercise
Price required upon such exercise against all or any specified principal amount
of and/or accrued but unpaid interest on, such Notes, in which case the Company
will accept the application of the Exercise Price against such specified
principal and/or interest amount in lieu of a like amount of cash payment.

              (d) To the extent that the Warrants have not been exercised at or
prior to the Expiration Date, such Warrants shall expire and the rights of the
holder shall become void and of no effect.

         2. ANTIDILUTION ADJUSTMENTS. The shares of Common Stock purchasable on
exercise of the Warrants are shares of Common Stock as constituted as of the
Issuance Date. The number and kind of securities purchasable upon the exercise
of the Warrants, and the Exercise Price, shall be subject to adjustment from
time to time upon the happening of certain events, as follows:

              (a) Mergers, Consolidations and Reclassifications. In case of any
reclassification or change of outstanding securities issuable upon exercise of
the Warrants at any time after the Issuance Date (other than a change in par
value, or from par value to no par value, or from no par value to par value or
as a result of a subdivision or combination to which subsection 2(b) applies),
or in case of any consolidation or merger of the Company with or into another
entity or other person (other than a merger with another entity or other person
in which the Company is the surviving corporation and which does not result in
any reclassification or change in the securities issuable upon exercise of this
Warrant Certificate), the holder of the Warrants shall have, and the Company, or
such successor corporation or other entity, shall covenant in the constituent
documents effecting any of the foregoing transactions that such holder does
have, the right to obtain upon the exercise of the Warrants, in lieu of each
share of Common Stock, other securities, money or other property theretofore
issuable upon exercise of a Warrant, the kind and amount of shares of stock,
other securities, money or other property receivable upon such



                                      -4-
<PAGE>   5

reclassification, change, consolidation or merger by a holder of the shares of
Common Stock, other securities, money or other property issuable upon exercise
of a Warrant if the Warrants had been exercised immediately prior to such
reclassification, change, consolidation or merger. The constituent documents
effecting any such reclassification, change, consolidation or merger shall
provide for adjustments which shall be as nearly equivalent as may be
practicable to the adjustments provided in this subsection 2(a). The provisions
of this subsection 2(a) shall similarly apply to successive reclassifications,
changes, consolidations or mergers.

         (b) Subdivisions and Combinations. If the Company, at any time after
the Issuance Date, shall subdivide its shares of Common Stock into a greater
number of shares, the Exercise Price in effect immediately prior to such
subdivision shall be proportionately reduced, and the number of shares of Common
Stock purchasable upon exercise of the Warrants shall be proportionately
increased, as at the effective date of such subdivision, or if the Company shall
take a record of holders of its Common Stock for such purpose, as at such record
date, whichever is earlier. If the Company, at any time after the Issuance Date,
shall combine its shares of Common Stock into a smaller number of shares, the
Exercise Price in effect immediately prior to such combination shall be
proportionately increased, and the number of shares of Common Stock purchasable
upon exercise of the Warrants shall be proportionately reduced, as at the
effective date of such combination, or if the Company shall take a record of
holders of its Common Stock for purposes of such combination, as at such record
date, whichever is earlier.

         (c) Dividends and Distributions. If the Company at any time after the
Issuance Date shall declare a dividend on its Common Stock payable in stock or
other securities of the Company to the holders of its Common Stock, the holder
of this Warrant Certificate shall, without additional cost, be entitled to
receive upon any exercise of a Warrant, in addition to the Common Stock to which
such holder would otherwise be entitled upon such exercise, the number of shares
of stock or other securities which such holder would have been entitled to
receive if he had been a holder immediately prior to the record date for such
dividend (or, if no record date shall have been established, the payment date
for such dividend) of the number of shares of Common Stock purchasable on
exercise of such Warrant immediately prior to such record date or payment date,
as the case may be.

         (d) Certain Issuances of Securities. If the Company at any time after
the Issuance Date shall issue any additional shares of Common Stock (otherwise
than as provided in paragraphs (a) through (c) of this Section 2) at a price per
share less than the average Price per share of Common Stock for the 20 trading
days immediately preceding the date of the authorization of such issuance (the
"Market Price") by the Board of Directors, then the Exercise Price upon each
such issuance shall be adjusted to that price determined by multiplying the
Exercise Price by a fraction:

              i. the numerator of which shall be the sum of (1) the number of
     shares of Common Stock outstanding immediately prior to the issuance of
     such additional shares of Common Stock multiplied by the Market Price, and
     (2) the consideration, if any, received by the Company upon the issuance of
     such additional shares of Common Stock, and




                                      -5-
<PAGE>   6

              ii. the denominator of which shall be the Market Price multiplied
     by the total number of shares of Common Stock outstanding immediately after
     the issuance of such additional shares of Common Stock.

     No adjustments of the Exercise Price shall be made under this paragraph (d)
upon the issuance of any additional shares of Common Stock that (y) are issued
pursuant to thrift plans, stock purchase plans, stock bonus plans, stock option
plans, employee stock ownership plans and other incentive or profit sharing
arrangements for the benefit of employees ("Employee Benefit Plans") that
otherwise would cause an adjustment under this paragraph (d); provided that the
aggregate number of shares of Common Stock so issued (including the shares
issued pursuant to any options, rights or warrants or convertible or
exchangeable securities issued under such Employee Benefit Plans containing the
right to purchase shares of Common Stock) pursuant to Employee Benefit Plans
after the closing date of the IPO, as adjusted for any stock splits, stock
dividends or subdivisions or combinations of Common Stock prior to the
Expiration Date, shall not in the aggregate exceed 5% of the Company's
outstanding Common Stock at the time of such issuance; or (z) are issued
pursuant to any Common Stock Equivalent (as hereinafter defined) (i) if upon the
issuance of any such Common Stock Equivalent, any such adjustments shall
previously have been made pursuant to paragraph (e) of this Section 2 or (ii) if
no adjustment was required pursuant to paragraph (e) of this Section 2.

         (e) Common Stock Equivalents. If the Company shall, after the Issuance
Date, issue any security or evidence of indebtedness which is convertible into
or exchangeable for Common Stock ("Convertible Security"), or any warrant,
option or other right to subscribe for or purchase Common Stock or any
Convertible Security, other than pursuant to Employee Benefit Plans (together
with Convertible Securities, "Common Stock Equivalent"), or if, after any such
issuance, the price per share for which additional shares of Common Stock may be
issuable thereunder is amended, then the Exercise Price upon each such issuance
or amendment shall be adjusted as provided in subsection (d) on the basis that
(i) the maximum number of additional shares of Common Stock issuable pursuant to
all such Common Stock Equivalents shall be deemed to have been issued as of the
earlier of (a) the date on which the Company shall enter into a firm contract
for the issuance of such Common Stock Equivalent, or (b) the date of actual
issuance of such Common Stock Equivalent; and (ii) the aggregate consideration
for such maximum number of additional shares of Common Stock shall be deemed to
be the minimum consideration received and receivable by the Company for the
issuance of such additional shares of Common Stock pursuant to such Common Stock
Equivalent; provided, however, that no adjustment shall be made pursuant to this
subsection (e) unless the consideration received and receivable by the Company
per share of Common Stock for the issuance of such additional shares of Common
Stock pursuant to such Common Stock Equivalent is less than the Market Price. No
adjustment of the Exercise Price shall be made under this subsection (e) upon
the issuance of any Convertible Security which is issued pursuant to the
exercise of any warrants or other subscription or purchase rights therefor, if
any adjustment shall previously have been made in the Exercise Price then in
effect upon the issuance of such warrants or other rights pursuant to this
subsection (e).



                                      -6-
<PAGE>   7

         (f) Miscellaneous. The following provisions shall be applicable to the
making of adjustments in the Exercise Price hereinbefore provided in this
Section 2:

              i. The consideration received by the Company shall be deemed to be
     the following: (I) to the extent that any additional shares of Common Stock
     or any Common Stock Equivalent shall be issued for cash consideration, the
     consideration received by the Company therefor, or, if such additional
     shares of Common Stock or Common Stock Equivalent are offered by the
     Company for subscription, the subscription price, or, if such additional
     shares of Common Stock or Common Stock Equivalent are sold to underwriters
     or dealers for public offering without a subscription offering, the initial
     public offering price, in any such case excluding any amounts paid or
     receivable for accrued interest or accrued dividends and without deduction
     of any compensation, discounts, commissions or expenses paid or incurred by
     the Company for and in the underwriting of, or otherwise in connection
     with, the issue thereof; (II) to the extent that such issuance shall be for
     a consideration other than cash, then, except as herein otherwise expressly
     provided, the fair value of such consideration at the time of such issuance
     as determined in good faith by the Board of Directors, as evidenced by a
     certified resolution of the Board of Directors delivered to the holder of
     this Warrant Certificate setting forth such determination. The
     consideration for any additional shares of Common Stock issuable pursuant
     to any Common Stock Equivalent shall be the consideration received by the
     Company for issuing such Common Stock Equivalent, plus the additional
     consideration payable to the Company upon the exercise, conversion or
     exchange of such Common Stock Equivalent. In case of the issuance at any
     time of any additional shares of Common Stock or Common Stock Equivalent in
     payment or satisfaction of any dividend upon any class of stock other than
     Common Stock, the Company shall be deemed to have received for such
     additional shares of Common Stock or Common Stock Equivalent (which shall
     not be deemed to be a dividend payable in, or other distribution of, Common
     Stock under subsection (c) above) consideration equal to the amount of such
     dividend so paid or satisfied.

              ii. Upon the expiration of the right to convert, exchange or
     exercise any Common Stock Equivalent the issuance of which effected an
     adjustment in the Exercise Price, if any such Common Stock Equivalent shall
     not have been converted, exercised or exchanged, the number of shares of
     Common Stock deemed to be issued and outstanding because they were issuable
     upon conversion, exchange or exercise of any such Common Stock Equivalent
     shall no longer be computed as set forth above, and the Exercise Price
     shall forthwith be readjusted and thereafter be the price which it would
     have been (but reflecting any other adjustments in the Exercise Price made
     pursuant to the provisions of subsection (d) after the issuance of such
     Common Stock Equivalent) had the adjustment of the Exercise Price made upon
     the issuance or sale of such Common Stock Equivalent been made on the basis
     of the issuance only of the





                                      -7-
<PAGE>   8

     number of additional shares of Common Stock actually issued upon exercise,
     conversion or exchange of such Common Stock Equivalent and thereupon only
     the number of additional shares of Common Stock actually so issued shall be
     deemed to have been issued and only the consideration actually received by
     the Company (computed as in subparagraph (i) of this paragraph (f)) shall
     be deemed to have been received by the Company.

              iii. The number of shares of Common Stock at any time outstanding
     shall not include any shares thereof then directly or indirectly owned or
     held by or for the account of the Company or its wholly owned subsidiaries.

              iv. For the purposes of this Section 2, the term "shares of Common
     Stock" shall mean shares of (i) the class of stock designated as the Common
     Stock at the date hereof or (ii) any other class of stock resulting from
     successive changes or reclassifications of such shares consisting solely of
     changes in par value, or from par value to no par value, or from no par
     value to par value. If at any time, because of an adjustment pursuant to
     subsection (a), the Warrants shall entitle the holders to purchase any
     securities other than shares of Common Stock, thereafter the number of such
     other securities so purchasable upon exercise of each Warrant and the
     Exercise Price of such securities shall be subject to adjustment from time
     to time in a manner and on terms as nearly equivalent as practicable to the
     provisions with respect to the Common Stock contained in this Section 2.

         (g) Calculation of Exercise Price. The Exercise Price in effect from
time to time shall be calculated to four decimal places and rounded to the
nearest thousandth.

     3. NOTICE OF ADJUSTMENTS. Whenever the Exercise Price or the number of
shares of Common Stock is required to be adjusted as provided in Section 2, the
Company shall forthwith compute the adjusted Exercise Price or the number of
shares of Common Stock issuable and shall prepare and mail to the holder hereof
a certificate setting forth such adjusted Exercise Price or such number of
shares of Common Stock, showing in reasonable detail the facts upon which the
adjustment is based.

     4. VOLUNTARY REDUCTION. (a) The Company may at its option, but shall not be
obligated to, at any time during the term of the Warrants, reduce the then
current Exercise Price by any amount selected by the Board of Directors;
provided that if the Company elects so to reduce the then current Exercise
Price, such reduction shall be irrevocable during its effective period and
remain in effect for a minimum of 30 days following the date of such election,
after which time the Company may, at its option, reinstate the Exercise Price in
effect prior to such reduction. Whenever the Exercise Price is reduced, the
Company shall mail to the holder a notice of the reduction at least 30 days
before the date the reduced Exercise Price takes effect, stating the reduced
Exercise Price and the period for which such reduced Exercise Price will be in
effect.




                                      -8-
<PAGE>   9

         (b) The Company may make such decreases in the Exercise Price, in
addition to those required or allowed by this Section 4, as shall be determined
by it, as evidenced by a certified resolution of the Board of Directors
delivered to the holders, to be advisable to avoid or diminish any income tax to
the holder resulting from any dividend or distribution of stock or issuance of
rights or warrants to purchase or subscribe for stock or from any event treated
as such for income tax purposes.

     5. NOTICES TO WARRANT HOLDERS. In the event:


         (a) the Company shall authorize any consolidation or merger to which
the Company is a party and for which approval of any stockholders of the Company
is required, or of the conveyance or sale of all or substantially all of the
assets of the Company, or of any reclassification or change of the Common Stock
or other securities issuable upon exercise of the Warrants (other than a change
in par value, or from par value to no par value, or from no par value to par
value or as a result of a subdivision or combination), or a tender offer or
exchange offer for shares of Common Stock (or other securities issuable upon the
exercise of the Warrants); or

         (b) the Company shall declare any dividend (or any other distribution)
on the Common Stock or any other class of its capital stock; or

         (c) the Company shall authorize the granting to the holders of Common
Stock or any other class of its capital stock of rights or warrants to subscribe
for or purchase any shares of any class or series of capital stock or any other
securities convertible into or exchangeable for shares of stock; or

         (d) of the voluntary or involuntary dissolution, liquidation or winding
up of the Company;

     then the Company shall cause to be sent to the holder hereof, at least 30
days prior to the applicable record date hereinafter specified, or promptly in
the case of events for which there is no record date, a written notice stating
(x) the date for the determination of the holders of record of shares of Common
Stock (or other securities issuable upon the exercise of the Warrants) entitled
to receive any such dividends or other distribution, (y) the initial expiration
date set forth in any tender offer or exchange offer for shares of Common Stock
(or other securities issuable upon the exercise of the Warrants), or (z) the
date on which any of the events specified in subsections (a)-(d) is expected to
become effective or consummated, and the date as of which it is expected that
holders of record of shares of Common Stock (or other securities issuable upon
the exercise of the Warrants) shall be entitled to exchange such shares for
securities or other property, if any, deliverable upon any such event. Failure
to give such notice or any defect therein shall not affect the legality or
validity of any such event, or the vote upon any such action.




                                      -9-
<PAGE>   10



     6. REPORTS TO WARRANT HOLDERS. The Company will cause to be delivered, by
first-class mail, postage prepaid, to the holder at such holder's address
appearing hereon, or such other address as the holder shall specify, a copy of
any reports delivered by the Company to the holders of Common Stock.

     7. COVENANTS OF THE COMPANY. The Company covenants and agrees that:

              (a) Until the Expiration Date, the Company shall at all times
reserve and keep available, free from preemptive rights, out of the aggregate of
its authorized but unissued Common Stock (and other securities), for the purpose
of enabling it to satisfy any obligation to issue shares of Common Stock (and
other securities) upon the exercise of the Warrants, the number of shares of
Common Stock (and other securities) issuable upon the exercise of such Warrants.

              (b) The Company shall pay all expenses, taxes and other charges
payable in connection with the preparation, issuance and delivery of new warrant
certificates on transfer of the Warrants.

              (c) All Common Stock (and other securities) which may be issued
upon exercise of the Warrants shall upon issuance be validly issued, fully paid,
non-assessable and free from all preemptive rights and all taxes, liens and
charges with respect to the issuance thereof, and will not be subject to any
restrictions on voting or transfer thereof except as set forth in any
stockholders agreement.

              (d) All original issue taxes payable in respect of the issuance of
shares of Common Stock to the registered holder hereof upon the exercise of the
Warrants shall be borne by the Company; provided, that the Company shall not be
required to pay any tax or charge imposed in connection with any transfer
involved in the issuance of any certificate representing shares of Common Stock
(and other securities) in any name other than that of the registered holder
hereof, and in such case the Company shall not be required to issue or deliver
any certificate representing shares of Common Stock (and other securities) until
such tax or other charge has been paid or it has been established to the
Company's satisfaction that no such tax or charge is due.

              (e) As soon as practicable after the receipt from the holder of
this Warrant Certificate of notice of the exercise of a number of warrants
sufficient to require a filing under the Hart-Scott-Rodino Antitrust
Improvements Act of 1976 and the rules, regulations and formal interpretations
thereunder, as amended from time to time (the "HSR Act"), but in any event no
later than the 10th business day after receipt of such notice, the Company will
(i) prepare and file with the Antitrust Division of the Department of Justice
(the "DOJ") and the Federal Trade Commission (the "FTC") the Notification and
Report Form (accompanied by all documentary attachments contemplated thereby)
required by the HSR Act, (ii) upon the request of the holder, request early
termination of the waiting period imposed by the HSR Act, (iii) coordinate and
cooperate with the






                                      -10-
<PAGE>   11


holder in responding to formal and informal requests for additional information
and documentary material from the DOJ and the FTC in connection with such
filing, (iv) use its best efforts to take, or cause to be taken, all reasonable
action and to do, or cause to be done, all things necessary and appropriate to
permit the issuance to the holder of the shares of Common Stock issuable upon
the exercise of the warrants with respect to which any filing is required under
the HSR Act, and (v) reimburse the holder for the entire amount of any filing
fee or any other costs and expenses incurred by the holder in connection
therewith (including legal fees), or as required to be paid under the HSR Act.

              (f) QUOTATION ON NASDAQ. The Company shall maintain the
designation and quotations, or listing, of its Common Stock on the NASDAQ
national market (or on the New York Stock Exchange or the American Stock
Exchange) until the date on which none of the Warrants or Warrant Shares remain
outstanding.

     8. NO RIGHTS AS STOCKHOLDER. The holder of the Warrants shall not, by
virtue of holding such Warrants, be entitled to any rights of a stockholder of
the Company either at law or in equity, and the rights of the holder of the
Warrants are limited to those expressed herein.

     9. NOTICES. All notices provided for hereunder shall be in writing and may
be given by registered or certified mail, return receipt requested, telex,
telegram, telecopier, air courier guaranteeing overnight delivery of personal
delivery, if to the holder at the following address:

        Joint Energy Development Investments II Limited Partnership
        1400 Smith Street
        Houston, Texas 77002
        Attention:  Donna Lowry
        Telecopier:  (713) 646-4039

     and, if to the Company:

        Brigham Exploration Company
        6300 Bride Point Parkway
        Building 2, Suite 500
        Austin, Texas 78730
        Attention: Curtis F. Harrell
        Telecopier: (512) 472-3400

     10. GOVERNING LAW. This Warrant Certificate shall be governed by and
construed in accordance with the laws of the State of Texas without regard to
principles of conflict of laws.





                                      -11-
<PAGE>   12

     11. LOST, STOLEN, MUTILATED OR DESTROYED WARRANT CERTIFICATES. Upon receipt
by the Company of evidence reasonably satisfactory to it of the ownership of and
the loss, theft, destruction or mutilation of any Warrant Certificate, then, in
the absence of notice to the Company that such Warrant Certificate has been
acquired by a bona fide purchaser, the Company shall execute and deliver, in
exchange for or in lieu of the lost, stolen, destroyed or mutilated Warrant
Certificate, a substitute Warrant Certificate of the same tenor and evidencing a
like number of Warrants.

     12. ASSIGNMENT. The holder of this Warrant Certificate shall be entitled,
without obtaining the consent of the Company, to transfer or assign its rights,
title and interest in (and rights, title and interest under) this Warrant
Certificate in whole or in part to any Person or Persons. Upon surrender of this
Warrant Certificate to the Company, with the Transfer Form annexed hereto as
Exhibit B duly executed, the Company shall, without charge, execute and deliver
a new warrant certificate or warrant certificates, identical in form to this
Warrant Certificate, evidencing the number of Warrants being transferred
pursuant to the Transfer Form in the name of the assignee or assignees named in
such Transfer Form. If the holder's entire interest is not being assigned, the
Company shall, without charge, execute and deliver one or more new warrant
certificates identical in form to this Warrant Certificate, but evidencing a
number of Warrants equal to the number of Warrants originally represented by
this Warrant Certificate less the number being transferred pursuant to the
Transfer Form, and this Warrant Certificate shall promptly be canceled. The
terms and provisions of this Warrant Certificate shall inure to the benefit of
the holder and its successors and assigns and shall be binding upon the Company
and its successors and assigns, including, without limitation, any Person
succeeding the Company by merger, consolidation or acquisition of all or
substantially all of the Company's assets.

     13. FAIR MARKET VALUE. Whenever the terms of this Warrant require a
determination of the fair market value of the Warrants or the Common Stock and,
at the time of such determination, the Common Stock or the Warrants, as the case
may be, are not Publicly Traded, such determination shall be made in good faith
by the Board of Directors of the Company within 30 days and the Company shall
notify the holder of such determination no later than two business days
following the date of such determination. If the holder disagrees with the fair
market value as so determined by the Board of Directors, such holder shall so
notify the Company within five business days after receipt of notice from the
Board of Directors of its determination and such holder shall include in such
notice (a "Dissenting Notice"), the holder's estimate of the fair market value.
In the event the holder and the Company are unable to reach agreement regarding
the fair market value with five business days after receipt by the Company of
the Dissenting Notice, then the fair market value shall be determined by an
independent third party, knowledgeable and experienced in the valuation of
private businesses, and who is mutually acceptable to the Company and the holder
(the "Appraiser"). In the event the Company and the holder are unable to agree
upon an Appraiser within two business days after receipt by the Company of the
Dissenting Notice, each party shall, within 2 business days, select an
investment banking firm and the two investment banking firms so selected shall,
within 5 business days, select a third investment banking firm to be the
Appraiser. The Appraiser shall make a




                                      -12-
<PAGE>   13

determination of fair market value within 20 business days of his appointment
and shall notify the Company and the holder of such determination, which shall
be binding on both parties. The costs associated with the determination of fair
market value shall be borne by the Company (as such value is determined by this
Section 15, the "Fair Market Value").







                                      -13-
<PAGE>   14

         IN WITNESS WHEREOF, the Company has caused this Warrant Certificate to
be executed as of February 17, 2000, by the undersigned, thereunto duly
authorized.


                                           BRIGHAM EXPLORATION COMPANY


                                           By:
                                              ---------------------------------
                                               Curtis F. Harrell
                                               Chief Financial Officer





                                      -14-
<PAGE>   15




                                   EXHIBIT A-1

                              ELECTION TO EXERCISE

     [To be executed on exercise of the Warrants evidenced by this Warrant
     Certificate pursuant to Section 1(a)]

TO:      Brigham Exploration Company

         The undersigned, the holder of the Warrants evidenced by the attached
Warrant Certificate, hereby irrevocably elects to exercise ______________ of
such Warrants, and herewith makes payment of ___________________________
($___________) representing the aggregate Exercise Price thereof, and requests
that the certificate representing the securities issuable hereunder be issued in
the name of _____________________ and delivered to, whose address is
__________________________________________.


The Exercise Price is being paid in the following manner: [ ] by bank draft or
cashier's check in the amount of ______________________________ ($_______), [ ]
by application of ________________________ ($___________) of the outstanding
principal balance of the holder's Notes, and/or [ ] by application of
__________________________ ($__________) of interest accrued on the holder's
Notes.




     Dated:
          -------------------

                               Name of Registered Holder:
                                                         ---------------------
                               Signature:
                                         -------------------------------------
                               Title:
                                     -----------------------------------------
                               Address:
                                       ----------------------------------------


NOTICE: The above signature(s) must correspond with the name as written on the
face of the Warrant Certificate in every detail, without alteration or
enlargement or any change whatsoever.



                                      -15-

<PAGE>   16

                                   EXHIBIT A-2

                        ALTERNATIVE ELECTION TO EXERCISE
[To be executed on exercise of the Warrants evidenced by this Warrant
Certificate pursuant to Section 1(b)]

TO:      Brigham Exploration Company (the "Company")

         The undersigned holder of the Warrants evidenced by the attached
Warrant Certificate, hereby elects to exercise ____________ Warrants.

[ ]      The undersigned elects to receive shares of Common Stock of the Company
         in an amount equal to the Appreciation Amount (as defined in the
         Warrant), in accordance with Section 1(b) of the Warrant, and requests
         that the securities issuable hereunder be issued in the name of
         ___________, whose address is _________________________________.




     Dated:
          -------------------

                               Name of Registered Holder:
                                                         ---------------------
                               Signature:
                                         -------------------------------------
                               Title:
                                     -----------------------------------------
                               Address:
                                       ----------------------------------------



NOTICE: The above signature(s) must correspond with the name as written on the
face of the Warrant Certificate in every detail, without alteration or
enlargement or any change whatsoever.





                                      -16-
<PAGE>   17



                                   EXHIBIT B

TRANSFER FORM [To be executed only upon transfer of the Warrants evidenced by
this Warrant Certificate]

         FOR VALUE RECEIVED, the undersigned hereby sells, assigns and transfers
unto ___________________________________ _________________ of the Warrants
represented by the within Warrant Certificate, together with all right, title
and interest therein, and does hereby irrevocably constitute and appoint
_____________________________________ Attorney-in-Fact, to transfer same on the
books of the Company with full power of substitution in the premises.




     Dated:
          -------------------

                               Name of Registered Holder:
                                                         ---------------------
                               Signature:
                                         -------------------------------------
                               Title:
                                     -----------------------------------------
                               Address:
                                       ----------------------------------------




WITNESS:


- ---------------------------------




NOTICE: The above signature(s) must correspond with the name as written on the
face of the Warrant Certificate in every detail, without alteration or
enlargement or any change whatsoever.




                                      -17-

<PAGE>   1


                                                                   EXHIBIT 10.14


                               WARRANT CERTIFICATE

Number of Warrants: 250,000                                    Warrant No.   A-5

          This warrant certificate ("Warrant Certificate") certifies that, for
value received,

                         ECT MERCHANT INVESTMENTS CORP.

is the registered holder of the number of warrants (the "Warrants") set forth
above. Each Warrant entitles the holder thereof, at any time or from time to
time during the Exercise Period, to purchase from the Company one fully paid and
nonassessable share of Common Stock at the Exercise Price, subject to adjustment
as provided herein. The Warrants constitute, as of February 17, 2000, 1.0338% of
the outstanding Common Stock on a fully diluted basis including, for purposes of
such calculation, the Acquired Shares and the Warrant Shares. Initially
capitalized terms used but not defined herein shall have the meanings ascribed
to them in the Securities Purchase Agreement. This Warrant Certificate amends
and restates Warrant No. A-3 issued to ECT Merchant Investments Corp. as of
March 26, 1999, which in turn had amended and restated Warrant No. A-1 issued to
Enron Capital & Trade Resources Corp. on August 20, 1998.

          "Acquired Shares" means the shares of Common Stock acquired by Enron
North America Corp. and Joint Energy Development Investments II Limited
Partnership pursuant to Section 2.01 of the Securities Purchase Agreement.

          "Appraiser" has the meaning set forth in Section 13.

          "Appreciation Amount" has the meaning set forth in Section 1(b).

          "Common Stock" means the common stock, $.01 par value per share, of
the Company and such other class of securities as shall then represent the
common equity of the Company.

          "Company" means Brigham Exploration Company, a Delaware corporation.

          "Exercise Period" means the period of time between the Funding Date,
as defined in the Securities Purchase Agreement and 5:00 p.m. (New York City
time) on the Expiration Date.

          "Exercise Price" subject in all circumstances to adjustment in
accordance with Section 2, means $______, which represents the average volume
weighted Price during the twenty (20) calendar day period that begins February
22, 2000 and ends March 12, 2000.

          "Expiration Date" means August 22, 2008.


<PAGE>   2


          "Dissenting Notice" has the meaning set forth in Section 13.

          "Fair Market Value" has the meaning set forth in Section 13.

          "Funding Date" is defined in the Securities Purchase Agreement.

          "IPO" shall mean the initial public offering of securities of the
Company consummated on May 24, 1997, pursuant to a registration statement filed
under the Securities Act of 1933, as amended, and the rules and regulations
promulgated thereunder.

          "Issuance Date" means August 20, 1998.

          "Notes" means the Senior Subordinated Secured Notes issued pursuant to
the Securities Purchase Agreement.

          "Person" means any individual, corporation, company, partnership,
joint venture, trust, limited liability company, unincorporated organization or
government or any agency, instrumentality or political subdivision thereof, or
any other form of entity.

          "Price" means the average of the "high" and "low" prices as reported
in The Wall Street Journal's listing for such day (corrected for obvious
typographical errors) or if such shares are not reported in such listing, the
average of the reported "high" and "low" sales prices on the largest national
securities exchange (based on the aggregate dollar value of securities listed)
on which such shares are listed or traded, or if such shares are not listed or
traded on any national securities exchange, then the average of the reported
"high" and "low" sales prices for such shares in the over-the-counter market, as
reported on the National Association of Securities Dealers Automated Quotations
System, or, if such prices shall not be reported thereon, the average of the
closing bid and asked prices so reported, or, if such prices shall not be
reported, then the average of the closing bid and asked prices reported by the
National Quotations Bureau Incorporated, or, in all other cases, the Fair Market
Value as determined in accordance with Section 13 below. The "average" Price per
share for any period shall be determined by dividing the sum of the Prices
determined for the individual trading days in such period by the number of
trading days in such period.

          "Publicly Traded" means, with respect to the Common Stock, that such
securities are listed for trading on the New York Stock Exchange, Inc., the
American Stock Exchange, Inc. or the NASDAQ National Market. The Common Stock
shall also be deemed to be Publicly Traded if the Common Stock is included in
the NASDAQ SmallCap Market.

          "Securities Purchase Agreement" means the Securities Purchase
Agreement, dated as of August 20, 1998, among the Company, Enron North America
Corp. (formerly named Enron Capital


                                      -2-
<PAGE>   3


& Trade Resources Corp.), and Joint Energy Development Investments II Limited
Partnership, individually and as agent, as amended from time to time.

          "Warrant Shares" means the shares of Common Stock and other securities
receivable upon exercise of the Warrants.

          "Warrants" means the Warrants issued by the Company to Enron North
America Corp. and Joint Energy Development Investments II Limited Partnership
pursuant to the Securities Purchase Agreement and any Warrants issued upon the
transfer thereof or in substitution therefor.

          1. EXERCISE OF WARRANTS. (a) The Warrants may be exercised in whole or
in part, at any time or from time to time, during the Exercise Period, by
presentation and surrender to the Company at its address set forth in Section 9
of (i) this Warrant Certificate with the Election To Exercise, attached hereto
as Exhibit A-1, duly completed and executed, and (ii) payment of the Exercise
Price for the number of Warrants being exercised. At the option of the holder
hereof, payment of the Exercise Price shall be made (w) by wire transfer of
funds, (x) by check payable to the order of the Company, (y) by application of
any Warrant Shares or credit against any Notes, as provided below, or (z) by any
combination of such methods.

If the holder of this Warrant Certificate at any time exercises less than all
the Warrants, the Company shall issue to such holder a warrant certificate
identical in form to this Warrant Certificate, but evidencing a number of
Warrants equal to the number of Warrants originally represented by this Warrant
Certificate less the number of Warrants previously exercised. Likewise, upon the
presentation and surrender of this Warrant Certificate to the Company at its
address set forth in Section 9 and at the request of the holder, the Company
will, without expense, at the option of the holder, issue to the holder in
substitution for this Warrant Certificate one or more warrant certificates in
identical form and for an aggregate number of Warrants equal to the number of
Warrants evidenced by this Warrant Certificate.

               (b) In lieu of exercise in accordance with paragraph (a) above,
the Warrants represented hereby may be exercised, in whole or in part, by
presentation and surrender at the office of the Company specified herein of this
Warrant Certificate with the "Alternative Election to Exercise", attached hereto
as Exhibit A-2, duly completed and executed. Upon such exercise, the holder
shall be entitled to receive from the Company, for each share of Common Stock
issuable upon exercise of each Warrant being exercised, shares of Common Stock
with a value equal to the amount by which either the Price or, in the event that
the Common Stock is not Publicly Traded, the Fair Market Value of one share of
Common Stock on the date of exercise exceeds the Exercise Price (the
"Appreciation Amount"). If the Common Stock is Publicly Traded on the date of
exercise of Warrants pursuant to this Section 1(b), the Company shall deliver
(or cause its transfer agent to deliver) certificates representing shares of
Common Stock issuable upon such exercise within five business days following the
date of exercise. If the Common Stock is not Publicly Traded on the date


                                      -3-
<PAGE>   4


of exercise of Warrants pursuant to this Section 1(b), such election may be
withdrawn by the holder at any time prior to the third business day following
the date on which the holder receives notice of the final determination of Fair
Market Value pursuant to Section 15. Unless the holder timely withdraws its
exercise, the Company shall deliver (or cause its transfer agent to deliver)
certificates representing Common Stock so issuable within 10 business days
following the date of determination of the Fair Market Value. In lieu of any
fractional shares otherwise issuable upon exercise pursuant hereto, the Company
shall pay to the holder cash in an amount equal to the Price, or in the event
the Company is not Publicly Traded, the Fair Market Value of such fractional
share.

               (c) Upon the exercise of this Warrant in whole or in part by the
holder of any Notes, such holder may, at its option, deliver written notice to
the Company that the holder has elected to apply some or all of the Exercise
Price required upon such exercise against all or any specified principal amount
of and/or accrued but unpaid interest on, such Notes, in which case the Company
will accept the application of the Exercise Price against such specified
principal and/or interest amount in lieu of a like amount of cash payment.

               (d) To the extent that the Warrants have not been exercised at or
prior to the Expiration Date, such Warrants shall expire and the rights of the
holder shall become void and of no effect.

          2. ANTIDILUTION ADJUSTMENTS. The shares of Common Stock purchasable on
exercise of the Warrants are shares of Common Stock as constituted as of the
Issuance Date. The number and kind of securities purchasable upon the exercise
of the Warrants, and the Exercise Price, shall be subject to adjustment from
time to time upon the happening of certain events, as follows:

               (a) Mergers, Consolidations and Reclassifications. In case of any
reclassification or change of outstanding securities issuable upon exercise of
the Warrants at any time after the Issuance Date (other than a change in par
value, or from par value to no par value, or from no par value to par value or
as a result of a subdivision or combination to which subsection 2(b) applies),
or in case of any consolidation or merger of the Company with or into another
entity or other person (other than a merger with another entity or other person
in which the Company is the surviving corporation and which does not result in
any reclassification or change in the securities issuable upon exercise of this
Warrant Certificate), the holder of the Warrants shall have, and the Company, or
such successor corporation or other entity, shall covenant in the constituent
documents effecting any of the foregoing transactions that such holder does
have, the right to obtain upon the exercise of the Warrants, in lieu of each
share of Common Stock, other securities, money or other property theretofore
issuable upon exercise of a Warrant, the kind and amount of shares of stock,
other securities, money or other property receivable upon such reclassification,
change, consolidation or merger by a holder of the shares of Common Stock, other
securities, money or other property issuable upon exercise of a Warrant if the
Warrants had been exercised immediately prior to such reclassification, change,
consolidation or merger. The constituent documents effecting any such


                                      -4-
<PAGE>   5


reclassification, change, consolidation or merger shall provide for adjustments
which shall be as nearly equivalent as may be practicable to the adjustments
provided in this subsection 2(a). The provisions of this subsection 2(a) shall
similarly apply to successive reclassifications, changes, consolidations or
mergers.

               (b) Subdivisions and Combinations. If the Company, at any time
after the Issuance Date, shall subdivide its shares of Common Stock into a
greater number of shares, the Exercise Price in effect immediately prior to such
subdivision shall be proportionately reduced, and the number of shares of Common
Stock purchasable upon exercise of the Warrants shall be proportionately
increased, as at the effective date of such subdivision, or if the Company shall
take a record of holders of its Common Stock for such purpose, as at such record
date, whichever is earlier. If the Company, at any time after the Issuance Date,
shall combine its shares of Common Stock into a smaller number of shares, the
Exercise Price in effect immediately prior to such combination shall be
proportionately increased, and the number of shares of Common Stock purchasable
upon exercise of the Warrants shall be proportionately reduced, as at the
effective date of such combination, or if the Company shall take a record of
holders of its Common Stock for purposes of such combination, as at such record
date, whichever is earlier.

               (c) Dividends and Distributions. If the Company at any time after
the Issuance Date shall declare a dividend on its Common Stock payable in stock
or other securities of the Company to the holders of its Common Stock, the
holder of this Warrant Certificate shall, without additional cost, be entitled
to receive upon any exercise of a Warrant, in addition to the Common Stock to
which such holder would otherwise be entitled upon such exercise, the number of
shares of stock or other securities which such holder would have been entitled
to receive if he had been a holder immediately prior to the record date for such
dividend (or, if no record date shall have been established, the payment date
for such dividend) of the number of shares of Common Stock purchasable on
exercise of such Warrant immediately prior to such record date or payment date,
as the case may be.

               (d) Certain Issuances of Securities. If the Company at any time
after the Issuance Date shall issue any additional shares of Common Stock
(otherwise than as provided in paragraphs (a) through (c) of this Section 2) at
a price per share less than the average Price per share of Common Stock for the
20 trading days immediately preceding the date of the authorization of such
issuance (the "Market Price") by the Board of Directors, then the Exercise Price
upon each such issuance shall be adjusted to that price determined by
multiplying the Exercise Price by a fraction:

                    i. the numerator of which shall be the sum of (1) the number
          of shares of Common Stock outstanding immediately prior to the
          issuance of such additional shares of Common Stock multiplied by the
          Market Price, and (2) the consideration, if any, received by the
          Company upon the issuance of such additional shares of Common Stock,
          and


                                      -5-
<PAGE>   6


                    ii. the denominator of which shall be the Market Price
          multiplied by the total number of shares of Common Stock outstanding
          immediately after the issuance of such additional shares of Common
          Stock.

          No adjustments of the Exercise Price shall be made under this
paragraph (d) upon the issuance of any additional shares of Common Stock that
(y) are issued pursuant to thrift plans, stock purchase plans, stock bonus
plans, stock option plans, employee stock ownership plans and other incentive or
profit sharing arrangements for the benefit of employees ("Employee Benefit
Plans") that otherwise would cause an adjustment under this paragraph (d);
provided that the aggregate number of shares of Common Stock so issued
(including the shares issued pursuant to any options, rights or warrants or
convertible or exchangeable securities issued under such Employee Benefit Plans
containing the right to purchase shares of Common Stock) pursuant to Employee
Benefit Plans after the closing date of the IPO, as adjusted for any stock
splits, stock dividends or subdivisions or combinations of Common Stock prior to
the Expiration Date, shall not in the aggregate exceed 5% of the Company's
outstanding Common Stock at the time of such issuance; or (z) are issued
pursuant to any Common Stock Equivalent (as hereinafter defined) (i) if upon the
issuance of any such Common Stock Equivalent, any such adjustments shall
previously have been made pursuant to paragraph (e) of this Section 2 or (ii) if
no adjustment was required pursuant to paragraph (e) of this Section 2.

               (e) Common Stock Equivalents. If the Company shall, after the
Issuance Date, issue any security or evidence of indebtedness which is
convertible into or exchangeable for Common Stock ("Convertible Security"), or
any warrant, option or other right to subscribe for or purchase Common Stock or
any Convertible Security, other than pursuant to Employee Benefit Plans
(together with Convertible Securities, "Common Stock Equivalent"), or if, after
any such issuance, the price per share for which additional shares of Common
Stock may be issuable thereunder is amended, then the Exercise Price upon each
such issuance or amendment shall be adjusted as provided in subsection (d) on
the basis that (i) the maximum number of additional shares of Common Stock
issuable pursuant to all such Common Stock Equivalents shall be deemed to have
been issued as of the earlier of (a) the date on which the Company shall enter
into a firm contract for the issuance of such Common Stock Equivalent, or (b)
the date of actual issuance of such Common Stock Equivalent; and (ii) the
aggregate consideration for such maximum number of additional shares of Common
Stock shall be deemed to be the minimum consideration received and receivable by
the Company for the issuance of such additional shares of Common Stock pursuant
to such Common Stock Equivalent; provided, however, that no adjustment shall be
made pursuant to this subsection (e) unless the consideration received and
receivable by the Company per share of Common Stock for the issuance of such
additional shares of Common Stock pursuant to such Common Stock Equivalent is
less than the Market Price. No adjustment of the Exercise Price shall be made
under this subsection (e) upon the issuance of any Convertible Security which is
issued pursuant to the exercise of any warrants or other subscription or
purchase rights therefor, if any adjustment shall previously have been made in
the Exercise Price then in effect upon the issuance of such warrants or other
rights pursuant to this subsection (e).


                                      -6-
<PAGE>   7


               (f) Miscellaneous. The following provisions shall be applicable
to the making of adjustments in the Exercise Price hereinbefore provided in this
Section 2:

                    i. The consideration received by the Company shall be deemed
          to be the following: (I) to the extent that any additional shares of
          Common Stock or any Common Stock Equivalent shall be issued for cash
          consideration, the consideration received by the Company therefor, or,
          if such additional shares of Common Stock or Common Stock Equivalent
          are offered by the Company for subscription, the subscription price,
          or, if such additional shares of Common Stock or Common Stock
          Equivalent are sold to underwriters or dealers for public offering
          without a subscription offering, the initial public offering price, in
          any such case excluding any amounts paid or receivable for accrued
          interest or accrued dividends and without deduction of any
          compensation, discounts, commissions or expenses paid or incurred by
          the Company for and in the underwriting of, or otherwise in connection
          with, the issue thereof; (II) to the extent that such issuance shall
          be for a consideration other than cash, then, except as herein
          otherwise expressly provided, the fair value of such consideration at
          the time of such issuance as determined in good faith by the Board of
          Directors, as evidenced by a certified resolution of the Board of
          Directors delivered to the holder of this Warrant Certificate setting
          forth such determination. The consideration for any additional shares
          of Common Stock issuable pursuant to any Common Stock Equivalent shall
          be the consideration received by the Company for issuing such Common
          Stock Equivalent, plus the additional consideration payable to the
          Company upon the exercise, conversion or exchange of such Common Stock
          Equivalent. In case of the issuance at any time of any additional
          shares of Common Stock or Common Stock Equivalent in payment or
          satisfaction of any dividend upon any class of stock other than Common
          Stock, the Company shall be deemed to have received for such
          additional shares of Common Stock or Common Stock Equivalent (which
          shall not be deemed to be a dividend payable in, or other distribution
          of, Common Stock under subsection (c) above) consideration equal to
          the amount of such dividend so paid or satisfied.

                    ii. Upon the expiration of the right to convert, exchange or
          exercise any Common Stock Equivalent the issuance of which effected an
          adjustment in the Exercise Price, if any such Common Stock Equivalent
          shall not have been converted, exercised or exchanged, the number of
          shares of Common Stock deemed to be issued and outstanding because
          they were issuable upon conversion, exchange or exercise of any such
          Common Stock Equivalent shall no longer be computed as set forth
          above, and the Exercise Price shall forthwith be readjusted and
          thereafter be the price which it would have been (but reflecting any
          other adjustments in the Exercise Price made pursuant to the
          provisions of subsection (d) after the issuance of such Common Stock
          Equivalent) had the adjustment of the Exercise Price made upon the
          issuance or sale of such Common Stock Equivalent been made on the
          basis of the issuance only of the number of additional shares of
          Common Stock actually issued upon exercise, conversion or exchange of
          such Common Stock Equivalent and thereupon only the


                                      -7-
<PAGE>   8


          number of additional shares of Common Stock actually so issued shall
          be deemed to have been issued and only the consideration actually
          received by the Company (computed as in subparagraph (i) of this
          paragraph (f)) shall be deemed to have been received by the Company.

                    iii. The number of shares of Common Stock at any time
          outstanding shall not include any shares thereof then directly or
          indirectly owned or held by or for the account of the Company or its
          wholly owned subsidiaries.

                    iv. For the purposes of this Section 2, the term "shares of
          Common Stock" shall mean shares of (i) the class of stock designated
          as the Common Stock at the date hereof or (ii) any other class of
          stock resulting from successive changes or reclassifications of such
          shares consisting solely of changes in par value, or from par value to
          no par value, or from no par value to par value. If at any time,
          because of an adjustment pursuant to subsection (a), the Warrants
          shall entitle the holders to purchase any securities other than shares
          of Common Stock, thereafter the number of such other securities so
          purchasable upon exercise of each Warrant and the Exercise Price of
          such securities shall be subject to adjustment from time to time in a
          manner and on terms as nearly equivalent as practicable to the
          provisions with respect to the Common Stock contained in this Section
          2.

               (g) Calculation of Exercise Price. The Exercise Price in effect
from time to time shall be calculated to four decimal places and rounded to the
nearest thousandth.

          3. NOTICE OF ADJUSTMENTS. Whenever the Exercise Price or the number of
shares of Common Stock is required to be adjusted as provided in Section 2, the
Company shall forthwith compute the adjusted Exercise Price or the number of
shares of Common Stock issuable and shall prepare and mail to the holder hereof
a certificate setting forth such adjusted Exercise Price or such number of
shares of Common Stock, showing in reasonable detail the facts upon which the
adjustment is based.

          4. VOLUNTARY REDUCTION. (a) The Company may at its option, but shall
not be obligated to, at any time during the term of the Warrants, reduce the
then current Exercise Price by any amount selected by the Board of Directors;
provided that if the Company elects so to reduce the then current Exercise
Price, such reduction shall be irrevocable during its effective period and
remain in effect for a minimum of 30 days following the date of such election,
after which time the Company may, at its option, reinstate the Exercise Price in
effect prior to such reduction. Whenever the Exercise Price is reduced, the
Company shall mail to the holder a notice of the reduction at least 30 days
before the date the reduced Exercise Price takes effect, stating the reduced
Exercise Price and the period for which such reduced Exercise Price will be in
effect.


                                      -8-
<PAGE>   9


               (b) The Company may make such decreases in the Exercise Price, in
addition to those required or allowed by this Section 4, as shall be determined
by it, as evidenced by a certified resolution of the Board of Directors
delivered to the holders, to be advisable to avoid or diminish any income tax to
the holder resulting from any dividend or distribution of stock or issuance of
rights or warrants to purchase or subscribe for stock or from any event treated
as such for income tax purposes.

          5. NOTICES TO WARRANT HOLDERS. In the event:

               (a) the Company shall authorize any consolidation or merger to
which the Company is a party and for which approval of any stockholders of the
Company is required, or of the conveyance or sale of all or substantially all of
the assets of the Company, or of any reclassification or change of the Common
Stock or other securities issuable upon exercise of the Warrants (other than a
change in par value, or from par value to no par value, or from no par value to
par value or as a result of a subdivision or combination), or a tender offer or
exchange offer for shares of Common Stock (or other securities issuable upon the
exercise of the Warrants); or

               (b) the Company shall declare any dividend (or any other
distribution) on the Common Stock or any other class of its capital stock; or

               (c) the Company shall authorize the granting to the holders of
Common Stock or any other class of its capital stock of rights or warrants to
subscribe for or purchase any shares of any class or series of capital stock or
any other securities convertible into or exchangeable for shares of stock; or

               (d) of the voluntary or involuntary dissolution, liquidation or
winding up of the Company;

          then the Company shall cause to be sent to the holder hereof, at least
30 days prior to the applicable record date hereinafter specified, or promptly
in the case of events for which there is no record date, a written notice
stating (x) the date for the determination of the holders of record of shares of
Common Stock (or other securities issuable upon the exercise of the Warrants)
entitled to receive any such dividends or other distribution, (y) the initial
expiration date set forth in any tender offer or exchange offer for shares of
Common Stock (or other securities issuable upon the exercise of the Warrants),
or (z) the date on which any of the events specified in subsections (a)-(d) is
expected to become effective or consummated, and the date as of which it is
expected that holders of record of shares of Common Stock (or other securities
issuable upon the exercise of the Warrants) shall be entitled to exchange such
shares for securities or other property, if any, deliverable upon any such
event. Failure to give such notice or any defect therein shall not affect the
legality or validity of any such event, or the vote upon any such action.


                                      -9-
<PAGE>   10


          6. REPORTS TO WARRANT HOLDERS. The Company will cause to be delivered,
by first-class mail, postage prepaid, to the holder at such holder's address
appearing hereon, or such other address as the holder shall specify, a copy of
any reports delivered by the Company to the holders of Common Stock.

          7. COVENANTS OF THE COMPANY. The Company covenants and agrees that:

               (a) Until the Expiration Date, the Company shall at all times
reserve and keep available, free from preemptive rights, out of the aggregate of
its authorized but unissued Common Stock (and other securities), for the purpose
of enabling it to satisfy any obligation to issue shares of Common Stock (and
other securities) upon the exercise of the Warrants, the number of shares of
Common Stock (and other securities) issuable upon the exercise of such Warrants.

               (b) The Company shall pay all expenses, taxes and other charges
payable in connection with the preparation, issuance and delivery of new warrant
certificates on transfer of the Warrants.

               (c) All Common Stock (and other securities) which may be issued
upon exercise of the Warrants shall upon issuance be validly issued, fully paid,
non-assessable and free from all preemptive rights and all taxes, liens and
charges with respect to the issuance thereof, and will not be subject to any
restrictions on voting or transfer thereof except as set forth in any
stockholders agreement.

               (d) All original issue taxes payable in respect of the issuance
of shares of Common Stock to the registered holder hereof upon the exercise of
the Warrants shall be borne by the Company; provided, that the Company shall not
be required to pay any tax or charge imposed in connection with any transfer
involved in the issuance of any certificate representing shares of Common Stock
(and other securities) in any name other than that of the registered holder
hereof, and in such case the Company shall not be required to issue or deliver
any certificate representing shares of Common Stock (and other securities) until
such tax or other charge has been paid or it has been established to the
Company's satisfaction that no such tax or charge is due.

               (e) As soon as practicable after the receipt from the holder of
this Warrant Certificate of notice of the exercise of a number of warrants
sufficient to require a filing under the Hart-Scott-Rodino Antitrust
Improvements Act of 1976 and the rules, regulations and formal interpretations
thereunder, as amended from time to time (the "HSR Act"), but in any event no
later than the 10th business day after receipt of such notice, the Company will
(i) prepare and file with the Antitrust Division of the Department of Justice
(the "DOJ") and the Federal Trade Commission (the "FTC") the Notification and
Report Form (accompanied by all documentary attachments contemplated thereby)
required by the HSR Act, (ii) upon the request of the holder, request early
termination of the waiting period imposed by the HSR Act, (iii) coordinate and
cooperate with the


                                      -10-
<PAGE>   11


holder in responding to formal and informal requests for additional information
and documentary material from the DOJ and the FTC in connection with such
filing, (iv) use its best efforts to take, or cause to be taken, all reasonable
action and to do, or cause to be done, all things necessary and appropriate to
permit the issuance to the holder of the shares of Common Stock issuable upon
the exercise of the warrants with respect to which any filing is required under
the HSR Act, and (v) reimburse the holder for the entire amount of any filing
fee or any other costs and expenses incurred by the holder in connection
therewith (including legal fees), or as required to be paid under the HSR Act.

               (f) QUOTATION ON NASDAQ. The Company shall maintain the
designation and quotations, or listing, of its Common Stock on the NASDAQ
national market (or on the New York Stock Exchange or the American Stock
Exchange) until the date on which none of the Warrants or Warrant Shares remain
outstanding.

          8. NO RIGHTS AS STOCKHOLDER. The holder of the Warrants shall not, by
virtue of holding such Warrants, be entitled to any rights of a stockholder of
the Company either at law or in equity, and the rights of the holder of the
Warrants are limited to those expressed herein.

          9. NOTICES. All notices provided for hereunder shall be in writing and
may be given by registered or certified mail, return receipt requested, telex,
telegram, telecopier, air courier guaranteeing overnight delivery of personal
delivery, if to the holder at the following address:

              ECT Merchant Investments Corp.
              1400 Smith Street
              Houston, Texas 77002
              Attention:  Donna Lowry
              Telecopier:  (713) 646-4039

          and, if to the Company:

              Brigham Exploration Company
              6300 Bride Point Parkway
              Building 2, Suite 500
              Austin, Texas 78730
              Attention: Curtis F. Harrell
              Telecopier: (512) 472-3400

          10. GOVERNING LAW. This Warrant Certificate shall be governed by and
construed in accordance with the laws of the State of Texas without regard to
principles of conflict of laws.


                                      -11-
<PAGE>   12


          11. LOST, STOLEN, MUTILATED OR DESTROYED WARRANT CERTIFICATES. Upon
receipt by the Company of evidence reasonably satisfactory to it of the
ownership of and the loss, theft, destruction or mutilation of any Warrant
Certificate, then, in the absence of notice to the Company that such Warrant
Certificate has been acquired by a bona fide purchaser, the Company shall
execute and deliver, in exchange for or in lieu of the lost, stolen, destroyed
or mutilated Warrant Certificate, a substitute Warrant Certificate of the same
tenor and evidencing a like number of Warrants.

          12. ASSIGNMENT. The holder of this Warrant Certificate shall be
entitled, without obtaining the consent of the Company, to transfer or assign
its rights, title and interest in (and rights, title and interest under) this
Warrant Certificate in whole or in part to any Person or Persons. Upon surrender
of this Warrant Certificate to the Company, with the Transfer Form annexed
hereto as Exhibit B duly executed, the Company shall, without charge, execute
and deliver a new warrant certificate or warrant certificates, identical in form
to this Warrant Certificate, evidencing the number of Warrants being transferred
pursuant to the Transfer Form in the name of the assignee or assignees named in
such Transfer Form. If the holder's entire interest is not being assigned, the
Company shall, without charge, execute and deliver one or more new warrant
certificates identical in form to this Warrant Certificate, but evidencing a
number of Warrants equal to the number of Warrants originally represented by
this Warrant Certificate less the number being transferred pursuant to the
Transfer Form, and this Warrant Certificate shall promptly be canceled. The
terms and provisions of this Warrant Certificate shall inure to the benefit of
the holder and its successors and assigns and shall be binding upon the Company
and its successors and assigns, including, without limitation, any Person
succeeding the Company by merger, consolidation or acquisition of all or
substantially all of the Company's assets.

          13. FAIR MARKET VALUE. Whenever the terms of this Warrant require a
determination of the fair market value of the Warrants or the Common Stock and,
at the time of such determination, the Common Stock or the Warrants, as the case
may be, are not Publicly Traded, such determination shall be made in good faith
by the Board of Directors of the Company within 30 days and the Company shall
notify the holder of such determination no later than two business days
following the date of such determination. If the holder disagrees with the fair
market value as so determined by the Board of Directors, such holder shall so
notify the Company within five business days after receipt of notice from the
Board of Directors of its determination and such holder shall include in such
notice (a "Dissenting Notice"), the holder's estimate of the fair market value.
In the event the holder and the Company are unable to reach agreement regarding
the fair market value with five business days after receipt by the Company of
the Dissenting Notice, then the fair market value shall be determined by an
independent third party, knowledgeable and experienced in the valuation of
private businesses, and who is mutually acceptable to the Company and the holder
(the "Appraiser"). In the event the Company and the holder are unable to agree
upon an Appraiser within two business days after receipt by the Company of the
Dissenting Notice, each party shall, within 2 business days, select an
investment banking firm and the two investment banking firms so selected shall,
within 5 business days, select a third investment banking firm to be the
Appraiser. The Appraiser shall make a


                                      -12-
<PAGE>   13


determination of fair market value within 20 business days of his appointment
and shall notify the Company and the holder of such determination, which shall
be binding on both parties. The costs associated with the determination of fair
market value shall be borne by the Company (as such value is determined by this
Section 15, the "Fair Market Value").


                                      -13-
<PAGE>   14


          IN WITNESS WHEREOF, the Company has caused this Warrant Certificate to
be executed as of February 17, 2000, by the undersigned, thereunto duly
authorized.


                                       BRIGHAM EXPLORATION COMPANY


                                       By:
                                          --------------------------------------
                                             Curtis F. Harrell
                                             Chief Financial Officer


                                      -14-
<PAGE>   15


                                   EXHIBIT A-1

                              ELECTION TO EXERCISE
      [To be executed on exercise of the Warrants evidenced by this Warrant
                     Certificate pursuant to Section 1(a)]

TO:       Brigham Exploration Company

         The undersigned, the holder of the Warrants evidenced by the attached
Warrant Certificate, hereby irrevocably elects to exercise ______________ of
such Warrants, and herewith makes payment of ________________ ($___________)
representing the aggregate Exercise Price thereof, and requests that the
certificate representing the securities issuable hereunder be issued in the name
of _____________________ and delivered to __________________, whose address is
_____________________________.

The Exercise Price is being paid in the following manner: [ ] by bank draft or
cashier's check in the amount of ___________________ ($________), [ ] by
application of __________________ ($_________) of the outstanding principal
balance of the holder's Notes, and/or [ ] by application of _______________
($_______) of interest accrued on the holder's Notes.



         Dated:
               -----------

                           Name of Registered Holder:
                                                     ---------------------------
                           Signature:
                                     -------------------------------------------
                           Title:
                                 -----------------------------------------------

                           Address:
                                   ---------------------------------------------


NOTICE: The above signature(s) must correspond with the name as written on the
face of the Warrant Certificate in every detail, without alteration or
enlargement or any change whatsoever.


                                      -15-
<PAGE>   16


                                   EXHIBIT A-2

                        ALTERNATIVE ELECTION TO EXERCISE
      [To be executed on exercise of the Warrants evidenced by this Warrant
                     Certificate pursuant to Section 1(b)]

TO:       Brigham Exploration Company (the "Company")

          The undersigned holder of the Warrants evidenced by the attached
Warrant Certificate, hereby elects to exercise ____________ Warrants.

[ ]       The undersigned elects to receive shares of Common Stock of the
          Company in an amount equal to the Appreciation Amount (as defined in
          the Warrant), in accordance with Section 1(b) of the Warrant, and
          requests that the securities issuable hereunder be issued in the name
          of ___________, whose address is ____________________________________.


          Dated:
                ------------------

                                  Name of Registered Holder:
                                                            --------------------
                                  Signature:
                                            ------------------------------------
                                  Title:
                                        ----------------------------------------

                                  Address:
                                          --------------------------------------


NOTICE: The above signature(s) must correspond with the name as written on the
face of the Warrant Certificate in every detail, without alteration or
enlargement or any change whatsoever.


                                      -16-
<PAGE>   17


                                    EXHIBIT B

                                  TRANSFER FORM
  [To be executed only upon transfer of the Warrants evidenced by this Warrant
                                  Certificate]

          FOR VALUE RECEIVED, the undersigned hereby sells, assigns and
transfers unto ______________________________________________________
_________________ of the Warrants represented by the within Warrant Certificate,
together with all right, title and interest therein, and does hereby irrevocably
constitute and appoint _____________________________________ Attorney-in-Fact,
to transfer same on the books of the Company with full power of substitution in
the premises.

          Dated:
                ------------------

                                  Name of Registered Holder:
                                                            --------------------
                                  Signature:
                                            ------------------------------------
                                  Title:
                                        ----------------------------------------

                                  Address:
                                          --------------------------------------




WITNESS:

- ----------------------------------





NOTICE: The above signature(s) must correspond with the name as written on the
face of the Warrant Certificate in every detail, without alteration or
enlargement or any change whatsoever.



                                      -17-

<PAGE>   1
                                                                   EXHIBIT 10.15

              SECURITIES PURCHASE AND REGISTRATION RIGHTS AGREEMENT


                                  by and among



                           Brigham Exploration Company


                                       and

                       GAP Coinvestment Partners II, L.P.,
                Special Situations Private Equity Fund, L.P. and
                            Aspect Resources, L.L.C.




                                February 22, 2000









<PAGE>   2


              SECURITIES PURCHASE AND REGISTRATION RIGHTS AGREEMENT

                                    RECITALS:

         (a) This SECURITIES PURCHASE AND REGISTRATION RIGHTS AGREEMENT (this
"Agreement") is dated as of February 22, 2000, by and among GAP Coinvestment
Partners II, L.P., Special Situations Private Equity Fund, L.P., and Aspect
Resources, L.L.C. (each individually, a "Buyer," and collectively, the "Buyers")
and Brigham Exploration Company, a Delaware corporation (the "Company"); and

         (b) The Company desires to issue to Buyers, and Buyers desire to
purchase, shares of the Company's common stock, par value $.01 per share and
warrants affording the right to purchase shares of the Company's common stock.

         NOW, THEREFORE, in consideration of the mutual covenants and agreements
herein contained, and intending to be legally bound hereby, the Company and
Buyers hereby agree as follows:

                                   ARTICLE I.

                            TERMS OF THE TRANSACTION

         1.1 Agreement to Issue Shares. Within five (5) business days of
Closing, and on the terms and subject to the conditions set forth in this
Agreement, the Company shall have issued to each Buyer, and each Buyer
(severally) shall purchase and accept from the Company, the number of shares of
common stock of the Company (the "Common Stock") as set forth beside its name on
Schedule I (as issued to all Buyers, collectively, the "Shares"); provided,
however, that in the case of Aspect and Special Situations, the Company shall
issue each such Buyer's shares concurrent with its delivery of such Buyer's
share of the Purchase Price to the Company, which shall occur within thirty (30)
days after Closing.

         1.2 Agreement to Issue Warrants . Within five (5) business days of
Closing, and on the terms and subject to the conditions set forth in this
Agreement, the Company shall issue and deliver to each Buyer the number of
warrants to purchase common stock of the Company as set forth beside its name on
Schedule I hereto (as issued to all Buyers, collectively, the "Warrants");
provided, however, that in the case of Aspect and Special Situations, the
Company shall issue such Buyer's warrants concurrent with such Buyer's delivery
of its share of the Purchase Price to the Company, which shall occur within
thirty (30) days after Closing.

         1.3 Purchase Price and Payment. In consideration of the sale of the
Shares and the Warrants, contemporaneously with its receipt of its portion of
the Shares and Warrants, each Buyer shall pay to the Company, the purchase price
set forth beside its name on Schedule I, the aggregate of which shall be the
"Purchase Price", the Purchase Price per Share (the "Issuance Price") was
determined by reference to the greater of (a) $2.05, and (b) the minimum Average
Price per Share necessary to prevent triggering antidilution provisions in any
agreement in existence as of the date hereof. Each Buyer shall pay its portion
of the Purchase Price to the Company in immediately available funds by confirmed
wire transfer to a bank account to be designated by the Company. Special
Situations and Aspect shall have a period of thirty (30) days after the Closing
Date to fund their respective allocable



                                       1
<PAGE>   3


shares of the Purchase Price; if Aspect fails to so timely fund its share of the
Purchase Price, Special Situations shall have no obligation to do so and this
Agreement shall automatically, unless Special Situations nonetheless voluntarily
funds its share of the Purchase Price within such 30-day period, have no further
force and effect relative to Special Situations. Nothing in this Section 1.3 or
elsewhere in this Agreement shall be construed to change or diminish Aspect's
absolute obligation to fund its share of the Purchase Price within 30 days after
the Closing Date.

         1.4 Limitations. The rights and interests afforded Buyers hereunder
and/or under the Warrant Certificate are subject to any pre-existing rights of
the Company's common stock, option and warrant holders.

                                   ARTICLE II.

                                     CLOSING

         The closing of the transactions contemplated hereby (the "Closing")
shall take place (i) at the offices of Brigham Exploration Company, 6300 Bridge
Point Parkway, Building 2, Suite 500, Austin, Texas, 78730, at 10:00 a.m., local
time, on February 22, 2000, or (ii) at such other time or place or on such other
date as the parties hereto shall agree. The date on which the Closing is
required to take place is herein referred to as the "Closing Date." All Closing
transactions shall, except as provided otherwise herein, be deemed to have
occurred simultaneously.

                                  ARTICLE III.

                  REPRESENTATIONS AND WARRANTIES OF THE COMPANY

         The Company represents and warrants to Buyers that:

         3.1 Corporate Organization. The Company is a corporation duly
organized, validly existing, and in good standing under the laws of Delaware and
has all requisite corporate power and corporate authority to own, lease, and
operate its properties and to carry on its business as now being conducted. No
actions or proceedings to dissolve the Company are pending or, to the best
knowledge of the Company, threatened.

         3.2 Qualification. The Company is duly qualified or licensed to do
business as a foreign corporation and is in good standing in each of the
jurisdictions in which such qualification or licensing is required for the
conduct of its business.

         3.3 Charter and Bylaws. Neither the Company nor any Subsidiary is in
violation of any provision of its charter or bylaws, other than violations
which, individually or in the aggregate, do not and will not have a Material
Adverse Effect on the Company.

         3.4 Capitalization of the Company. The authorized capital stock of the
Company consists of (a) 30,000,000 shares of common stock and, after giving
effect to the transactions contemplated herein and all other issuances of
capital stock of the Company on or prior to the date hereof, 16,712,908 shares
of common stock will be issued and outstanding and 731,707 shares will be



                                       2
<PAGE>   4


reserved for future issuance pursuant hereto, and (b) 10,000,000 shares of
preferred stock, none of which are presently outstanding. Schedule III sets
forth a description of the outstanding capital stock of the Company, including
options and warrants.

         3.5 Authority Relative to This Agreement. The Company has full
corporate power and corporate authority to execute, deliver, and perform this
Agreement and the Ancillary Documents (as hereinafter defined) to which it is a
party and to consummate the transactions contemplated hereby and thereby. The
execution, delivery, and performance by the Company of this Agreement and the
Ancillary Documents to which it is a party, and the consummation by it of the
transactions contemplated hereby and thereby, have been duly authorized by all
necessary corporate action of the Company. This Agreement has been duly executed
and delivered by the Company and constitutes, and each Ancillary Document
executed or to be executed by the Company has been, or when executed will be,
duly executed and delivered by the Company and constitute, or when executed and
delivered will constitute, valid and legally binding obligations of the Company,
enforceable against the Company in accordance with their respective terms,
except that such enforceability may be limited by (i) applicable bankruptcy,
insolvency, reorganization, moratorium, and similar laws affecting creditors'
rights generally and (ii) equitable principles which may limit the availability
of certain equitable remedies (such as specific performance) in certain
instances.

         3.6 Shares and Warrants. The Shares to be issued by the Company within
five (5) business days of Closing or, in the case of Special Situations and
Aspect, within thirty (30) days after Closing, and the Shares issuable upon
exercise of the Warrants (the "Warrant Shares") have been duly authorized for
such issuance. When issued and delivered by the Company in accordance with the
provisions of this Agreement, the Shares, the Warrants and the Warrant Shares
will be validly issued, fully paid, and nonassessable. The issuance of the
Shares, the Warrants and the Warrant Shares pursuant to this Agreement is not
subject to any preemptive or similar rights.

         3.7 Approvals. Except for registration of the Shares under the
Securities Act of 1933, as amended (the "Securities Act"), and/or the rules and
regulations of the Securities and Exchange Commission (the "Commission")
promulgated thereunder, there, no authorizations, approvals or consents of, and
no filings or registrations with, any governmental authority are necessary for
the execution, delivery or performance by the Company of this Agreement or for
the validity or enforceability thereof.

         3.8 Disclosure. No representation or warranty made by the Company in
this Agreement, and no statement of the Company contained in (a) any document
filed by the Company with the Commission pursuant to the Company's reporting
obligations under the Securities Act and the Securities Exchange Act of 1934, as
amended (the "Exchange Act"), or (b) any document, certificate, or other writing
furnished or to be furnished by the Company pursuant hereto or in connection
herewith, contains or will contain, at the time of delivery, any untrue
statement of a material fact or omits or will omit to state any material fact
necessary in order to make the statements contained therein, in light of the
circumstances under which they are made, not misleading. The Company knows of no
matter (other than matters of a general character not relating solely to the
Company or any subsidiary in any specific manner) which has not been disclosed
to Buyer pursuant to this Agreement which has or, so far as the Company can now
reasonably foresee, will have a Material Adverse Effect. The Company has
complied in all material respects with its obligations under the Securities Act
and the Exchange Act.




                                       3
<PAGE>   5


         3.9 Representations and Warranties on Closing Date. The representations
and warranties made in this Article III will be true and correct in all material
respects on and as of the Closing Date with the same force and effect as if such
representations and warranties had been made on and as of the Closing Date,
except that any such representations and warranties which expressly relate only
to an earlier date shall be true and correct on the Closing Date as of such
earlier date.

                                   ARTICLE IV.

                    REPRESENTATIONS AND WARRANTIES OF BUYERS

         Each Buyer, only with respect to itself, represents and warrants to the
Company that:

         4.1 Organization and Formation. Each corporate Buyer is duly organized,
validly existing, and in good standing under the laws of the jurisdiction of its
incorporation and has all requisite corporate power and corporate authority to
own, lease, and operate its properties and to carry on its business as now being
conducted. Each partnership Buyer is duly formed and is in good standing (as
applicable) under the laws of the jurisdiction of its formation. No actions or
proceedings to dissolve any Buyer are pending or, to the best knowledge of
Buyers, threatened.

         4.2 Authority Relative to This Agreement. Each Buyer has full power and
authority to execute, deliver, and perform this Agreement and the Ancillary
Documents to which it is a party and to consummate the transactions contemplated
hereby and thereby. The execution, delivery, and performance by Buyers of this
Agreement and the Ancillary Documents to which they are parties, and the
consummation by them of the transactions contemplated hereby and thereby, have
been duly authorized by all necessary corporate or partnership action, as
applicable, of Buyers. This Agreement has been duly executed and delivered by
Buyers and constitutes, and each Ancillary Document executed or to be executed
by Buyers has been, or when executed will be, duly executed and delivered by
each Buyer and constitute, or when executed and delivered will constitute, valid
and legally binding obligations of each Buyer, enforceable against each Buyer in
accordance with their respective terms, except that such enforceability may be
limited by (i) applicable bankruptcy, insolvency, reorganization, moratorium,
and similar laws affecting creditors' rights generally and (ii) equitable
principles which may limit the availability of certain equitable remedies (such
as specific performance) in certain instances.

         4.3 Financing. Each Buyer has, and at the Closing will have, such funds
as are necessary for the consummation by it of the transactions contemplated
hereby.

         4.4 Disclosure of Information. Buyers represent that they have had an
opportunity to ask questions of and receive answers from the Company regarding
the Company and its business, assets, results of operation, and financial
condition and the terms and conditions of the issuance of the Shares. Each Buyer
further represents that it has access to all filings duly made by the Company
with the Securities and Exchange Commission.

         4.5 Investment Experience. Each Buyer acknowledges that it can bear the
economic risk of




                                       4
<PAGE>   6


its investment in the Shares, and has such knowledge and experience in financial
and business matters that it is capable of evaluating the merits and risks of an
investment in the Shares.

         4.6 Restricted Securities. Each Buyer understands that the Shares will
not have been registered pursuant to the Securities Act or any applicable state
securities laws, that the Shares will be characterized as "restricted
securities" under federal securities laws, and that under such laws and
applicable regulations the Shares cannot be sold or otherwise disposed of
without registration under the Securities Act or an exemption therefrom. In this
connection, each Buyer represents that it is familiar with Rule 144 promulgated
under the Securities Act, as currently in effect, and understands the resale
limitations imposed thereby and by the Securities Act. Appropriate stop transfer
instructions may be issued to the transfer agent for securities of the Company
(or a notation may be made in the appropriate records of the Company) in
connection with the Shares.

         4.7 Accredited Investor; Investment Intent. Each Buyer is an accredited
investor as defined in Regulation D under the Securities Act. Each Buyer is
acquiring its portion of the Shares for its own account for investment and not
with a view to, or for sale or other disposition in connection with, any
distribution of all or any part thereof, except in compliance with applicable
federal and state securities laws.

         4.8 Representations and Warranties on Closing Date. The representations
and warranties made in this Article IV will be true and correct in all material
respects on and as of the Closing Date with the same force and effect as if such
representations and warranties had been made on and as of the Closing Date,
except that any such representations and warranties which expressly relate only
to an earlier date shall be true and correct on the Closing Date as of such
earlier date.

                                   ARTICLE V.

                              ADDITIONAL AGREEMENTS

         5.1 Reasonable Best Efforts. Each party hereto agrees that it will not
voluntarily undertake any course of action inconsistent with the provisions or
intent of this Agreement and will use its reasonable best efforts to take, or
cause to be taken, all action and to do, or cause to be done, all things
reasonably necessary, proper, or advisable under Applicable Laws to consummate
the transactions contemplated by this Agreement, including, without limitation,
(i) cooperation in determining whether any consents, approvals, orders,
authorizations, waivers, declarations, filings, or registrations of or with any
Governmental Entity or third party are required in connection with the
consummation of the transactions contemplated hereby; (ii) reasonable best
efforts to obtain any such consents, approvals, orders, authorizations, and
waivers and to effect any such declarations, filings, and registrations; (iii)
reasonable best efforts to cause to be lifted or rescinded any injunction or
restraining order or other order adversely affecting the ability of the parties
to consummate the transactions contemplated hereby; (iv) reasonable best efforts
to defend, and cooperation in defending, all lawsuits or other legal proceedings
challenging this Agreement or the consummation of the transactions contemplated
hereby; and (v) the execution of any additional instruments necessary to
consummate the transactions contemplated hereby.




                                       5
<PAGE>   7


         5.2 Public Announcements. Except as may be required by Applicable Law
or this Section 5.2, no Buyer shall issue any press release or otherwise make
any public statement with respect to this Agreement or the transactions
contemplated hereby without the prior written consent of the other parties
(which consent shall not be unreasonably withheld). The Company shall prepare
and issue any press release or public statement required by Applicable Law.

         5.3 Notice of Litigation. Until the Closing, (i) Buyers, upon learning
of the same, shall promptly notify the Company of any Proceeding which is
commenced or threatened against a Buyer and which affects this Agreement or the
transactions contemplated hereby and (ii) the Company, upon learning of the
same, shall promptly notify Buyers of any Proceeding which is commenced or
threatened against the Company and which affects this Agreement or the
transactions contemplated hereby and any Proceeding which is commenced or
threatened against the Company or any Subsidiary.

         5.4 Fees and Expenses. The Company shall be responsible for the payment
of all of the Company's fees and expenses incurred in connection with this
Agreement and the transactions contemplated hereby and, except as expressly
provided otherwise in Section 9.7 hereof, the Buyers shall be responsible for
the payment of all the Buyers' fees and expenses incurred in connection with
this Agreement and the transactions contemplated hereby.

         5.5 Transfer Taxes. All sales, transfer, filing, recordation,
registration, stamp, and similar Taxes and fees arising from or associated with
the sale and transfer of the Shares as contemplated hereunder shall be borne by
the Buyers.

         5.6 Survival of Covenants. Except for any covenant or agreement, which
by its terms expressly terminates as of a specific date or event, the covenants
and agreements of the parties hereto contained in this Agreement shall survive
the Closing without contractual limitation.

                                   ARTICLE VI.

                    CONDITIONS TO OBLIGATIONS OF THE COMPANY

         The obligations of the Company to consummate the transactions
contemplated by this Agreement shall be subject to the fulfillment on or prior
to the Closing Date of each of the following conditions:

         6.1 Representations and Warranties True. All the representations and
warranties of Buyers contained in this Agreement, and in any agreement,
instrument, or document delivered pursuant hereto or in connection herewith on
or prior to the Closing Date, shall be true and correct in all material respects
as of the date made and (having been deemed to have been made again on and as of
the Closing Date in the same language) shall be true and correct in all material
respects on and as of the Closing Date, except as affected by transactions
permitted by this Agreement and except to the extent that any such
representation or warranty is made as of a specified date, in which case such
representation or warranty shall have been true and correct in all material
respects as of such specified date.




                                       6
<PAGE>   8


         6.2 Covenants and Agreements Performed. Buyers shall have performed and
complied with in all material respects all covenants and agreements required by
this Agreement to be performed or complied with by them on or prior to the
Closing Date.

         6.3 Legal Proceedings. No Proceeding shall, on the Closing Date, be
pending or threatened seeking to restrain, prohibit, or obtain damages or other
relief in connection with this Agreement or the consummation of the transactions
contemplated hereby.

         6.4 Consents.

         (a) There shall have been obtained any and all material permits,
consents, and approvals of Governmental Entities that reasonably may be deemed
necessary so that the consummation of the transactions contemplated hereby will
be in compliance with Applicable Law, the failure to comply with which would
have a Material Adverse Effect on the Company.

         (b) All consents and approvals of private persons, (i) the granting of
which is necessary for the consummation of the transactions contemplated hereby
and (ii) the non-receipt of which would have a Material Adverse Effect on the
Company, shall have been obtained.

                                   ARTICLE VII

                       CONDITIONS TO OBLIGATIONS OF BUYERS

         The obligations of Buyers to consummate the transactions contemplated
by this Agreement shall be subject to the fulfillment on or prior to the Closing
Date of each of the following conditions:

         7.1 Representations and Warranties True. All the representations and
warranties of the Company contained in this Agreement, and in any agreement,
instrument, or document delivered pursuant hereto or in connection herewith on
or prior to the Closing Date, shall be true and correct in all material respects
(except for such representations and warranties that are limited by materiality,
in which case they shall be true and correct in all respects) as of the date
made and (having been deemed to have been made again on and as of the Closing
Date in the same language) shall be true and correct in all material respects on
and as of the Closing Date, except as affected by transactions permitted by this
Agreement and except to the extent that any such representation or warranty is
made as of a specified date, in which case such representation or warranty shall
have been true and correct in all material respects as of such specified date.

         7.2 Covenants and Agreements Performed. The Company shall have
performed and complied with in all material respects all covenants and
agreements required by this Agreement to be performed or complied with by it on
or prior to the Closing Date.

         7.3 Legal Proceedings. No Proceeding shall, on the Closing Date, be
pending or threatened seeking to restrain, prohibit, or obtain damages or other
relief in connection with this Agreement or the consummation of the transactions
contemplated hereby.




                                       7
<PAGE>   9


         7.4 Ancillary Documents. Buyers shall have received the certificates,
instruments, and documents listed below (the "Ancillary Documents"):

                  (a) In accordance with the denominations designated in
         Schedule I, stock certificates in definitive form and duly executed on
         behalf of the Company, representing the portion of the Shares
         registered in the name of each Buyer.

                  (b) In accordance with the denominations designed in Schedule
         I, Warrant Certificates in substantially the form attached hereto as
         Schedule II.

                  (c) A copy of the resolutions of the Board of Directors of the
         Company authorizing the execution, delivery, and performance by the
         Company of this Agreement, certified by the secretary or an assistant
         secretary of the Company.

                  (d) Such other certificates, instruments, and documents as may
         be reasonably requested by Buyers to carry out the intent and purposes
         of this Agreement.

         7.5 Special Conditions Precedent. As a precondition to the obligations
of Buyers, (a) the Company shall have entered, or shall have caused Brigham Oil
& Gas, L.P. ("BOG") to enter, into an Amended and Restated Credit Agreement with
its senior lenders affording the Company and/or BOG additional availability up
to, but not exceeding total availability of $15,000,000, and (b) the total
Purchase Price for all shares issued to the Buyers hereunder equals or exceeds
$4,500,000.

                                  ARTICLE VIII.

                       TERMINATION, AMENDMENT, AND WAIVER

         8.1 Termination. This Agreement may be terminated and the transactions
contemplated hereby abandoned at any time prior to the Closing in the following
manner:

               (a)  by mutual written consent of the Company and Buyers; or

               (b)  by either the Company or Buyers, if:

                    (i) the Closing shall not have occurred on or before
                    February 23, 2000, unless such failure to close shall be due
                    to a breach of this Agreement by the party seeking to
                    terminate this Agreement pursuant to this clause (i); or

                    (ii) there shall be any statute, rule, or regulation that
                    makes consummation of the transactions contemplated hereby
                    illegal or otherwise prohibited or a Governmental Entity
                    shall have issued an order, decree, or ruling or taken any
                    other action permanently restraining, enjoining, or
                    otherwise prohibiting the consummation of the transactions
                    contemplated hereby, and such order, decree, ruling, or
                    other action shall have become final and nonappealable; or

               (c)  by the Company, if (i) any of the representations and
                    warranties of Buyers



                                       8
<PAGE>   10


                    contained in this Agreement shall not be true and correct in
                    any respect which is material to Buyers or the ability of
                    Buyers to consummate the transactions contemplated hereby,
                    or (ii) Buyers shall have failed to fulfill in any material
                    respect any of their obligations under this Agreement, and,
                    in the case of each of clauses (i) and (ii), such
                    misrepresentation, breach of warranty, or failure (provided
                    it can be cured) has not been cured within ten days after
                    written notice thereof from the Company to Buyers; or

               (d)  by Buyers, if (i) any of the representations and warranties
                    of the Company contained in this Agreement shall not be true
                    and correct in any respect which is material to the Company
                    and the Subsidiaries considered as a whole or the ability of
                    the Company to consummate the transactions contemplated
                    hereby, or (ii) the Company shall have failed to fulfill in
                    any material respect any of its obligations under this
                    Agreement, and, in the case of each of clauses (i) and (ii),
                    such misrepresentation, breach of warranty, or failure
                    (provided it can be cured) has not been cured within ten
                    days after written notice thereof from Buyers to the
                    Company.

         8.2 Effect of Termination. In the event of the termination of this
Agreement pursuant to Section 8.1 by the Company, on the one hand, or Buyer, on
the other, written notice thereof shall forthwith be given to the other party
specifying the provision hereof pursuant to which such termination is made, and
this Agreement shall become void and have no effect, except that the agreements
contained in this Section and in Sections 5.2, 5.4, and 11.1 shall survive the
termination hereof. Nothing contained in this Section shall relieve any party
from liability for damages actually incurred as a result of any breach of this
Agreement.

         8.3 Amendment. This Agreement may not be amended except by an
instrument in writing signed by or on behalf of all the parties hereto.

         8.4 Waiver. The Company, on the one hand, or Buyers, on the other, may:
(i) waive any inaccuracies in the representations and warranties of the other
contained herein or in any document, certificate, or writing delivered pursuant
hereto, or (ii) waive compliance by the other with any of the other's agreements
or fulfillment of any conditions to its own obligations contained herein. Any
agreement on the part of a party hereto to any such waiver shall be valid only
if set forth in an instrument in writing signed by or on behalf of such party.
No failure or delay by a party hereto in exercising any right, power, or
privilege hereunder shall operate as a waiver thereof nor shall any single or
partial exercise thereof preclude any other or further exercise thereof or the
exercise of any other right, power, or privilege.

         8.5 Remedies Not Exclusive. The rights and remedies herein provided
shall be cumulative and not exclusive of any rights or remedies provided by law.
The rights and remedies of any party based upon, arising out of, or otherwise in
respect of any inaccuracy in or breach of any representation, warranty,
covenant, or agreement contained in this Agreement shall in no way be limited by
the fact that the act, omission, occurrence, or other state of facts upon which
any claim of any such inaccuracy or breach is based may also be the subject
matter of any other representation, warranty, covenant, or agreement contained
in this Agreement (or in any other agreement between the parties) as to which
there is no inaccuracy or breach.



                                       9
<PAGE>   11


                                   ARTICLE IX

              RESTRICTIONS ON TRANSFERABILITY; REGISTRATION RIGHTS

         9.1 Transfers.

         (a) General. The Shares and the Warrants shall not be transferred
before satisfaction of the conditions specified in this Article IX, which
conditions are intended to reflect the intent of the Company and Buyers and
further to ensure compliance with the provisions of the Securities Act and
applicable state securities laws. Each Buyer, by entering into this Agreement
and accepting the Shares and the Warrants, agrees to be bound by the provisions
of this Article IX.

         (b) Restrictive Legend. Except as otherwise provided in this Article
IX, each certificate representing Warrants, Shares or Warrant Shares shall be
stamped or otherwise imprinted with a legend in substantially the following
form:

         "THE SECURITIES REPRESENTED BY THIS CERTIFICATE HAVE NOT BEEN
         REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED, OR ANY
         APPLICABLE STATE SECURITIES LAWS, AND MAY NOT BE SOLD OR TRANSFERRED IN
         THE ABSENCE OF SUCH REGISTRATION OR AN EXEMPTION THEREFROM. SUCH
         SECURITIES ARE SUBJECT TO THE RESTRICTIONS AND PRIVILEGES SPECIFIED IN
         A SECURITIES PURCHASE AND REGISTRATION RIGHTS AGREEMENT, DATED AS OF
         FEBRUARY 22, 2000, BETWEEN BRIGHAM EXPLORATION COMPANY AND THE INITIAL
         HOLDERS OF SECURITIES NAMED THEREIN, A COPY OF WHICH IS ON FILE WITH
         THE SECRETARY OF BRIGHAM EXPLORATION COMPANY AND WILL BE FURNISHED
         WITHOUT CHARGE TO THE HOLDER HEREOF UPON WRITTEN REQUEST, AND THE
         HOLDER OF THIS CERTIFICATE AGREES TO BE BOUND THEREBY."

         9.2 Registration. The Company shall utilize reasonable best efforts to,
within 90 days after the Closing Date, register on a Form S-3 (or Form S-1 or
successor form to either) Registration Statement all of the Registrable
Securities that are held by any Buyer(s) that, on or before the Closing Date,
have elected to have their Registrable Securities so registered. The Company
shall use its reasonable best efforts to keep such Registration Statement
effective until the twenty-four (24) month anniversary of such Effective Date.

         9.3 Incidental Registration.

         If the Company at any time proposes to file on its behalf and/or on
behalf of any of its security holders (the "Demanding Security Holders") a
Registration Statement under the Securities Act on any form (other than a
Registration Statement (i) filed pursuant to demand under the Company's
Registration Rights Agreement with Joint Energy Development Investments II
Limited Partnership, a Delaware limited partnership, and Enron Capital & Trade
Resources Corp., a Delaware corporation, dated August 20, 1998, as amended, or
(ii) on Form S-8 or any similar or successor form or any other registration
statement relating to an offering of securities solely to the Company's



                                       10
<PAGE>   12


existing security holders or employees) to register the offer and sale of its
common stock for cash, it will give written notice to all Buyers at least five
(5) days before the anticipated date of initial filing with the Commission of
such Registration Statement, which notice shall set forth the Company's
intention to effect such a registration, the class or series and number of
equity securities proposed to be registered and the intended method of
disposition of the securities proposed to be registered by the Issuer. The
notice shall offer to include in such filing all of each Buyer's Registrable
Securities.

         Each Buyer desiring to have Registrable Securities registered under
this Section 9.3 shall advise the Company in writing within fifteen (15) days
after the date of receipt of such offer from the Company, setting forth the
amount of such Registrable Securities for which registration is requested. The
Company shall thereupon include in such filing the number of Registrable
Securities for which registration is so requested, subject to the next sentence,
and shall use its best efforts to effect registration under the Securities Act
of such securities. If the managing underwriter of a proposed public offering
shall advise the Company in writing that, in its opinion, the distribution of
the Registrable Securities requested to be included in the registration
concurrently with the securities being registered by the Company or the
Demanding Security Holder, as the case may be, would materially and adversely
affect the distribution of such securities by the Company or such Demanding
Security Holders, as the case may be, then all selling security holders (but not
the Company or such Demanding Security Holders, as the case may be) shall reduce
the amount of securities each intended to distribute through such offering on a
pro rata basis to the greatest aggregate amount which, in the opinion of such
managing underwriter, would not materially and adversely affect the distribution
of such securities.

         Nothing in this Section 9.3 shall preclude the Company from
discontinuing the registration of its securities being effected on its behalf
under this Section 9.3 at any time prior to the effective date of the
registration relating thereto. Notwithstanding any provision herein, the rights
of the Buyers under this Section 9.3 are subject to the express limitations
contained in registration rights agreements (and registration rights provisions
in agreements) in effect on the date hereof between the Company and other
parties.

         9.4 Requests for Registration. Each Buyer agrees that it will not sell,
transfer or otherwise dispose of any Registrable Securities in whole or part,
except pursuant to an effective Registration Statement under the Securities Act
or an exemption from registration thereunder. Each certificate, if any,
evidencing such Registrable Securities issued upon such transfer shall bear the
restrictive legend set forth in Section 9.1, and each Warrant Certificate issued
upon such transfer shall bear the restrictive legend set forth in Section 9.1 of
this Agreement, unless in the opinion of the transferee's or Buyer's reputable
counsel delivered to the Company in connection with such transfer, such legend
is not required in order to ensure compliance with the Securities Act.

         9.5 Registration Procedures. In its efforts to effect registration of
the Registrable Securities pursuant to Section 9.2 or 9.3, above, the Company
will, as expeditiously as possible:

         (a) furnish to the selling security holders such number of copies or a
summary prospectus or other prospectus, including a preliminary prospectus, in
conformity with the requirements of the Securities Act, and such other
documents, as such selling security holders may reasonably request;




                                       11
<PAGE>   13


         (b) use its best efforts to register or qualify the securities covered
by such Registration Statement under such other securities or blue sky laws of
such jurisdictions within the United States as each holder of such securities
shall request (provided, however, the Company shall not be obligated to qualify
as a foreign corporation to do business under the laws of any jurisdiction in
which it is not then qualified or to file any general consent to service or
process), and do such other reasonable acts and things as may be requited of it
to enable such holder to consummate the disposition in such jurisdiction of the
securities covered by such Registration Statement;

         (c) enter into customary agreements (including an underwriting
agreement in customary form) and take such other actions as are reasonably
required in order to expedite or facilitate the disposition of such Shares; and

         (d) otherwise use its best efforts to comply with all applicable rules
and regulations of the Commission, and make available to its security holders,
as soon as reasonably practicable, but not later than 18 months after the
effective date of the Registration Statement, an earnings statement covering the
period of at least 12 months beginning with the first full month after the
effective date of such Registration Statement, which earnings statements shall
satisfy the provisions of Section 11(a) of the Securities Act.

         It shall be a condition precedent to the obligation of the company to
take any action pursuant to this Article IX in respect of the Registrable
Securities which are to be registered at the request of any Buyer that such
Buyer shall refurnish to the Company such information regarding the Registrable
Securities held by such Buyer and the intended method of disposition thereof as
the Company shall reasonably request and as shall be required in connection with
the action taken by the Company.

         9.6 Rights of Others.

         (a) The Company and any party to any existing agreements with the
Company who are entitled to piggy-back registration rights ("Other Holders")
with respect to a Registration Statement filed pursuant to Section 9.2 or 9.3
may include securities of the Company in such Registration Statement.

         (b) Notwithstanding any provision herein, the rights of the Buyers
under this Article IX are subject to the express limitations contained in
registration rights agreements (and registration rights provisions in
agreements) in effect on the date hereof between the Company and other parties.

         9.7 Expenses. All registration and filing fees (including those
incident to filing with the NASD), incurred in complying with this Article IX
(all of such fees shall be collectively referred to herein as "Registration
Expenses"), shall be paid by the Company; provided, however, the Company shall
not be responsible for any attorneys' fees or discount or commission or cost
reimbursement to any underwriter in respect of the securities sold by such
Buyer, or any other expenses incurred by Buyers in relation to this Agreement,
except as set forth in this Section 9.7.




                                       12
<PAGE>   14


         9.8 Liquidated Damages. The parties hereto agree that, without
limitation of any other remedies that may be available to Buyers, upon the
failure of the Company to register the shares of Registrable Securities that are
held by Buyers that have elected on or before the Closing Date to have their
Registrable Securities registered, within 180 days of the Closing Date, the
Buyers that have so elected to have their Registrable Securities registered
shall each be entitled to liquidated damages from the Company in an amount equal
to 1% per month of the Purchase Price paid by such Buyer, with the total
liquidated damages payable by the Company to all Buyers together not to exceed
$100,000. The parties agree that the liquidated damages set forth herein are
reasonable and not a penalty because of the difficulty of ascertaining the
actual damages that would be sustained by the Buyers in the event of such a
material breach of this Agreement by the Company.

                                   ARTICLE X.

                                  MISCELLANEOUS

         10.1 Notices. All notices, requests, demands, and other communications
required or permitted to be given or made hereunder by any party hereto shall be
in writing and shall be deemed to have been duly given or made if (i) delivered
personally, (ii) transmitted by first class registered or certified mail,
postage prepaid, return receipt requested, (iii) sent by prepaid overnight
courier service, or (iv) sent by telecopy or facsimile transmission, answer back
requested, to the parties at the following addresses (or at such other addresses
as shall be specified by the parties by like notice):

              If to:  GAP Coinvestment Partners II, L.P.
                      c/o General Atlantic Service Corporation
                      3 Pickwick Plaza
                      Greenwich, CT  06830
                      Attention: Mr. Steve Reynolds
                      Telefax:   (203) 622-8818

              with a copy to:
                      Paul, Weiss, Rifkind, Wharton & Garrison
                      1285 Avenue of the Americas
                      New York, NY  10019-6064
                      Attention: Douglas A. Cifu, Esq.
                      Telefax:   (212) 757-3990

              If to:  Special Situations Private Equity Fund
                      153 East 53rd Street
                      New York, NY  10022
                      Attention: Mr. Steven R. Becker
                      Telefax:   (212) 207-6515

              If to:  Aspect Resources, L.L.C.
                      511 16th Street, Suite 300
                      Denver, CO  80202
                      Attention: Mr. Alex Cranberg
                      Telefax:   (303) 573-7340




                                       13
<PAGE>   15


              If to the Company:

                      Brigham Exploration Company
                      6300 Bridge Point Parkway
                      Building 2, Suite 500
                      Austin, TX  78730
                      Attention: Chief Financial Officer
                      Telefax:   (512) 427-3400

Such notices, requests, demands, and other communications shall be effective (i)
if delivered personally or sent by courier service, upon actual receipt by the
intended recipient, (ii) if mailed, upon the earlier of five days after deposit
in the mail or the date of delivery as shown by the return receipt therefor, or
(iii) if sent by telecopy or facsimile transmission, when the answer back is
received.

         10.2 Entire Agreement. This Agreement, together with the Schedules,
Exhibits, Annexes, and other writings referred to herein or delivered pursuant
hereto, constitute the entire agreement between the parties hereto with respect
to the subject matter hereof and supersede all prior agreements and
understandings, both written and oral, between the parties with respect to the
subject matter hereof.

         10.3 Binding Effect; Assignment; No Third Party Benefit. This Agreement
shall be binding upon and inure to the benefit of the parties hereto and their
respective heirs, legal representatives, successors, and permitted assigns.
Except as otherwise expressly provided in this Agreement, neither this Agreement
nor any of the rights, interests, or obligations hereunder shall be assigned by
any of the parties hereto without the prior written consent of the other
parties. Nothing in this Agreement, express or implied, is intended to or shall
confer upon any person other than the parties hereto, and their respective
heirs, legal representatives, successors, and permitted assigns, any rights,
benefits, or remedies of any nature whatsoever under or by reason of this
Agreement.

         10.4 Severability. If any provision of this Agreement is held to be
unenforceable, this Agreement shall be considered divisible and such provision
shall be deemed inoperative to the extent it is deemed unenforceable, and in all
other respects this Agreement shall remain in full force and effect; provided,
however, that if any such provision may be made enforceable by limitation
thereof, then such provision shall be deemed to be so limited and shall be
enforceable to the maximum extent permitted by Applicable Law.

         10.5 GOVERNING LAW. THIS AGREEMENT SHALL BE GOVERNED BY AND CONSTRUED
AND ENFORCED IN ACCORDANCE WITH THE INTERNAL LAWS OF THE STATE OF TEXAS, WITHOUT
REGARD TO THE PRINCIPLES OF CONFLICTS OF LAWS THEREOF.

         10.6 Counterparts. This Agreement may be executed by the parties hereto
in any number of counterparts, each of which shall be deemed an original, but
all of which shall constitute one and the same agreement. Each counterpart may
consist of a number of copies hereof each signed by less than all, but together
signed by all, the parties hereto.




                                       14
<PAGE>   16


         10.7 Consent to Jurisdiction

         (a) The parties hereto hereby irrevocably submit to the jurisdiction of
the courts of the State of Texas and the federal courts of the United States of
America located in Dallas, Texas, and appropriate appellate courts therefrom,
over any dispute arising out of or relating to this Agreement or any of the
transactions contemplated hereby, and each party hereby irrevocably agrees that
all claims in respect of such dispute or proceeding may be heard and determined
in such courts.

         (b) Each of the parties hereto hereby consents to process being served
by any party to this Agreement in any suit, action, or proceeding of the nature
specified in subsection (a) above by the mailing of a copy thereof in the manner
specified by the provisions of Section 10.1.

         10.8 Liability of Buyers. The liability of each Buyer with respect to
the agreements, covenants, representations and warranties of Buyers contained in
this Agreement or in any certificate, instrument, or document delivered pursuant
hereto shall be to the extent such agreements, covenants, representations or
warranties applies to himself, herself, or itself and not with respect to any
other Buyer.

         10.9 Consent to Certain Stock Issuances. By its execution hereof, each
Buyer hereby consents to the issuance of Common Stock upon exercise of warrants
and options to purchase Common Stock outstanding as of the date hereof.

         10.10 Loss or Mutilation. Upon receipt by the Company from any Buyer of
evidence reasonably satisfactory to it of the ownership of and the loss, theft,
destruction or mutilation of a certificate representing Shares and indemnity
reasonably satisfactory to it (it being understood that the written agreement of
the Buyer or an Affiliate thereof shall be sufficient indemnity) and in case of
mutilation upon surrender and cancellation hereof or thereof, the Company will
execute and deliver in lieu hereof or thereof a new stock certificate, of like
tenor to such Buyer, provided, in the case of mutilation, no indemnity shall be
required if the certificate representing Shares in identifiable form is
surrendered to the Company for cancellation.

                                   ARTICLE XI.

                                   DEFINITIONS

         11.1 Certain Defined Terms. As used in this Agreement, each of the
following terms has the meaning given it below:

                  "Affiliate" means, with respect to any person, any other
         person that, directly or indirectly, through one or more
         intermediaries, controls, is controlled by, or is under common control
         with, such person. For the purposes of this definition, "control" when
         used with respect to any person means the possession, directly or
         indirectly, of the power to direct or cause the direction of the
         management and policies of such person, whether through the ownership
         of voting securities, by contract, or otherwise; and the terms
         "controlling" and "controlled" have meanings correlative to the
         foregoing.




                                       15
<PAGE>   17


                  "Applicable Law" means any statute, law, rule, or regulation
         or any judgment, order, writ, injunction, or decree of any Governmental
         Entity to which a specified person or property is subject.

                  "Code" means the Internal Revenue Code of 1986, as amended.

                  "Exchange Act" means the Securities Exchange Act of 1934, as
         amended.

                  "Governmental Entity" means any court or tribunal in any
         jurisdiction (domestic or foreign) or any federal, state, municipal, or
         other governmental body, agency, authority, department, commission,
         board, bureau, or instrumentality (domestic or foreign), as well as the
         New York Stock Exchange, The NASDAQ Stock Market, and any exchange upon
         which the Common Stock is listed from time to time.

                  "Material Adverse Effect" means any change, development, or
         effect (individually or in the aggregate) which is, or is reasonably
         likely to be, materially adverse (i) to the business, assets, results
         of operations or condition (financial or otherwise) of a party, or (ii)
         to the ability of a party to perform on a timely basis any material
         obligation under this Agreement or any agreement, instrument, or
         document entered into or delivered in connection herewith.




                                       16
<PAGE>   18


                  "Person" means any individual, corporation, partnership, joint
         venture, association, joint-stock company, trust, enterprise,
         unincorporated organization, or Governmental Entity.

                  "Proceedings" means all proceedings, actions, claims, suits,
         investigations, and inquiries by or before any arbitrator or
         Governmental Entity.

                  "Registrable Securities" means the Shares, the Warrant Shares
         and any shares issued upon exercise of the Warrants.

                  "Securities Act" means the Securities Act of 1933, as amended.

         "Taxes" means any income taxes or similar assessments or any sales,
excise, occupation, use, ad valorem, property, production, severance,
transportation, employment, payroll, franchise, or other tax imposed by any
United States federal, state, or local (or any foreign or provincial) taxing
authority, including any interest, penalties, or additions attributable thereto.

     IN WITNESS WHEREOF, the parties have executed this Agreement, or caused
this Agreement to be executed by their duly authorized representatives, all as
of the day and year first above written.

                                              THE COMPANY:

                                              BRIGHAM EXPLORATION COMPANY


                                              By:
                                                 -------------------------------
                                                 Name:   Ben M. Brigham
                                                       -------------------------
                                                 Title:  President and CEO
                                                       -------------------------

                                              BUYERS:


                                              GAP COINVESTMENT PARTNERS II, L.P.



                                              By:
                                                 -------------------------------
                                                 Name:
                                                       -------------------------
                                                 Title:
                                                       -------------------------




                                       17
<PAGE>   19


                                              SPECIAL SITUATIONS PRIVATE
                                              EQUITY FUND, L.P.



                                              By:
                                                 -------------------------------
                                                 Name:
                                                       -------------------------
                                                 Title:
                                                       -------------------------



                                              ASPECT RESOURCES, L.L.C.
                                              By its Manager, Aspect Management
                                              Corporation


                                              By:
                                                 -------------------------------
                                                 Name:
                                                       -------------------------
                                                 Title:
                                                       -------------------------




                                       18
<PAGE>   20


                                   SCHEDULE I




<TABLE>
<CAPTION>

                                                                                Shares of              Purchase
               Buyers                                       Warrants           Common Stock             Price
              --------                                    -------------        -------------        -------------
<S>                                                       <C>                  <C>                  <C>
GAP Coinvestment Partners II, L.P.                              325,203              975,610        $2,000,000.00
                                                          -------------        -------------        -------------
Special Situations Private Equity Fund, L.P.                    243,902              731,707        $1,500,000.00
                                                          -------------        -------------        -------------
Aspect Resources, L.L.C                                         162,602              487,805        $1,000,000.00
                                                          -------------        -------------        -------------

                        Total                                   731,707            2,195,122        $4,500,000.00
                                                          =============        =============        =============
</TABLE>







<PAGE>   21



                                   SCHEDULE II

                               WARRANT CERTIFICATE


Number of Warrants: ____________                                Warrant No. ____

     This Warrant certificate ("Warrant Certificate") certifies that, for value
received,

- ----------------------------------------------------

is the registered holder of the number of warrants (the "Warrants") set forth
above. Each Warrant entitles the holder thereof, at any time to time during the
Exercise Period, to purchase from the Company one fully paid and nonassessable
share of Common Stock at the Exercise Price, subject to adjustment as provided
herein. Initially capitalized terms used but not defined herein shall have the
meanings ascribed to them in the Securities Purchase Agreement.

                  "Common Stock" means the common stock, $.01 per value per
         share, of the Company and such other class of securities as shall then
         represent the common equity of the Company.

                  "Company" means Brigham Exploration Company, a Delaware
         corporation.

                  "Exercise Period" means the period of time between the Closing
         Date, as defined in the Securities Purchase Agreement and 5:00 p.m.
         (New York City time) on the Expiration Date.

                  "Exercise Price," subject in all circumstances to adjustment
         in accordance with Section 2, means 125% of the Issuance Price.

                  "Expiration Date" means February 22, 2003.

                  "IPO" shall mean the initial public offering of securities of
         the Company consummated on May 24, 1997, pursuant to a registration
         statement filed under the Securities Act of 1933, as amended, and the
         rules and regulations promulgated thereunder.

                  "Issuance Date" means February 22, 2000.

                  "Person" means any individual, corporation, company,
         partnership, joint venture, trust, limited liability company,
         unincorporated organization or government or any agency,
         instrumentality or political subdivision thereof, or any other form of
         equity.

                  "Price" means the average of the "high" and "low" prices as
         reported in The Wall Street Journal's listing for such day (corrected
         for obvious typographical errors) or if such shares are not reported in
         such listing, the average of the reported "high" and "low" sales





                                    Sch II-1



<PAGE>   22



         prices on the largest national securities exchange (based on the
         aggregate dollar value of securities listed) on which such shares are
         listed or traded, or if such shares are not listed or traded on any
         national securities exchange, then the average of the reported "high"
         and "low" sales prices for such shares in the over-the-counter market,
         as reported on the National Association of Securities Dealers Automated
         Quotations System, or, if such prices shall not be reported thereon,
         the average of the closing bid and asked prices reported by the
         National Quotations Bureau Incorporated, or, in all other cases, the
         Estimated Private Market Equity Value divided by the number of
         outstanding shares (on a fully diluted basis using the treasury stock
         method). The "Average" Price per share for any period shall be
         determined by dividing the sum of the Prices determined for the
         individual trading days in such period by the number of trading days in
         such period.

                  "Publicly Traded" means, with respect to the Common Stock,
         that such securities are listed for trading on the New York Exchange,
         Inc., the American Stock Exchange, Inc. or the NASDAQ National Market.
         The Common Stock shall also be deemed to be Publicly Traded if the
         Common Stock is included in the NASDAQ SmallCap Market.

                  "Registrable Securities" means the Shares, the Warrant Shares
         and any shares issued upon exercise of the Warrants.

                  "Securities Purchase Agreement" means the Securities Purchase
         and Registration Agreement, dated as of February 22, 2000, among the
         Company and the Buyers.

         1. EXERCISE OF WARRANTS. (a) The Warrants may be exercised in whole or
in part, at any time or from time to time, during the Exercise Period, by (i)
presentation and surrender to the Company at its address set forth in Section 9
of this Warrant Certificate with the Election To Exercise, attached hereto as
Exhibit A, duly completed and executed, and (ii) payment of the Exercise Price,
by bank draft or cashier's check, for the number of Warrants being exercised. If
the holder of this Warrant Certificate at any time exercises less than all the
Warrants, the Company shall issue to such a holder a warrant certificate
identical in form to this Warrant Certificate, but evidencing a number of
Warrants equal to the number of Warrants originally represented and surrender of
this Warrant Certificate to the Company at its address set forth in Section 9
and at the request of the holder, the Company will, without expense, at the
option of the holder, issue to the holder in substitution for this Warrant
Certificate one or more warrant certificates in identical form and for an
aggregate number of Warrants equal to the number of Warrants evidenced by this
Warrant Certificate.

                (b) To the extent that the Warrants have not been exercised at
or prior to the Expiration Date, such Warrants expire and the rights of the
holder shall become void and of no effect.

                (c) In lieu of exercise in accordance with Section 1(a) above,
the Warrants represented hereby may be exercised, in whole or in part, by
presentation and surrender at the office of the Company specified herein of this
Warrant Certificate with the "Alternative Election to Exercise", attached hereto
as Exhibit A-1, duly completed and executed. Upon such exercise, the





                                    Sch II-2

<PAGE>   23


holder shall be entitled to receive from the Company, for each share of Common
Stock issuable upon exercise of each Warrant being exercised, shares of Common
Stock with a value equal to the amount by which either the Price or, in the
event that the Common Stock is not Publicly Traded, the Fair Market Value (as
defined below) of one share of Common Stock on the date of exercise exceeds the
Exercise Price (the "Appreciation Amount"). If the Common Stock is Publicly
Traded on the date of exercise of Warrants pursuant to this Section 1(c), the
Company shall deliver (or cause its transfer agent to deliver) certificates
representing shares of Common Stock issuable upon such exercise within ten
business days following the date of exercise. For purposes of this subsection,
in the event that the Common Stock is not Publicly Traded, the "Fair Market
Value" of the share of Common Stock shall be established by the Board of
Directors of the Company in its reasonable discretion. If the Common Stock is
not Publicly Traded on the date of exercise of Warrants pursuant to this Section
1(c), such election may be withdrawn by the holder at any time prior to the
third business day following the date on which the holder receives notice of the
final determination of the Fair Market Value of the share of Common Stock.
Unless the holder timely withdraws its exercise, the Company shall deliver (or
cause its transfer agent to deliver) certificates representing Common Stock so
issuable within 10 business days following the date of determination of the Fair
Market Value. In lieu of any fractional shares otherwise issuable upon exercise
pursuant hereto, the Company shall pay to the holder cash in an amount equal to
the Price, or in the event the Company is not Publicly Traded, the Fair Market
Value of such fractional share.

         2. ANTIDILUTION ADJUSTMENTS. The shares of Common Stock purchasable on
exercise of the Warrants are shares of Common Stock as constituted as of the
Issuance Date. The number and kind of securities purchasable upon the exercise
of the Warrants, and the Exercise Price, shall be subject to adjustment from
time to time upon the happening of certain events, as follows:

            Mergers, Consolidations and Reclassifications. In case of any
reclassification or change of outstanding securities issuable upon exercise of
the Warrants at any time after the Issuance Date (other than a change in par
value, or from par value to no par value or as a result of a subdivision or
combination to which subsection 2(b) applies), or in case of any consolidation
or merger of the Company with or into any entity or other person (other than a
merger with another entity or other person in which the Company is the surviving
corporation and which does not result in any reclassification or change in the
securities issuable upon exercise of this Warrant Certificate), the holder of
the Warrants shall have, and the Company, or such successor corporation or other
entity, shall covenant in the constituent documents effecting any of the
foregoing transactions that such holder does have the right to obtain, upon the
exercise of the Warrants, in lieu of each share of Common Stock, other
securities, money or other property theretofore issuable upon exercise of a
Warrant, the kind and amount of shares of stock, other securities, money or
other property receivable upon such reclassification, change, consolidation or
merger by a holder of the shares of Common Stock, other securities, money or
other property issuable upon exercise of a Warrant if the Warrants had been
exercised immediately prior to such reclassification, change, consolidation or
merger. The constituent documents effecting such reclassification, change,
consolidation or merger shall provide for adjustments which shall be as nearly
equivalent as may be practicable to the adjustments provided in this subsection
2(a). The provisions of this subsection 2(a) shall similarly apply to successive
reclassifications, changes, consolidations or mergers.



                                    Sch II-3


<PAGE>   24


            Subdivisions and Combinations. If the Company, at any time after the
Issuance Date, shall subdivide its shares of Common Stock into a greater number
of shares, the Exercise price in effect immediately prior to such subdivision
shall be proportionately reduced, and the number of shares of Common Stock
purchasable upon exercise of the Warrants shall be proportionately increased, as
at the effective date of such subdivision, or if the Company shall take a record
of holders of its Common Stock for such purpose, as at such record date,
whichever is earlier. If the Company, at any time after Issuance Date, shall
combine its shares of Common Stock into a smaller number of shares, the Exercise
Price in effect immediately prior to such combination shall be proportionately
increased, and the number of shares of Common Stock purchasable upon exercise of
the Warrants shall be proportionately reduced, as at the effective date of such
combination, or if the Company shall take a record of holders of its Common
Stock for purposes of such combination, as at such record date, whichever is
earlier.

            Dividends and Distributions. If the Company at any time after the
Issuance Date shall declare a dividend on its Common Stock payable in stock or
other securities of the Company to the holders of its Common Stock, the holder
of this Warrant Certificate shall, without additional cost, be entitled to
receive upon any exercise of a Warrant, in addition to the Common Stock to which
such holder would otherwise be entitled upon exercise, the number of shares of
stock or other securities which such holder would have been entitled to receive
if he had been a holder immediately prior to the record date for such dividend
(or, if no record date shall have been established, the payment date for such
dividend) of the number of shares of Common Stock purchasable on exercise of
such Warrant immediately prior to such record date or payment date, as the case
may be.

            Certain Issuances of Securities. If the Company at any time after
the Issuance Date shall issue any additional shares of Common Stock (otherwise
than as provided in paragraphs (a) through (c) of this Section 2) at a price per
share less than the average Price per share of Common Stock for the 20 trading
days immediately preceding the date of the authorization of such issuance (the
"Market Price") by the Board of Directors, then the Exercise Price upon each
such issuance shall be adjusted to that price determined by multiplying the
Exercise Price by a fraction:

     the numerator of which shall be the sum of (1) the number of shares of
Common Stock outstanding immediately prior to the issuance of such additional
shares of Common Stock multiplied by the Market Price, and (2) the
consideration, if any, received by the Company upon the issuance of such
additional shares of Common Stock, and

     the denominator of which shall be the Market Price multiplied by the total
number of shares of Common Stock outstanding immediately after the issuance of
such additional shares of Common Stock.

     No adjustments of the Exercise Price shall be made under this paragraph (d)
upon the issuance of any additional shares of Common Stock that (w) are issued
pursuant to thrift plans, stock purchase plans, stock bonus plans, stock option
plans, employee stock ownership plans, incentive or profit sharing arrangements
for the benefit of employees ("Employee Benefit Plans") that are approved by the
Board of Directors of the Company or its compensation committee and that
otherwise would cause an adjustment under this paragraph (d); provided that the
aggregate number





                                    Sch II-4

<PAGE>   25


of shares of Common Stock so issued (including the shares issued pursuant to any
options, rights or warrants or convertible or exchangeable securities issued
under such Employee Benefit Plans containing the right to purchase shares of
Common stock) pursuant to Employee Benefit Plans after the closing date of the
IPO, as adjusted for any stock splits, stock dividends or subdivisions or
combinations of Common Stock prior to the Expiration Date, shall not in the
aggregate exceed 10% of the Company's outstanding Common Stock at the time of
such issuance; (x) are issued pursuant to any Common Stock Equivalent (as
hereinafter defined) (i) if upon the issuance of any such Common Stock
Equivalent, any such adjustments shall previously have been made pursuant to
paragraph (e) of the Section 2, (ii) if no adjustment was required pursuant to
paragraph (e) of this Section 2, or (iii) if such Common Stock Equivalent was
issued prior to this Warrant Certificate; or (z) are issued pursuant to a public
offering by the Company.

            Common Stock Equivalents. If the Company shall, after the Issuance
Date, issue any security or evidence of indebtedness which is convertible into
or exchangeable for Common Stock or any ("Convertible Security"), other than
pursuant to Employee Benefit Plans (together with Convertible Securities,
"Common Stock Equivalent "), or if, after any such issuance, the price per Share
for which additional shares of Common Stock may be issuable thereunder is
amended, then the Exercise Price upon each such issuance or amendment shall be
adjusted as provided in subsection (d) on the basis that (i) the maximum number
of additional shares of Common Stock issuable pursuant to all such Common Stock
Equivalents shall be deemed to have been issued as of the earlier of (a) the
date on which the Company shall enter into a firm contract for the issuance of
such Common Stock Equivalent, or (b) the date of actual issuance of such Common
Stock Equivalent; and (ii) the aggregate consideration for such maximum number
of additional shares of Common Stock shall be deemed to be the minimum
consideration received and receivable by the Company for the issuance of such
additional shares of Common Stock pursuant to such Common Stock Equivalent;
provided, however, that no adjustment shall be made pursuant to this subsection
(e) unless the consideration received and receivable by the Company per share of
Common Stock for the issuance of such additional shares of Common Stock pursuant
to such Common Stock Equivalent is less than the Market Price. No adjustment of
the Exercise Price shall be made under this subsection (e) upon the issuance of
any Convertible Security which is issued pursuant to the exercise of any
warrants or other subscription or purchase rights therefor, if any adjustment
shall previously have been made in the Exercise Price then in effect upon the
issuance of such warrants or other rights pursuant to this subsection (e).

            Miscellaneous. The following provisions shall be applicable to the
making of adjustments in the Exercise Price hereinbefore provided in this
Section 2:

               The consideration received by the Company shall be deemed to be
the following: (I) to the extent that any additional shares of Common Stock or
any Common Stock Equivalent shall be issued for cash consideration, the
consideration received by the Company therefor, or, if such additional shares of
Common Stock or Common Stock Equivalent are offered by the Company for
subscription, the subscription price, or, if such additional shares of Common
Stock or Common Stock Equivalent are sold to underwriters or dealers for public
offering without a subscription offering, the initial public offering price, in
any such case excluding any amounts paid or receivable for accrued interest or
accrued dividends and without deduction of any compensation,





                                    Sch II-5

<PAGE>   26


discounts, commissions or expenses paid or incurred by the Company for and in
the underwriting of , or otherwise in connection with, the issue thereof; (II)
to the extent that such issuance shall be for a consideration other than cash,
then, except as herein otherwise expressly provided, the fair value of such
consideration at the time of such issuance as determined in good faith by the
Board of Directors, as evidenced by a certified resolution of the Board of
Directors delivered to the holder of this Warrant Certificate setting forth such
determination. The consideration for any additional shares of Common Stock
issuable pursuant to any Common Stock Equivalent shall be the consideration
received by the Company for issuing such Common Stock Equivalent, plus the
additional consideration payable to the Company Upon the exercise, conversion or
exchange of such Common Stock or Common Stock Equivalent in payment of
satisfaction of any dividend upon any class of stock other that Common Stock,
the Company shall be deemed to have received for such additional shares of
Common Stock or Common Stock Equivalent (which shall not be deemed to be a
dividend payable in, or other distribution of, Common Stock under subsection (c)
above) consideration equal to the amount of such dividend so paid or satisfied.

            Upon the expiration of the right to convert, exchange or exercise
any Common Stock Equivalent the issuance of which effected an adjustment in the
Exercise Price, if any such Common Stock Equivalent shall not have been
converted, exercised or exchanged, the number of shares of Common Stock deemed
to be issued and outstanding because they were issuable upon conversion,
exchange or exercise of any such Common Stock Equivalent shall no longer be
computed as set forth above, and the Exercise Price shall forthwith be
readjusted and thereafter be the price which it would have been (but reflecting
any other adjustments in the Exercise Price made pursuant to the provisions of
subsection (d) after the issuance of such Common Stock Equivalent) had the
adjustment of the Exercise Price made upon the issuance or sale of such Common
Stock Equivalent been made on the basis of the issuance only of the number of
additional shares of Common Stock actually issued upon exercise, conversion or
exchange of such Common Stock actually so issued shall be deemed to have been
issued and only the consideration actually received by the Company (computed as
in subparagraph (i) of this paragraph (f) shall be deemed to have been received
by the Company.

            The number of shares of Common Stock at any time outstanding shall
not include any shares thereof then directly or indirectly owned or held by or
for the account of the Company or its wholly owned subsidiaries.

            For the purpose of this Section 2, the term "shares of Common Stock"
shall mean shares of (i) the class of stock designated as the Common Stock at
the date hereof or (ii) any other class of stock resulting from successive
changes or reclassifications of such shares consisting solely of changes in par
value, or from par value to no value, or from no par value to par value. If at
any time, because of an adjustment pursuant to subsection (a), the Warrants
shall entitle the holders to purchase any securities other than shares of Common
Stock, thereafter the number of such other securities so purchasable upon
exercise of each Warrant and the Exercise Price of such securities shall be
subject to adjustment from time to time in a manner and on terms as nearly
equivalent as practicable to the provisions with respect to the Common Stock
contained in this Section 2.




                                    Sch II-6

<PAGE>   27


            Calculation of Exercise Price. The exercise Price in effect from
time to time shall be calculated to four decimal places and rounded to the
nearest thousandth.

            Notice of Adjustments. Whenever the Exercise Price or the number of
shares of Common Stock is required to be adjusted as provided in Section 2, the
Company shall forthwith compute the adjusted Exercise Price or the number of
shares of Common Stock issuable and shall prepare and mail to the holder hereof
a certificate setting forth such adjusted Exercise Price or such number of
shares of Common Stock, showing in reasonable detail the facts upon which the
adjustment is based.

            Voluntary Reduction. (a) The Company may at its option, but shall
not be obligated to, at any time during the term of the Warrants, reduce the
then current Exercise Price by any amount selected by the Board of Directors;
provided that is the Company elects so to reduce the then current Exercise Price
to, such reduction shall be irrevocable during its effective period and remain
in effect for a minimum of 30 days following the date of such election, after
which time the Company may, at its option, reinstate the Exercise Price in
effect prior to such reduction. Whenever the Exercise Price is reduced, the
Company shall mail to the holder a notice of the reduction at least 30 days
before the date the reduced Exercise Price takes effect, stating the reduced
Exercise Price and the period for which such Exercise Price will be in effect.

            The Company may make such decreases in the Exercise Price, in
addition to those required or allowed by this Section 4, as shall be determined
by it, as evidenced by a certified resolution of the Board of Directors
delivered to the holders, to be advisable to avoid or diminish any income tax to
the holder resulting from any dividend or distribution of stock or issuance of
rights or warrants to purchase or subscribe for stock or from any event treated
as such for income tax purposes.

     Notices to Warrant Holders. In the event:

            (a) the Company shall authorize any consideration or merger to which
the Company is a party and for which approval of any stockholders of the Company
is required, or of the conveyance or sale of all or substantially all of the
assets of the Company, or of any reclassification or change if the Common Stock
or other securities issuable upon exercise of the Warrants (other than a change
in par value, or from par value to no par value, or from no par value to par
value or as result of a subdivision or combination), or a tender offer or
exchange offer for shares of Common Stock (or other securities issuable upon the
exercise of the Warrants); or

            (b) the Company shall declare any dividend (or any other
distribution) on the Common Stock or any other class of its capital stock ; or

            (c) the Company shall authorize the granting to the holders of
Common Stock or any other class of its capital stock of rights or warrants to
subscribe for or purchase any shares of any class or series of capital stock or
any other securities convertible into or exchangeable for shares of stock; or



                                    Sch II-7

<PAGE>   28



            (d) of the voluntary or involuntary dissolution, liquidation or
winding up of the Company; then the Company shall cause to be sent to the holder
hereof, at least 30 days prior to the applicable record date hereinafter
specified, or promptly in the case of events for which there is no record date,
a written notice stating (x) the date for the determination of the holders of
record of shares of Common Stock (or other securities issuable upon the exercise
of the Warrants) entitled to receive any such dividends other distribution, (y)
the initial expiration date set forth in any tender offer or exchange offer for
shares of Common Stock (or other securities issuable upon the exercise of the
Warrants), or (z) the date on which any of the events specified in subsections
(a)-(d) is expected to become effective or consummated, and the date as of which
it is expected that holders of record of shares of Common Stock (or securities
issuable upon the exercise of the Warrants) shall be entitled to exchange such
shares for securities or other property, if any, deliverable upon any such
event. Failure to give such notice or any defect therein shall not affect the
legality or validity of any such event, or the vote upon any such action.

     6. Reports to Warrant Holders. The Company will cause to be delivered, by
first-class mail, postage prepaid, to holder at such holder's address appearing
hereon, or such other address as the holder shall specify, a copy of any reports
delivered by the Company to the holders of Common Stock.

     7. Covenants of the Company. The Company covenants and agrees that:

        (a) Until the Expiration Date, the Company shall at all times reserve
and keep available, out of the aggregate of its authorized but unissued Common
Stock (and other securities), for the purpose for enabling it to satisfy any
obligation to issue shares of Common Stock (and other securities) upon the
exercise of the Warrants, the number of shares of Common Stock (and other
securities) issuable upon the exercise of such Warrants.

        (b) The Company shall pay all expenses, taxes and other charges payable
in connection with the preparation, issuance and delivery of new warrant
certificates on transfer of the Warrants.

        (c) All Common Stock (and other securities) which may be issued upon
exercise of the Warrants shall upon issuance be validly issued, fully paid,
non-assessable and free from all preemptive rights and all taxes, liens and
charges with respect to the issuance thereof, and will not be subject to any
restrictions on voting or transfer thereof except as set forth in any
stockholders agreement.

        (d) All original issue taxes payable in respect of the issuance of
shares of Common Stock to the registered holder hereof upon the exercise of the
Warrants shall be borne by the Company; provided, that the Company shall not be
required to pay any tax or charge imposed in connection with any transfer
involved in the issuance of any certificates representing shares of Common Stock
(and other securities) in any name other than that of the registered holder
hereof, and in such case the Company shall not be required to issue or deliver
any certificate representing shares of Common Stock (and other securities) until
such tax or other charge has been paid or it has been established to the
Company's satisfaction that no such tax or charge is due.



                                    Sch II-8

<PAGE>   29


            (e) As soon as practicable after the receipt from the holder of this
Warrant Certificate of notice of the exercise of a number of warrants sufficient
to require a filing under the Hart-Scott- Rodino Antitrust Improvements Act of
1976 and the rules, regulations and formal interpretations thereunder, as
amended from time to time (the "HSR Act:), but in any event no later than the
10th business day after receipt of such notice, the Company will (i) prepare and
file with Antitrust Division of the Department of Justice (the "DOJ") and the
Federal Trade Commission (the "FTC") the Notification and Report Form
(accompanied by all documentary attachments contemplated thereby) required by
the HSR Act, (ii) upon request of the holder, request early termination of the
waiting period imposed by the HSR Act, (iii) coordinate and cooperate with the
holder in responding to formal and informal requests for additional information
and documentary material from the DOJ and the FTC in connection with such
filing, (iv) use its best efforts to take, or cause to be taken, all reasonable
action to do, or cause to be done, all things necessary and appropriate to
permit the issuance to the holder of the shares of Common Stock issuable upon
the exercise of the warrants with respect to which any filing is required under
the HSR Act, and (v) reimburse the holder for the entire amount of any filing
fee or any other costs and expenses incurred by the holder in connection
therewith (including legal fees), or as required to be paid under the HSR Act.

        8. No Rights as Stockholder. The holder of the Warrants shall not, by
virtue of holding such Warrants, be entitled to any rights of a stockholder of
the Company either at law or in equity, and the rights of the holder of the
Warrants are limited to those expressed herein.

        9. Notices. All notices provided for hereunder shall be in writing and
may be given by registered or certified mail, return receipt requested, telex,
telegram, telecopier, air courier guaranteeing overnight delivery of personal
delivery, if to the holder at the following address:


               ------------------------------
               ------------------------------
               ------------------------------
               ------------------------------
               ------------------------------

           and, if to the Company:

               Brigham Exploration Company
               6300 Bridge Point Parkway
               Building 2, Suite 500
               Austin, Texas  78730
               Attention: Chief Financial Officer
               Telecopier: (512) 472-3400

        10. Governing Law. This Warrant Certificate shall be governed by and
construed in accordance with the laws of the State of Texas without principles
to conflict of laws.


                                    Sch II-9

<PAGE>   30


        11. Lost, Stolen, Mutilated or Destroyed Warrant Certificates. Upon
receipt by the Company of evidence reasonably satisfactory to it of the
ownership of and the loss, theft, destruction or mutilation of any Warrant
Certificate, then, in the absence of notice to the Company that such warrant
Certificate has been acquired by a bona fide purchaser, the Company shall
execute and deliver, in exchange for or in lieu of the lost, stolen, destroyed
or mutilated Warrant Certificate, a substitute Warrant Certificate of the same
tenor and evidencing a like number of Warrants.

     IN WITNESS WHEREOF, the Company has caused this Warrant Certificate to be
executed as of February _____, 2000, by the undersigned, thereunto duly
authorized.




                                       BRIGHAM EXPLORATION COMPANY



                                       By:
                                          --------------------------------------
                                                Karen E. Lynch
                                                Vice President





                                    Sch II-10

<PAGE>   31



                                    EXHIBIT A

                              ELECTION TO EXERCISE

          [To be executed on exercise of the Warrant evidenced by this
                 Warrant Certificate pursuant to Section 1(a)]


          TO:    Brigham Exploration Company

                  The undersigned, the holder of the Warrants evidenced by the
attached Warrant Certificate, hereby irrevocably elects to exercise Warrants,
and herewith makes payment of_____________________ delivered to
_____________________________, whose address is _______________________________.

                  The undersigned hereby directs payment of the Exercise Price
to be made by application of [specify Notes/Warrant Shares/cash].

          Dated:
                -------------------

                                      Name of Registered Holder:
                                                                ----------------
                                      Signature:
                                                --------------------------------
                                      Title:
                                            ------------------------------------
                                      Address:
                                              ----------------------------------


         Notice: The above signature(s) must correspond with the name as written
on the face of the Warrant Certificate in every detail, without alteration or
enlargement or any change whatsoever.





                                    Sch II-11

<PAGE>   32



                                   EXHIBIT A-1

                              ELECTION TO EXERCISE

          [To be executed on exercise of the Warrant evidenced by this
Warrant Certificate pursuant to Section 1(c)]

          TO:    Brigham Exploration Company

                  The undersigned, the holder of the Warrants evidenced by the
         attached Warrant Certificate, hereby elects to exercise _____________
         Warrants.

[ ]      The undersigned elects to receive shares of Common Stock of the Company
         in an amount equal to the Appreciation Amount (as defined in the
         Warrant), in accordance with Section 1(c) of the Warrant, and requests
         that the securities issuable hereunder be issued in the name of
         _________________ whose address is ________________________________.

         Dated:
               --------------------

                                      Name of Registered Holder:
                                                                ----------------
                                      Signature:
                                                --------------------------------
                                      Title:
                                            ------------------------------------
                                      Address:
                                              ----------------------------------



         Notice: The above signature(s) must correspond with the name as written
on the face of the Warrant Certificate in every detail, without alteration or
enlargement or any change whatsoever.



                                    Sch II-12

<PAGE>   33


                                  SCHEDULE III*

<TABLE>
<CAPTION>

SHARES OF                             STOCK OPTIONS OUTSTANDING
COMMON                 ----------------------------------------------------        WARRANTS **
STOCK OUTSTANDING         VESTED             UNVESTED             TOTAL            OUTSTANDING
- -----------------      ------------        ------------        ------------        ------------
<S>                    <C>                 <C>                 <C>                 <C>
14,517,786                  360,671           1,485,390           1,846,061           2,000,000
</TABLE>


*As of February 16, 2000.


**    1. These outstanding warrants do not include up to 5,416,667 warrants that
      may be issued, under certain circumstances, to Shell Capital, Inc. under
      that certain Equity Conversion Agreement dated as of February 17, 2000,
      between the Company and Shell Capital, Inc.

**    2. Of the 2,000,000 warrants outstanding as reflected in the table above,
      the exercise price of 1,000,000 warrants was repriced on February 17,
      2000, from $2.25 per share to $2.02 per share, and the exercise price of
      the remaining 1,000,000 warrants will be repriced from $3.50 per share to
      the average closing market price of Brigham Common Stock for the 20
      trading days subsequent to February 22, 2000.




                                    Sch III-1





<PAGE>   1
                                                                    EXHIBIT 99.1

[BRIGHAM EXPLORATION COMPANY LOGO]
                                                                    NEWS RELEASE
                                                           FOR IMMEDIATE RELEASE

BRIGHAM EXPLORATION CLOSES FINANCINGS TO FUND 2000 DRILLING PROGRAM

- --------------------------------------------------------------------------------

         Austin, TX -- (Business Wire) - February 22, 2000 -- Brigham
Exploration Company (NASDAQ:BEXP) today announced that it has entered into a
series of financing agreements that provide funding for its planned 2000 capital
expenditure program and working capital obligations. These transactions include
(i) a restructuring of its senior credit facility to provide from $14 million to
$19 million in borrowing availability, (ii) amendments to the terms of its
senior subordinated notes to provide for the restructured credit facility and
additional financial flexibility, and (iii) the issuance of $4.5 million of
common stock and warrants to purchase common stock in a private placement.
Through these related financing transactions, Brigham has secured a total of
$18.5 million to $23.5 million in capital availability to fund its planned $20
million drilling program in 2000.

         Brigham has entered into an amended senior credit facility with its
existing lenders, Bank of Montreal and Societe Generale, and a new lender, Shell
Capital Inc. This amended facility provides the Company with $70 million in
borrowing availability for a three-year term, an increase from the $56 million
in availability under the existing facility. If Brigham exceeds certain asset
value and interest coverage tests in the second or third quarters of 2000, the
total borrowing availability under this credit facility will increase to $75
million. Borrowings under the senior credit facility in excess of $45 million
are convertible into shares of Brigham common stock in the following amounts:
(i) the first $10 million of borrowings is convertible at $3.90 per share, (ii)
the second $10 million is convertible at $6.00 per share and (iii) the final $10
million is convertible at $8.00 per share. All borrowings under the senior
credit facility bear interest at annual rates of LIBOR plus 3.00%, or
approximately 8.875% based on current LIBOR rates.

         In its amendments to the terms of its outstanding $45.5 million of
senior subordinated notes due 2003 (the "Notes"), the Company has been granted
an extension of its right to pay interest through the issuance of additional
Notes in lieu of cash (or "in-kind") through the third quarter of 2000, and
potentially through the fourth quarter of 2000 if certain conditions are met. In
exchange for the amendments to the Notes, the Company has agreed to grant to the
holders of the Notes a term overriding royalty interest that provides for the
limited right to receive 4%, or 3% if certain conditions are met, of the
Company's net production revenue to reduce any Notes that have been or will be
issued as interest paid in-kind.

         Brigham has also agreed to issue 2,195,122 shares of common stock and
731,707 warrants to purchase common stock for total consideration of $4.5
million in a private placement to a group of institutional investors led by
affiliates of two members of the Company's board of directors. The equity sale
consists of units that include one share of common stock priced at $2.05 per
share and one-third of a warrant to purchase Brigham common stock at an exercise
price of $2.5625 per share with a three-year term. Pricing of this private
equity placement was based on the average market price of Brigham common stock
during a twenty trading day period prior to issuance.

         Curtis Harrell, the Company's Chief Financial Officer, stated, "We are
pleased to announce the closing of this significant series of coordinated
financing transactions for our Company. Despite the recent improvements in
market prices for crude oil and natural gas, capital available for investment in
exploration and production firms remains a challenge for our sector. We view the
investments by Shell Capital, a sophisticated, high-quality energy investor, and
members of our board of directors to be indicative of the substantial value that
exists in our undrilled prospect inventory. Through this combination of debt and
equity financings, we have successfully raised the capital necessary to fund our
planned drilling projects in 2000. We have positioned Brigham to continue to
create value through the execution of our balanced exploration and development
drilling program which should yield further opportunities to improve our
capitalization and capital resources during 2000."

ABOUT BRIGHAM EXPLORATION

         Brigham Exploration Company (www.bexp3d.com) is an independent
exploration and production company that applies 3-D seismic imaging and other
advanced technologies to systematically explore and develop onshore domestic
natural gas and oil provinces.



<PAGE>   2


Page 2

FORWARD LOOKING STATEMENTS DISCLOSURE

         Except for the historical information contained herein, the matters
discussed in this news release are forward looking statements that are based
upon current expectations. Important factors that could cause actual results to
differ materially from those in the forward looking statements include risks
inherent in exploratory drilling activities, the timing and extent of changes in
commodity prices, unforeseen engineering and mechanical or technological
difficulties in drilling wells, availability of drilling rigs, land issues,
federal and state regulatory developments and other risks more fully described
in the Company's filings with the Securities and Exchange Commission.

Contact:    Christopher A. Phelps, Vice President - Finance & Strategic Planning
            (512) 427-3300 / [email protected]



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