BRIGHAM EXPLORATION CO
SC 13D, 1998-09-02
CRUDE PETROLEUM & NATURAL GAS
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<PAGE>
 
                             ____________________

                                 UNITED STATES
                      SECURITIES AND EXCHANGE COMMISSION
                            WASHINGTON, D.C. 20549
                             ____________________
                                 SCHEDULE 13D
                   Under the Securities Exchange Act of 1934
 
                          BRIGHAM EXPLORATION COMPANY
                               (Name of Issuer)
                                  ___________

                         COMMON STOCK, $.01 PAR VALUE
                        (Title of Class of Securities)
                                  ___________

                                 109178  10  3
                                (CUSIP Number)

                                  ___________

                                 Julia Murray
                            General Counsel-Finance
                     Enron Capital & Trade Resources Corp.
                               1400 Smith Street
                             Houston, Texas 77002
                                (713) 853-6161

                      (Name, Address and Telephone Number
                    of Person Authorized to Receive Notices
                              and Communications)
                                  ___________

                                August 24, 1998
            (Date of Event which Requires Filing of this Statement)

  If the filing person has previously filed a statement  on Schedule 13G to 
     report this acquisition that is the subject of this Schedule 13D, and
       is filing this Schedule because of Rule 13d-1(e), Rule 13d-1(f) 
                or Rule 13d-1(g), check the following box:  [_]

     The information required on the remainder of this cover page shall not be
deemed to be "filed" for the purpose of Section 18 of the Securities Exchange
Act of 1934 ("Act") or otherwise subject to the liabilities of that section of
the Act but shall be subject to all other provisions of the Act.
                             ____________________
<PAGE>
 
CUSIP NO.: 109178 10 3                                        PAGE 2 OF 10 PAGES
          ------------

                                 SCHEDULE 13D

=============================================================================== 
 1    NAME OF REPORTING PERSON
      S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON
                          
      Enron Capital & Trade Resources Corp.
- ------------------------------------------------------------------------------
 2    CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*
      (a) [_]
      (b) [X]
- ------------------------------------------------------------------------------
 3    SEC USE ONLY
  
- ------------------------------------------------------------------------------
 4    SOURCE OF FUNDS*
      
      WC
- ------------------------------------------------------------------------------
 5    CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED PURSUANT 
      TO ITEMS 2(d) or 2(e) [_]
      [_]
- ------------------------------------------------------------------------------
 6    CITIZENSHIP OR PLACE OF ORGANIZATION

      Delaware
 ------------------------------------------------------------------------------
 7    SOLE VOTING POWER
 
      0
- ------------------------------------------------------------------------------
 8    SHARED VOTING POWER

      2,052,632*
- ------------------------------------------------------------------------------
 9    SOLE DISPOSITIVE POWER
 
 -----------------------------------------------------------------------------
10    SHARED DISPOSITIVE POWER

      2,052,632*
- ------------------------------------------------------------------------------
11    AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON
      
      2,052,632*
- ------------------------------------------------------------------------------
12    CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES CERTAIN SHARES*

      [_]
- ------------------------------------------------------------------------------
13    PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

      16.8%
- ------------------------------------------------------------------------------
14    TYPE OF REPORTING PERSON*

      CO
================================================================================

*Includes shares issuable upon the exercise of Warrants to Purchase Common 
 Stock.

                                      -2-
<PAGE>
 
CUSIP NO.: 109178 10 3                                        PAGE 3 OF 10 PAGES
          ------------

                                 SCHEDULE 13D

=============================================================================== 
 1    NAME OF REPORTING PERSON
      S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

      Enron Corp.
- ------------------------------------------------------------------------------
 2    CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*
      (a) [_]
      (b) [X]
- ------------------------------------------------------------------------------
 3    SEC USE ONLY
  
- ------------------------------------------------------------------------------
 4    SOURCE OF FUNDS*
      
      WC
- ------------------------------------------------------------------------------
 5    CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED PURSUANT 
      TO ITEMS 2(d) or 2(e) [_]
      [_]
- ------------------------------------------------------------------------------
 6    CITIZENSHIP OR PLACE OF ORGANIZATION
 
      Oregon
 ------------------------------------------------------------------------------
 7    SOLE VOTING POWER
 
      0
- ------------------------------------------------------------------------------
 8    SHARED VOTING POWER

      2,052,632*
- ------------------------------------------------------------------------------
 9    SOLE DISPOSITIVE POWER

      0 
 -----------------------------------------------------------------------------
10    SHARED DISPOSITIVE POWER

      2,052,632*
- ------------------------------------------------------------------------------
11    AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON
      
      2,052,632*
- ------------------------------------------------------------------------------
12    CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES CERTAIN SHARES*

      [_]
- ------------------------------------------------------------------------------
13    PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

      16.8%
- ------------------------------------------------------------------------------
14    TYPE OF REPORTING PERSON*

      CO
================================================================================

*Includes shares issuable upon the exercise of Warrants to Purchase Common 
 Stock.

                                      -3-
<PAGE>
 
CUSIP NO.: 109178 10 3                                        PAGE 4 OF 10 PAGES
          ------------

                                 SCHEDULE 13D

=============================================================================== 
 1    NAME OF REPORTING PERSON
      S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON
                          
      Joint Energy Development Investments II Limited Partnership
- ------------------------------------------------------------------------------
 2    CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*
      (a) [_]
      (b) [X]
- ------------------------------------------------------------------------------
 3    SEC USE ONLY
  
- ------------------------------------------------------------------------------
 4    SOURCE OF FUNDS*
      
      WC
- ------------------------------------------------------------------------------
 5    CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED PURSUANT 
      TO ITEMS 2(d) or 2(e) [_]
      [_]
- ------------------------------------------------------------------------------
 6    CITIZENSHIP OR PLACE OF ORGANIZATION

      Delaware
 ------------------------------------------------------------------------------
 7    SOLE VOTING POWER
 
      0
- ------------------------------------------------------------------------------
 8    SHARED VOTING POWER

      1,539,474*
- ------------------------------------------------------------------------------
 9    SOLE DISPOSITIVE POWER

      0
 -----------------------------------------------------------------------------
10    SHARED DISPOSITIVE POWER

      1,539,474*
- ------------------------------------------------------------------------------
11    AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON
      
      1,539,474*
- ------------------------------------------------------------------------------
12    CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES CERTAIN SHARES*

      [_]
- ------------------------------------------------------------------------------
13    PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

      12.6%
- ------------------------------------------------------------------------------
14    TYPE OF REPORTING PERSON*

      PN
================================================================================

*Includes shares issuable upon the exercise of Warrants to Purchase Common 
 Stock.

                                      -4-
<PAGE>
 
                                                              Page 5 of 10 Pages

                           STATEMENT ON SCHEDULE 13D

     Introductory Note: All information herein with respect to Brigham
Exploration Company, a Delaware corporation is to the best knowledge and belief
of the Reporting Entities, as defined herein.

ITEM 1.   SECURITY AND ISSUER.

     This Statement on Schedule 13D relates to the common stock, par value $.01
per share of Brigham Exploration Company, a Delaware corporation ("Issuer").
The principal executive offices of Issuer are located at 6300 Bridge Point
Parkway, Building 2, Suite 500, Austin, Texas 78730.

ITEM 2.   IDENTITY AND BACKGROUND.

     This Statement is filed by (i) Enron Capital & Trade Resources Corp., a
Delaware corporation ("ECT"), whose principal business is the purchase of
natural gas, gas liquids and power through a variety of contractual arrangements
and marketing these energy products to local distribution companies, electric
utilities, cogenerators and both commercial and industrial end users, as well as
the provision of risk management services; (ii) Enron Corp., an Oregon
corporation ("Enron"), which is an integrated natural gas, and electricity
company that engages, primarily through subsidiaries, in the transportation and
wholesale marketing of natural gas, the exploration for and production of
natural gas and crude oil, the production, purchase, transportation and
worldwide marketing and trading of natural gas liquids, crude oil and refined
petroleum products, and the purchasing and marketing of electricity and other
energy-related commitments; and (iii) Joint Energy Development Investments II
Limited Partnership, a Delaware limited partnership ("JEDI II"), which is
engaged primarily in the business of investing in and managing certain energy
related assets.  ECT, Enron and JEDI II are referred to herein as the "Reporting
Entities."  ECT is a wholly-owned subsidiary of Enron.  Additional entities that
may be deemed to be control persons of JEDI II are (a) Enron Capital Management
II Limited Partnership, a Delaware limited partnership and the general partner
of JEDI II ("ECMLP II"), whose principal business is to manage oil and gas
related investments, (b) Enron Capital II Corp., a Delaware corporation and the
general partner of ECMLP II ("ECC II"), whose principal business is to manage
oil and gas related investments, and ECT.  ECC II is a wholly owned subsidiary
of ECT and an indirect, wholly owned subsidiary of Enron.

     The address of the principal business offices of ECT, JEDI II, ECMLP II,
ECC II and Enron is 1400 Smith Street, Houston, Texas 77002.  Schedule I
attached hereto sets forth certain additional information with respect to each
director and each executive officer of ECT, Enron and ECC II.  The filing of
this statement on Schedule 13D shall not be construed as an admission that
Enron, ECMLP II, ECC II or any person listed on Schedule I hereto is, for the
purposes of Section 13(d) or 13(g) of the Securities Exchange Act of 1934, as
amended (the "Act"), the beneficial owner of any securities covered by this
statement.

     None of the Reporting Entities, nor to their knowledge ECMLP II or ECC II
or any person listed on Schedule I hereto, has been during the last five years
(a) convicted of any criminal proceeding (excluding traffic violations or
similar misdemeanors) or (b) a party to a civil proceeding of a judicial or
administrative body of competent jurisdiction and as a result of such proceeding
was or is subject to a judgment, decree or final order enjoining future
violations of, or prohibiting or mandating activities subject to United States
federal or state securities laws or finding any violations with respect to such
laws.

                                      -5-
<PAGE>
 
                                                              Page 6 of 10 Pages

ITEM 3.   SOURCE AND AMOUNT OF FUNDS OR OTHER CONSIDERATION.

     On August 24, 1998, pursuant to a Securities Purchase Agreement dated as of
August 20, 1998, among  ECT, JEDI II and the Issuer (the "Securities Purchase
Agreement"), (i) ECT purchased from the Issuer an aggregate of 263,158 shares of
the Issuer's Common Stock and 250,000 Warrants to Purchase Common Stock (the
"Warrants") and (ii) JEDI II purchased from the Issuer an aggregate of 789,474
shares of the Issuer's Common Stock and 750,000 Warrants.  The aggregate
purchase price for such securities was $10,000,000 in cash, of which $ 2,500,000
was paid by ECT and $ 7,500,000 was paid by JEDI II. In addition, pursuant to
the Securities Purchase Agreement, ECT and JEDI II purchased an aggregate
principal amount of $50,000,000 Senior Subordinated Secured Notes due 2003 (the
"Secured Notes") for aggregate cash consideration of $40,000,000.   See Item 4
for a more complete description of the Common Stock, the Warrants, the Secured
Notes and the transactions contemplated by the Securities Purchase Agreement.

     The source of the funds used for the purchases of the Common Stock and
Warrants by ECT and JEDI II was working capital on hand.

ITEM 4.   PURPOSE OF THE TRANSACTION.

     The purchase of the Common Stock, Warrants and Secured Notes of the Issuer
was the result of a negotiated transaction with the Issuer and were acquired for
investment purposes.  ECT and JEDI II intend to review their investment in the
Issuer on a continuing basis and, depending upon the price of, and other market
conditions relating to the Common Stock, subsequent developments affecting the
Issuer (including opportunities to provide financing from time to time to the
Issuer for expansion of its business), the Issuer's business and prospects,
other investment and business opportunities available to ECT or JEDI II, general
stock market and economic conditions, tax considerations and other factors
deemed relevant, may decide to increase or decrease the size of their investment
in the Issuer.

     The Securities Purchase Agreement, the Registration Rights Agreement, the
certificates evidencing the Warrants and the Indenture, all as defined below,
are each attached as exhibits to this statement on Schedule 13D and incorporated
herein by reference, and the following summaries of the terms of such agreements
or instruments are qualified by reference to the actual agreements or
instruments.

     Securities Purchase Agreement.  On August 20, 1998, ECT and JEDI II entered
into a Securities Purchase Agreement which provided for the purchase by ECT and
JEDI II, or their assignees, prior to September 1, 1998, of (i) an aggregate
principal amount of $50,000,000 of Secured Notes; (ii) 1,000,000 Warrants to
purchase Common Stock; and (iii) shares of Common Stock of the Issuer valued at
$10,000,000, for the aggregate cash consideration of $50,000,000.  The number of
shares of Common Stock to be purchased by ECT and JEDI II was determined by
dividing $10,000,000 by the average share price of $9.50.  The Securities
Purchase Agreement includes customary representations and warranties and
indemnification provisions.   The Securities Purchase Agreement also contains
provisions intended to limit ECT's and JEDI II's obligations or liability to the
Issuer.   In addition, the Securities Purchase Agreement provides that ECT or
its designated Affiliate  is entitled to designate one person to attend meetings
of the board of directors of the Issuer as an observer and to receive certain
written information and reports distributed to the board of directors, so long
as ECT and JEDI II and/or their respective affiliates beneficially own 5% or
more of the outstanding Common Stock of the Issuer (including the shares of
Common Stock issuable upon exercise of the Warrants, irrespective of whether
such Warrants are exercised).  As of the date hereof, ECT had not designated a
representative to serve on the Board of Directors, but intends to do so.

                                      -6-
<PAGE>
 
                                                              Page 7 of 10 Pages

     The Secured Notes.  The Secured Notes are issued pursuant to an Indenture
between the Issuer and Chase Bank of Texas, National Association, as Trustee.
Interest on the Secured Notes will be payable quarterly, beginning on November
20, 1998.  Interest rates payable on the Secured Notes will vary depending upon
whether accrued interest is paid in cash or in kind.  The Issuer may exercise
its option to pay interest in kind ("PIK Interest") by delivering written notice
thereof to holders of the Secured Notes on or before the quarterly interest
payment date.  The Company may not pay PIK Interest for more than six quarters
over the term of the Secured Notes.  The Secured Notes may be prepaid at any
time in whole or in par, without premium or penalty, provided that all partial
prepayments must be pro rata to the various holders of the Secured Notes.  The
Secured Notes will be fully and unconditionally guaranteed on a joint and
several basis by each of the Issuer's current and future material subsidiaries
and by any other current or future subsidiaries which guarantee the Senior
Indebtedness (as defined in the Indenture) of the Issuer.  The Secured Notes
rank subordinate in right of payment to the Senior Indebtedness (as defined in
the Indenture) and senior to all other financings, other than any permitted
capital leases and permitted purchase money financings.   The guaranty
agreements of the Issuer's subsidiaries will be similarly subordinated.

     Registration Rights Agreement.  In connection with the Securities Purchase
Agreement, the Issuer, ECT and JEDI II entered into a Registration Rights
Agreement dated as of August 20, 1998 (the "Registration Rights Agreement"),
which requires the Issuer to register for sale under the Securities Act of 1933,
as amended (the "Securities Act") the shares of Common Stock, the Warrants, and
shares of Common Stock (and any other securities) issuable upon exercise of the
Warrants (collectively, the "Registrable Securities"), acquired by ECT and JEDI
II, at the expense of the Issuer. These rights include "piggy back" rights to
include the Registrable Securities in Securities Act registrations effected by
the Issuer, as well as certain "demand" registration rights.  ECT and JEDI II
(and their transferees) can request an aggregate of two demand registrations and
can request to include shares of Common Stock in any Registration Statement
(other than registration statements on Form S-4, S-8 or with respect to
transactions subject to Rule 145 under the Securities Act) covering equity
securities of the Issuer.

     The Warrants.  In addition to the Secured Notes and Common Stock purchased
by ECT and JEDI II pursuant to the Securities Purchase Agreement, ECT purchased
250,000 Warrants and JEDI II purchased 750,000 Warrants to Purchase Common
Stock, which are evidenced by Warrant Certificates A-1 and A-2, respectively.
Each Warrant entitles the holder thereof  to purchase one fully paid and
nonassessable share of Common Stock of the Issuer at the exercise price of
$10.45,  subject to adjustment in certain circumstances. The Warrants may be
exercised immediately in whole or in part, at any time and from time to time
until 5:00 p.m. on August 22, 2005 (the "Expiration Date"), by surrendering  the
Warrant, together with a completed Election To Exercise and payment of the
exercise  price for each Warrant being exercised.  On the Expiration Date, the
Warrants will expire and the rights of the holders shall become void and of no
effect.

     Other than the transactions described herein, none of the Reporting
Entities, nor to their knowledge ECMLP II or ECC II or any person listed on
Schedule I hereto, has any plan or proposal that would result in any of the
consequences listed in paragraphs (a) - (j) of Item 4 of Schedule 13D.

ITEM 5.   INTEREST IN SECURITIES OF THE ISSUER.

     (a)  As set forth in this Schedule 13D, ECT owns 263,158 shares of Common
Stock and JEDI II owns 789,474 shares of Common Stock of the Issuer.  In
addition, ECT and JEDI II own 250,000 and 750,000 Warrants, respectively, that
are immediately exercisable into shares of Common Stock of the Issuer.   If such
Warrants were exercised in full by ECT and JEDI II, the shares of Common Stock
issuable upon the exercise of such Warrants, together with the Common Stock
owned by ECT and JEDI II, would represent approximately 4.2% and 12.6%,
respectively, of the outstanding Common Stock (based on the number of


                                      -7-
<PAGE>
 
                                                              Page 8 of 10 Pages

shares of Common Stock outstanding as of August 20, 1998 as represented by the
Issuer in the Securities Purchase Agreement).  See Item 4.

     Enron, ECT, ECMLP II and ECC II may be deemed to beneficially own the
Common Stock and shares of Common Stock issuable upon exercise of the Warrants
described herein which are held by JEDI II.  Enron may also be deemed to
beneficially own the Common Stock and shares issuable upon exercise of the
Warrants described herein which are held by ECT. See Item 2.  Enron disclaims
beneficial ownership of any shares of Common Stock or shares of Common Stock
issuable upon exercise of the Warrants. JEDI II disclaims beneficial ownership
of the shares of Common Stock and shares of Common Stock issuable upon exercise
of the Warrants issued to ECT.  ECT disclaims beneficial ownership of the shares
of Common Stock and shares of Common Stock issuable upon exercise of the
Warrants issued to JEDI II.

     (b)  ECT and Enron may be deemed to share voting and dispositive power over
the Common Stock and the shares of Common Stock issuable upon exercise of the
Warrants held directly by ECT.  In addition, Enron, ECT, ECMLP II, ECC II and
JEDI II may be deemed to share voting and dispositive power over the Common
Stock and the shares of Common Stock issuable upon exercise of the Warrants held
by JEDI II.  See Item 2.

     (c)  Other than the transactions described herein, none of the Reporting
Entities, nor to their knowledge ECMLP II, ECC II or any of the persons named in
Schedule I hereto, has effected any transactions in the Common Stock during the
preceding sixty days.

ITEM 6.   CONTRACTS, ARRANGEMENTS, UNDERSTANDINGS OR RELATIONSHIPS WITH RESPECT
TO SECURITIES OF THE ISSUER.

     See the description of the Securities Purchase Agreement, the Common Stock,
the Warrants and the Registration Rights Agreement in Item 4 above.

ITEM 7.   MATERIAL TO BE FILED AS EXHIBITS.

          (i)   Securities Purchase Agreement dated as of August 20, 1998 among
                the Issuer, ECT and JEDI II.
          (ii)  Registration Rights Agreement dated as of August 20, 1998, by
                and among the Issuer, ECT and JEDI II.
          (iii) Warrant Certificate A-1 dated August 20, 1998, by and between
                Issuer and ECT.
          (iv)  Warrant Certificate A-2 dated August 20, 1998, by and between
                Issuer and JEDI II.
          (v)   Indenture between the Issuer and Chase Bank of Texas, National
                Association, as Trustee.
          (vi)  Joint Filing Agreement by and among the Reporting Persons.

                              -8-
<PAGE>
 
                                                              Page 9 of 10 Pages

                                  SIGNATURES


     After reasonable inquiry and to the best of the undersigned's knowledge and
belief, each of the undersigned hereby certifies that the information set forth
in this statement is true, complete and correct.


Dated: September 2, 1998    ENRON CAPITAL & TRADE RESOURCES CORP.



                            By: /s/ Peggy B. Menchaca
                                -------------------------------
                            Name: Peggy B. Menchaca
                            Title: Vice President and Secretary


Dated: September 2, 1998    ENRON CORP.

                            By: /s/ Peggy B. Menchaca
                                -------------------------------
                            Name: Peggy B. Menchaca
                            Title: Vice President and Secretary


Dated: September 2, 1998    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: /s/ Peggy B. Menchaca
                                -------------------------------
                            Name: Peggy B. Menchaca
                            Title: Vice President and Secretary

                                      -9-
<PAGE>
 
                                                             Page 10 of 10 Pages

                                INDEX TO EXHIBITS


     (i)   Securities Purchase Agreement dated as of August 20, 1998 among the
           Issuer, ECT and JEDI II.

     (ii)  Registration Rights Agreement dated as of August 20, 1998, by and
           among the Issuer, ECT and JEDI II.

     (iii) Warrant Certificate A-1 dated August 20, 1998, by and between Issuer
           and ECT.

     (iv)  Warrant Certificate A-2 dated August 20, 1998, by and between Issuer
           and JEDI II.

     (v)   Indenture between the Issuer and Chase Bank of Texas, National
           Association, as Trustee.

     (vi)  Joint Filing Agreement by and among the Reporting Persons.

                                     -10-
<PAGE>
 
                                  SCHEDULE I
                       DIRECTORS AND EXECUTIVE OFFICERS
                     ENRON CAPITAL & TRADE RESOURCES CORP.


<TABLE>
<CAPTION>
<S>                             <C>              <C> 
    Name and Business Address    Citizenship         Position and Occupation
- -------------------------------------------------------------------------------------------------
1400 Smith Street
Houston, Texas 77002
- -------------------------------------------------------------------------------------------------
Mark A. Frevert                    U.S.A.         Director; President-ECT Europe and
                                                  Managing Director
- -------------------------------------------------------------------------------------------------
Mark E. Haedicke                   U.S.A.         Director; Managing Director - Legal
- -------------------------------------------------------------------------------------------------
Kevin P. Hannon                    U.S.A.         Director; President and Chief Operating
                                                  Officer
- -------------------------------------------------------------------------------------------------
Kenneth D. Rice                    U.S.A.         Director; Chairman of the Board; Chief
                                                  Executive Officer and Managing Director;
                                                  Chairman and Chief Executive Officer--ECT
                                                  North America
- -------------------------------------------------------------------------------------------------
Gene E.Humphrey                    U.S.A.         Vice Chairman
- -------------------------------------------------------------------------------------------------
Amanda K. Martin                   U.S.A.         President--Energy and Finance Services
- -------------------------------------------------------------------------------------------------
Robert J. Hermann                  U.S.A.         Vice President and General Tax Counsel
- -------------------------------------------------------------------------------------------------
</TABLE>

                                      S-1
<PAGE>
 
                       DIRECTORS AND EXECUTIVE OFFICERS
                                  ENRON CORP.


<TABLE>
<CAPTION>
<S>                                  <C>                <C> 
    Name and Business Address         Citizenship           Position and Occupation
- -------------------------------------------------------------------------------------------------- 
Robert A Belfer                                        Director; Chairman, President and Chief
767 Fifth Avenue, 46th Floor             U.S.A.        Executive Officer, Belco Oil & Gas Corp.     
New York, New York 10153
- -------------------------------------------------------------------------------------------------- 
Norman P. Blake, Jr.                                   Director; Chairman, United States Fidelity
USF&G Corporation                        U.S.A.        and Guaranty Company                       
6225 Smith Avenue.  LA0300                                                                   
Baltimore, Maryland 21209
- -------------------------------------------------------------------------------------------------- 
Ronnie C. Chan                                         Director; Chairman of Hang Lung Development
Hang Lung Development Company Limited    U.S.A.        Group                                      
28/F, Standard Chartered Bank Building                                                       
4 Des Vouex Road Central                     
Hong Kong
- -------------------------------------------------------------------------------------------------- 
John H. Duncan                                                         
5851 San Felipe, Suite 850               U.S.A.        Director; Investments
Houston, Texas 77057                     
- -------------------------------------------------------------------------------------------------- 
Joe H. Foy
404 Highridge Drive                      U.S.A.        Director; Retired Senior Partner, Bracewell
Kerrville, Texas 78028                                 & Patterson, L.L.P.                        
- -------------------------------------------------------------------------------------------------- 
Wendy L. Gramm
P.O. Box 39134                           U.S.A.        Director; Former Chairman, U.S. Commodity
Washington, D.C.  20016                                Futures Trading Commission               
- -------------------------------------------------------------------------------------------------- 
Ken L. Harrison
121 S.W. Salmon Street                   U.S.A.        Director; Vice Chairman of Enron Corp.
Portland, Oregon 97204                      
- -------------------------------------------------------------------------------------------------- 
Robert K. Jaedicke
Graduate School of Business              U.S.A.        Director; Professor (Emeritus), Graduate
Stanford University                                    School of Business, Stanford University 
Stanford, California 94305               
- -------------------------------------------------------------------------------------------------- 
Charles A. LeMaistre
13104 Travis View Loop                   U.S.A.        Director; President (Emeritus), University
Austin, Texas  78732                                   of Texas M.D. Anderson Cancer Center      
- -------------------------------------------------------------------------------------------------- 
</TABLE> 

                                      S-2
<PAGE>
 
<TABLE>
<CAPTION>
<S>                                  <C>                <C> 
    Name and Business Address         Citizenship           Position and Occupation
- -------------------------------------------------------------------------------------------------- 
Jerome J. Meyer
26600 S.W. Parkway                       U.S.A.        Director; Chairman and Chief Executive
Building 63, P. O. Box 1000                            Officer, Tektronix, Inc.              
Wilsonville, Oregon 97070-1000           
- -------------------------------------------------------------------------------------------------- 
John A. Urquhart
John A. Urquhart Associates              U.S.A.        Director; Senior Advisor to the Chairman of
111 Beach Road                                         Enron Corp.; President, John A. Urquhart  
Fairfield, Connecticut 06430                           Associates                                 
- -------------------------------------------------------------------------------------------------- 
John Wakeham
Pingleston House                         U.K.          Director; Former U.K. Secretary of State
Old Alresford                                          for Energy and Leader of the Houses of  
Hampshire S024 9TB                                     Commons and Lords                       
United Kingdom                                                                                 
- -------------------------------------------------------------------------------------------------- 
Charles E. Walker
Walker & Walker, LLC                     U.S.A.        Director; Chairman, Walker & Walker, LLC
10220 River Road, Suite 105                                                                      
Potomac, Maryland 20854
- -------------------------------------------------------------------------------------------------- 
G. Willison
4900 Rivergrade Road                     U.S.A.        Director; President and Chief Operating
Irwindale, California 91706                            Officer, Home Savings of America       
- -------------------------------------------------------------------------------------------------- 
Herbert S. Winokur, Jr.
Winokur & Associates, Inc.               U.S.A.        Director; President, Winokur & Associates,
30 East Elm Ct.                                        Inc.                                      
Greenwich, Connecticut 06830                                                                
- -------------------------------------------------------------------------------------------------- 
Kenneth L. Lay
1400 Smith Street                        U.S.A.        Director; Chairman and Chief Executive
Houston, Texas 77002                                   Officer, Enron Corp.                  
- -------------------------------------------------------------------------------------------------- 
J. Clifford Baxter
1400 Smith Street                        U.S.A.        Senior Vice President, Corporate
Houston, Texas 77002                                   Development; Enron Corp.        
- -------------------------------------------------------------------------------------------------- 
Richard A. Causey
1400 Smith Street                        U.S.A.        Senior Vice President, Chief Accounting,
Houston, Texas 77002                                   Information and Administrative Officer,
                                                       Enron Corp.
- -------------------------------------------------------------------------------------------------- 
James V. Derrick, Jr.
1400 Smith Street                        U.S.A.        Senior Vice President and General Counsel,
Houston, Texas 77002                                   Enron Corp.                               
- -------------------------------------------------------------------------------------------------- 
</TABLE> 

                                      S-3
<PAGE>
 
<TABLE>
<CAPTION>
<S>                                  <C>                <C> 
    Name and Business Address         Citizenship           Position and Occupation
- -------------------------------------------------------------------------------------------------- 
Andrew S. Fastow
1400 Smith Street                        U.S.A.        Senior Vice President and Chief Financial
Houston, Texas 77002                                   Officer, Enron Corp.                     
- -------------------------------------------------------------------------------------------------- 
Mark A. Frevert
1400 Smith Street                        U.S.A.        President and Chief Executive Officer,
Houston, Texas 77002                                   Enron Europe, Ltd.                    
- -------------------------------------------------------------------------------------------------- 
Stanley C. Horton
1400 Smith Street                        U.S.A.        Chairman and Chief Executive Officer, Enron
Houston, Texas 77002                                   Gas Pipeline Group                         
- -------------------------------------------------------------------------------------------------- 
Rebecca P. Mark
1400 Smith Street                        U.S.A.        Vice Chairman, Enron Corp. and Chairman,
Houston, Texas 77002                                   Enron International, Inc.               
- -------------------------------------------------------------------------------------------------- 
Lou L. Pai
1400 Smith Street                        U.S.A.        Chairman and Chief Executive Officer, Enron
Houston, Texas 77002                                   Energy Services, Inc.                      
- -------------------------------------------------------------------------------------------------- 
Kenneth D. Rice                          U.S.A.        Chairman and Chief Executive Officer, Enron
1400 Smith Street                                      Capital and Trade Resources Corp. - North 
Houston, Texas 77002                                   America                                    
- -------------------------------------------------------------------------------------------------- 
Jeffrey K. Skilling
1400 Smith Street                        U.S.A.        Director; President and Chief Operating
Houston, Texas 77002                                   Officer, Enron Corp.                   
- -------------------------------------------------------------------------------------------------- 
Joseph W. Sutton
1400 Smith Street                        U.S.A.        President and Chief Executive Officer,
Houston, Texas 77002                                   Enron International, Inc.             
- -------------------------------------------------------------------------------------------------- 
Thomas E. White
1400 Smith Street                        U.S.A.        Chairman, Chief Executive Officer and
Houston, Texas 77002                                   President, Enron Ventures Corp.      
- -------------------------------------------------------------------------------------------------- 
</TABLE> 

                                      S-4
<PAGE>
 
                       DIRECTORS AND EXECUTIVE OFFICERS
                            ENRON CAPITAL II CORP.

<TABLE>
<CAPTION>
<S>                                  <C>                <C> 
    Name and Business Address         Citizenship           Position and Occupation
- -------------------------------------------------------------------------------------------------- 
1400 Smith Street
Houston, Texas 77002
- -------------------------------------------------------------------------------------------------- 
James V. Derrick, Jr.
1400 Smith Street                        U.S.A.        Director
Houston, Texas 77002
- -------------------------------------------------------------------------------------------------- 
Mark A. Frevert
1400 Smith Street                        U.S.A.        Director
Houston, Texas 77002
- -------------------------------------------------------------------------------------------------- 
Kenneth D. Rice
1400 Smith Street                        U.S.A.        Director; Chairman, Chief Executive
Houston, Texas 77002                                   Officer and Managing Director
- -------------------------------------------------------------------------------------------------- 
Gene E. Humphrey
1400 Smith Street                        U.S.A.        President and Managing Director
Houston, Texas 77002
- -------------------------------------------------------------------------------------------------- 
Richard B. Buy
1400 Smith Street                        U.S.A.        Managing Director
Houston, Texas 77002
- -------------------------------------------------------------------------------------------------- 
Andrew S. Fastow
1400 Smith Street                        U.S.A.        Managing Director
Houston, Texas 77002
- -------------------------------------------------------------------------------------------------- 
Jeffrey McMahon
1400 Smith Street                        U.S.A.        Managing Director, Finance and Treasurer
Houston, Texas 77002                                   
- --------------------------------------------------------------------------------------------------  
Mark E. Haedicke
1400 Smith Street                        U.S.A.        Managing Director and General Counsel
Houston, Texas 77002                                   
- -------------------------------------------------------------------------------------------------- 
Jeremy M. Blachman
1400 Smith Street                        U.S.A.        Vice President
Houston, Texas 77002
- --------------------------------------------------------------------------------------------------  
William W. Brown
1400 Smith Street                        U.S.A.        Vice President
Houston, Texas 77002
- -------------------------------------------------------------------------------------------------- 
</TABLE> 

                                      S-5
<PAGE>
 
<TABLE>
<CAPTION>
<S>                                  <C>                <C> 
    Name and Business Address         Citizenship           Position and Occupation
- -------------------------------------------------------------------------------------------------- 
Rebecca C. Carter
1400 Smith Street                        U.S.A.        Vice President
Houston, Texas 77002
- -------------------------------------------------------------------------------------------------- 
Robert J. Hermann
1400 Smith Street                        U.S.A.        Vice President and General Tax Counsel
Houston, Texas 77002
- -------------------------------------------------------------------------------------------------- 
Jordan H.Mintz
1400 Smith Street                        U.S.A.        Vice President, Tax and Tax Counsel
Houston, Texas 77002
- -------------------------------------------------------------------------------------------------- 
Kristina M. Mordaunt
1400 Smith Street                        U.S.A.        Vice President and Assistant General
Houston, Texas 77002                                   Counsel        
- -------------------------------------------------------------------------------------------------- 
Julia Heintz Murray
1400 Smith Street                        U.S.A.        Vice President and General Counsel,
Houston, Texas 77002                                   Finance                    
- -------------------------------------------------------------------------------------------------- 
Raymond M. Bowen
1400 Smith Street                        U.S.A.        Vice President
Houston, Texas 77002
- -------------------------------------------------------------------------------------------------- 
Theodore R. Murphy
1400 Smith Street                        U.S.A.        Vice President
Houston, Texas 77002
- -------------------------------------------------------------------------------------------------- 
</TABLE> 

                                      S-6

<PAGE>
 
                                                            DRAFT DATED 8/19/98


===============================================================================


                         SECURITIES PURCHASE AGREEMENT

                                    BETWEEN

                          BRIGHAM EXPLORATION COMPANY

                                      AND

                     ENRON CAPITAL & TRADE RESOURCES CORP.
                                      AND
                    JOINT ENERGY DEVELOPMENT INVESTMENTS II
                              LIMITED PARTNERSHIP

                          DATED AS OF AUGUST 20, 1998



            $50,000,000 SENIOR SUBORDINATED SECURED NOTES DUE 2003,

            Warrants to Purchase 1,000,000 Shares of Common Stock;

                                      AND

                ACQUISITION OF 1,052,632 SHARES OF COMMON STOCK

===============================================================================
<PAGE>
 
                                 TABLE OF CONTENTS
<TABLE>
<CAPTION>
 
 
<S>                 <C>                                                     <C>
ARTICLE I
     DEFINITIONS..........................................................    1
     Section 1.01    Definitions..........................................    1
     Section 1.02    Accounting Procedures and Interpretation.............   10
 
ARTICLE II
     ISSUANCE OF SECURITIES; RIGHTS OF PURCHASERS.........................   10
     Section 2.01    Issuance of Securities...............................   10
     Section 2.02    The Closing; Funding Date............................   11
     Section 2.03    Delivery.............................................   11
     Section 2.04    Payment..............................................   11
     Section 2.05    Tax Matters..........................................   11
     Section 2.06    Rights of Purchasers.................................   12
 
ARTICLE III
     SECURITY FOR THE OBLIGATIONS.........................................   12
     Section 3.01    Security.............................................   12
 
ARTICLE IV
     REPRESENTATIONS AND WARRANTIES OF THE SELLER.........................   12
     Section 4.01    Corporate Existence..................................   12
     Section 4.02    Financial Condition..................................   13
     Section 4.03    Litigation...........................................   13
     Section 4.04    No Breach............................................   13
     Section 4.05    Authority............................................   14
     Section 4.06    Approvals............................................   14
     Section 4.07    Use of Loans.........................................   14
     Section 4.08    ERISA................................................   14
     Section 4.09    Taxes................................................   15
     Section 4.10    Titles, etc..........................................   15
     Section 4.11    No Material Misstatements............................   16
     Section 4.12    Investment Company Act...............................   17
     Section 4.13    Public Utility Holding Company Act...................   17
     Section 4.14    Subsidiaries.........................................   17
     Section 4.15    Location of Business and Offices.....................   17
     Section 4.16    Defaults.............................................   17
     Section 4.17    Environmental Matters................................   17
     Section 4.18    Compliance with the Law..............................   18
     Section 4.19    Insurance............................................   19
     Section 4.20    Hedging Agreements...................................   19
     Section 4.21    Restriction on Liens.................................   20
</TABLE> 

                                      -i-
<PAGE>
 
     Section 4.22    Material Agreements..................................   20
     Section 4.23    Gas Imbalances.......................................   20
     Section 4.24    Capitalization.......................................   20
     Section 4.25    Acquired Shares......................................   20
     Section 4.26    Warrant Shares.......................................   21
     Section 4.27    No Restrictions......................................   21
     Section 4.28    Certain Fees.........................................   21
 
ARTICLE V
     REPRESENTATIONS AND WARRANTIES OF THE PURCHASERS.....................   21
     Section 5.01    Investment...........................................   21
     Section 5.02    Nature of Purchasers.................................   22
     Section 5.03    Receipt of Information; Authorization................   22
 
ARTICLE VI
     CONDITIONS PRECEDENT TO FUNDING......................................   22
     Section 6.01    Conditions Precedent to Obligations of the Purchasers   22
     Section 6.02    Conditions Precedent to Obligations of the Seller....   25
     Section 6.03    Conditions Precedent to the Obligations of
                     Purchasers and Seller................................   26
 
ARTICLE VII
     AFFIRMATIVE COVENANTS................................................   26
     Section 7.01    Warrants.............................................   26
     Section 7.02    Hart-Scott -Rodino Compliance........................   26
     Section 7.03    Board Representation.................................   27
     Section 7.04    Common Stock; Dividends; Voting Rights...............   27
 
ARTICLE VIII
     [OMITTED BY THE PARTIES HERETO]......................................   27
 
ARTICLE IX
     [OMITTED BY THE PARTIES HERETO]......................................   27
 
ARTICLE X
     [OMITTED BY THE PARTIES HERETO]......................................   27
 
ARTICLE XI
     [OMITTED BY THE PARTIES HERETO]......................................   27
 
ARTICLE XII
     MISCELLANEOUS........................................................   28
     Section 12.01   INTERPRETATION AND SURVIVAL OF PROVISIONS............   28
     Section 12.02   COSTS, EXPENSES AND TAXES............................   28
     Section 12.03   NO WAIVER; MODIFICATIONS IN WRITING..................   30


                                      -ii-
<PAGE>

     Section 12.04   BINDING EFFECT; ASSIGNMENT...........................   30
     Section 12.05   REPLACEMENT SECURITIES...............................   30
     Section 12.06   COMMUNICATIONS.......................................   31
     Section 12.07   GOVERNING LAW........................................   31
     Section 12.08   ARBITRATION..........................................   31
     Section 12.09   EXECUTION IN COUNTERPARTS............................   32 

Exhibits:

Exhibit A  -  Form of Warrants


Schedules:

Schedule 4.02  -  Liabilities
Schedule 4.03  -  Litigation
Schedule 4.09  -  Taxes
Schedule 4.10  -  Titles, Etc.
Schedule 4.14  -  Subsidiaries and Addresses
Schedule 4.19  -  Insurance
Schedule 4.20  -  Hedging Agreements
Schedule 4.22  -  Material Agreements
Schedule 4.23  -  Gas Imbalances
Schedule 4.24  -  Voting Agreements; Registration Rights

                                     -iii-
<PAGE>
 
                         SECURITIES PURCHASE AGREEMENT


     SECURITIES PURCHASE AGREEMENT, dated as of August 20, 1998 (this
"Agreement"), among BRIGHAM EXPLORATION COMPANY, a Delaware corporation, ENRON
CAPITAL & TRADE RESOURCES CORP., a Delaware corporation ("ECT") and JOINT ENERGY
DEVELOPMENT INVESTMENTS II LIMITED PARTNERSHIP, a Delaware limited partnership
("JEDI-II").

     In consideration of the mutual covenants and agreements set forth herein
and for good and valuable consideration, the receipt of which is hereby
acknowledged, the parties agree as follows:

                                   ARTICLE I
                                  DEFINITIONS

     Section 1.01  DEFINITIONS.  As used in this Agreement, and unless the
context requires a different meaning, the following terms have the meanings
indicated:

     "Acquired Shares" means 1,052,632 shares of Common Stock acquired by the
Purchasers on the Funding Date in accordance with Section 2.01 and any
additional shares of Common Stock of the Seller issued to the Purchasers after
the Funding Date in accordance with Section 2.01(ii).

     "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 is
the sole general partner of a limited partnership, or 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" is defined in the Indenture.

     "Average Share Price" means $9.50.

     "Basic Documents" means, collectively, this Agreement, the other Loan
Documents, the Structuring Fee Agreement and the Equity Documents.

     "Board of Directors" means the Board of Directors of the Seller.

     "BOG" means Brigham Oil & Gas, L.P., a Delaware limited partnership.

                                      -1-
<PAGE>
 
     "Business Day" means any day other than a Saturday, Sunday, or a legal
holiday for commercial banks in Houston, Texas, or New York, New York.

     "Business Opportunities Agreement" means the Corporate Opportunities
Shareholders' Agreement dated as of even date herewith between the Purchasers
and the Seller.

     "Capital Stock" of any Person means any and all shares, interests,
participations, or other equivalents (however designated) of, or rights,
warrants, or options to purchase, corporate stock, partnership interests, or any
other equity interest (however designated) of or in such Person.

     "Closing" has the meaning provided therefor in Section 2.02.

     "Closing Date" means the date upon which the Closing occurs as provided in
Section 2.02.

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

     "Collateral" is defined in the Indenture.

     "Collateral Documents" is defined in the Indenture.

     "Commission" means the United States Securities and Exchange Commission.

     "Common Stock" means the common stock, par value $0.01 per share, of the
Seller or such other class of securities as shall, after the date of this
Agreement, constitute the common equity of the Seller.

     "Consolidated Subsidiaries" shall mean each Subsidiary of the Seller
(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 the Seller in accordance with GAAP.

     "Debt" means, 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
and past due issuance fees); (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 (or $500,000 in the aggregate) 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 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

                                      -2-
<PAGE>
 
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, provided that
"Debt" shall not include (a) interest and fees (other than past due issuance
fees) on any of the foregoing, (b) obligations associated with bid, performance,
surety or appeal bonds (including those required by Governmental Requirements in
connection with Oil and Gas Properties), (c) gas balancing obligations (whether
volumetric or dollar denominated), (d) intercompany obligations among the Seller
and its Consolidated Subsidiaries, (e) indemnity obligations which have not
matured into fixed liabilities, and (f) purchase price adjustments and similar
post-closing obligations (but excluding the deferred payment of any purchase
price) incurred in connection with the permitted purchase and sale of Property
or stock, and which is to be determined and payable no later than 180 days
following the closing of such purchase and sale.

     "Designee" shall have the meaning set forth in Section 7.03.

     "Effective Date" means the date this Agreement is executed by all the
parties hereto.

     "Employee Plan" means any employee benefit plan, program or policy with
respect to which the Seller or any ERISA Affiliate may have any liability or any
obligation to contribute, other than a Plan or a Multiemployer Plan.

     "Environmental Laws" means any and all Governmental Requirements pertaining
to the environment in effect in any and all jurisdictions in which the Seller or
any Subsidiary is conducting or at any time has conducted business, or where any
Property of the Seller or any Subsidiary is located, including, without
limitation, the Oil Pollution Act of 1990 ("OPA"), as amended, 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" has 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

                                      -3-
<PAGE>
 
"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 Seller 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 Documents" means the Warrants, the stock certificates representing
the Acquired Shares, the Registration Rights Agreement and the Business
Opportunities Agreement.

     "ERISA" means 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 Seller or any Subsidiary of the Seller
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.

     "Excepted Liens" means (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 workman'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 the 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 for which such
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

                                      -4-
<PAGE>
 
obligations and other obligations of a like nature incurred in the ordinary
course of business; and (vii) Liens permitted by the Loan Documents.

     "Financial Statements" means the financial statement or statements
described or referred to in Section 4.02.

     "Financing Agreement" means an agreement between the Seller and ECT
Securities Corp. pursuant to which the Seller grants to ECT Securities Corp. the
right and option to participate during the three years following the Closing
Date for up to 20% on any public or private (e.g. 144A) high yield debt offering
by the Seller with gross proceeds in excess of $50,000,000.

  "Funding Date" means the first Business Day following the date all of the
conditions precedent to funding in Article VI have been satisfied.

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

     "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 Seller,
the Subsidiaries or any of their Property or any Purchaser.

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

     "Guarantors" means Brigham, Inc., Brigham Holdings I, LLC, Brigham Holdings
II, LLC, BOG and any other Person who becomes party to a Guaranty Agreement
pursuant to the terms of the Loan Documents.

     "Guaranty Agreements" means the agreements executed by the Guarantors in
form and substance satisfactory to the Trustee and the Purchasers guarantying,
unconditionally, payment of the Obligations, as the same may be amended,
modified or supplemented from time to time.

     "Hedging Agreements" means 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.

                                      -5-
<PAGE>
 
     "Hydrocarbon Interests" means 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" means oil, gas, casinghead gas, drip gasoline, natural
gasoline, condensate, distillate, liquid hydrocarbons, gaseous hydrocarbons and
all products refined or separated therefrom.

     "Indenture" means that certain Indenture dated as of August 20, 1998,
executed by Seller.

     "Investment Unit" has the meaning provided therefor in Section 2.05 of this
Agreement.

     "Lien" means 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
purpose 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" means this Agreement, the Indenture, the Notes, the
Structuring Fee Agreement, the Collateral Documents, and any and all other
agreements or instruments now or hereafter executed and delivered by the Seller
or any Subsidiary or Affiliate of the Seller (other than the Equity Documents
and any assignments, participation or similar agreements between any Purchaser
and any other lender or creditor with respect to any Obligations 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.

     "Majority Purchasers" means, at any time, the Purchasers holding more than
50% of the  Warrants.

     "Material Adverse Effect" means any material and adverse effect on (i) the
assets, liabilities, financial condition, business, operations or affairs of the
Seller 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 at the time made, or (ii) the ability of the Seller and its
Subsidiaries taken as a whole to carry out their business as of the Closing Date
or as proposed as of the Closing Date to be conducted or to meet their
obligations under the Loan Documents on a timely basis.

                                      -6-
<PAGE>
 
     "Mortgage" is defined in the Indenture.

     "Mortgaged Property" means the Property owned by the Seller and its
Subsidiaries which is subject to the Liens existing and to exist under the Loan
Documents.

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

     "NASDAQ" means  the National Association of Securities Dealers Automated
Quotation System.

     "Notes" means the Senior Subordinated Secured Notes issued pursuant to
Section 2.03 of this Agreement and the Indenture, in the aggregate face amount
of $50,000,000, dated as of the date hereof, made by the Seller and initially
payable to the order of the Purchasers in their respective Participations.

     "Noteholders" means, from time to time, the holders of the Notes.

     "Obligations" means any and all amounts, liabilities and obligations owing
from time to time by Seller to the Agent or the Noteholders, pursuant to any of
the Loan Documents and all renewals, extensions and/or rearrangements thereof,
whether such amounts, liabilities or obligations be liquidated or unliquidated,
now existing or hereafter arising, absolute or contingent.

     "Oil and Gas Properties" means 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 hereafter 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 rights, automotive
equipment or other personal property which may be on such premises for the
purpose of drilling a well or other similar temporary use) 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-

                                      -7-
<PAGE>
 
of-way, easements and servitudes together with all additions, substitutions,
replacements, accessions and attachments to any and all of the foregoing.

     "Participation" means, for each Purchaser, such Purchaser's proportionate
share of the Obligations and the Warrants.  As of the Effective Date, ECT's
Participation shall be 25% and JEDI-II's Participation shall be 75%.

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

     "Person" means 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" means 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 Seller, 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 Seller, any Subsidiary or an ERISA Affiliate.

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

     "Purchasers" means ECT and JEDI-II and/or, to the extent then applicable,
each assignee of ECT or JEDI-II or their respective successors or assigns
pursuant to Section 12.04.

     "Registration Rights Agreement" means the Registration Rights Agreement
dated as of the date hereof, made by the Seller in favor of the Purchasers
relating to the Warrants, the Warrant Shares and the Acquired Shares.

     "Reportable Event" means an event described in Section 4043(c) of ERISA
with respect to a Plan, other than an event described in paragraphs (1) through
(8) as to which the 30 day notice requirement has been waived by the PBGC.

     "Reserve Report" is defined in the Indenture.

     "Responsible Officer" means, 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 Seller.

     "Securities" means the Notes, the Warrants and the Acquired Shares.

     "Securities Act" means the Securities Act of 1933, as amended from time to
time, and the rules and regulations of the Commission promulgated thereunder.

                                      -8-
<PAGE>
 
     "Seller" means Brigham Exploration Company, a Delaware corporation.

     "Senior Credit Agreement" means the Credit Agreement dated as of January
26, 1998, among BOG, the Senior Loan Agent, and the Senior Lenders, as it may
from time to time be amended, modified or supplemented from time to time, and
any Credit Agreement or similar agreement executed in connection with any
refinancing of the Senior Loan permitted hereunder and under the Subordination
Agreement.

     "Senior Loan Agent" means the agent or agents designated under the Senior
Credit Agreement.  Bank of Montreal is the Senior Loan Agent as of the date
hereof.

     "Senior Lenders" means each of the lenders from time to time under the
Senior Credit Agreement.

     "Senior Loan" shall mean, collectively, any advance or advances of
principal made by the Senior Lenders to BOG under the Senior Credit Agreement
and the other Senior Loan Documents.

     "Senior Loan Documents" means the Senior Credit Agreement and all
promissory notes, collateral documents and other agreements, documents and
instruments executed or delivered in connection therewith, as such agreements
may be amended, modified or supplemented from time to time.

     "Special Entity" means 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).

     "Structuring Fee Agreement" means the agreement between the Seller and ECT
Securities Corp. dated as of the date hereof.

     "Subordination Agreement" means the Intercreditor and Subordination
Agreement dated as of even date herewith, by and among the Senior Loan Agent,
the Agent, the Purchasers, the Seller and certain Subsidiaries, as the same may
be supplemented or amended from time to time.

     "Subsidiary" means (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 

                                      -9-
<PAGE>
 
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 Seller. Quest Resources L.L.C. and
Venture Acquisitions L.P. shall not be considered Subsidiaries of Seller.

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

     "Trustee" means the Trustee as defined in the Indenture.

     "Warrant Shares" means the shares of Common Stock and other securities
receivable upon exercise of the Warrants.

     "Warrants" means the Warrants issued by the Seller to the Purchasers in
their respective Participations pursuant to Section 2.03, for the purchase of an
aggregate of 1,000,000 shares of Common Stock, and any Warrants issued upon the
transfer thereof or in substitution therefor, pursuant to the Warrant
Certificates to be issued to ECT and JEDI-II, forms of which are attached hereto
as Exhibit A.

     Section  1.02.  ACCOUNTING PROCEDURES AND INTERPRETATION.  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 by the Seller hereunder shall be prepared, in
accordance with GAAP, applied on a basis consistent with the Financial
Statements (except for changes concurred with by the Seller's independent public
accountants).

                                  ARTICLE II
                 ISSUANCE OF SECURITIES; RIGHTS OF PURCHASERS

     Section 2.01  ISSUANCE OF SECURITIES.  Subject to the terms and
conditions herein set forth, the Seller agrees that it will issue the Securities
to the Purchasers and the Purchasers agree that they shall each purchase the
Securities from the Seller for an aggregate 
cash consideration of $50,000,000,
as follows:

               (i)  The Notes and the Warrants will be purchased by the
          Purchasers in their respective participations and sold for an
          aggregate cash consideration of $40,000,000.

               (ii)  The Acquired Shares will be purchased by the Purchasers or
          their respective Affiliates for a total cash consideration of
          $10,000,000.  The number of Acquired Shares to be purchased and sold
          on the Funding Date shall be determined by dividing the $10,000,000
          purchase price by the Average Share Price.  If within 180 days
          following the Funding Date the Seller enters into an agreement to
          issue or issues new Common Stock for a price per share that is less
          than the Average Share

                                      -10-
<PAGE>
 
          Price (a "Post Funding Sale Price"), the Seller shall,
          contemporaneously with the issuance of such new Common Stock, issue
          and deliver to the Purchasers or their respective Affiliates
          additional shares of Common Stock (which shall be deemed additional
          Acquired Shares) such that, after issuance and delivery of such
          additional Acquired Shares, the total number of Acquired Shares
          received by the Purchasers or their respective Affiliates multiplied
          by the Post Funding Date Sale Price, shall aggregate $10,000,000.

     Section 2.02  THE CLOSING; FUNDING DATE.

          (a)  The execution of the Basic Documents and all other instruments
required pursuant to Section 6.01 will take place at a closing (the "Closing")
to be held at the offices of Bracewell & Patterson, L.L.P. on such date as the
Seller and the Purchasers shall agree.  The date and time at which the Closing
occurs is the "Closing Date".

          (b)  Delivery of the Securities by the Seller to the Purchasers, and
payment by the Purchasers to the Seller of the consideration therefor as set
forth in Section 2.01, shall occur on the Funding Date.

     Section 2.03  DELIVERY.   Delivery of the Securities pursuant to this
Agreement shall be made on the Funding Date by the Seller delivering to the
Purchasers, against payment of the purchase price therefor, as follows: (i) one
Note executed by the Seller in the face amount of $12,500,000.00, payable to the
order of ECT and one Note executed by the Seller in the face amount of
$37,500,000.00, payable to the order of JEDI-II, (ii) one certificate executed
by the Seller representing ECT's Participation in the Warrants and one
certificate executed by the Seller representing JEDI-II's Participation in the
Warrants, registered in the names of ECT and JEDI-II, respectively (or such
other Person as either Purchaser may have designated in writing to the Seller at
least three Business Days prior to the Funding Date) and (iii) a certificate or
certificates of Common Stock executed by the Seller representing the Purchasers
and/or their respective Affiliates share of the Acquired Shares registered in
the name(s) of the Purchasers and/or their respective Affiliates (or such other
Person as either Purchaser may have designated in writing to the Seller at least
three Business Days prior to the Funding Date).

     Section 2.04  PAYMENT.  Payment of the consideration for the Securities
shall be made on the Funding Date by wire transfer of immediately available
funds to such account of the Seller as shall have been designated to ECT at
least two Business Days prior to the Funding Date.

     Section 2.05 TAX MATTERS. The Seller and the Purchasers agree as follows:
(i) Purchasers' acquisition of the Securities constitutes the purchase of an
"investment unit" (the "Investment Unit") for purposes of Treas. Reg. (S)1.1273-
2(h)(1); (ii) the issue price of the Investment Unit is $50,000,000, as
determined in accordance with Treas. Reg. (S)1.1273-2(a)(1); (iii) the issue
price for the Investment Unit shall be allocated among the Notes, the Warrants,
and the Acquired Shares in accordance with their relative fair market values, as
required by Treas. Reg. (S)1.1273-2(h)(1); and 

                                      -11-
<PAGE>
 
(iv) the parties agree that the issue price shall be allocated among the Notes,
the Warrants, and the Acquired Shares as follows and the parties shall be bound
by such allocation for all tax-related purposes:

<TABLE>
<CAPTION>
 
<S>           <C>                   <C> 
               Notes:                $39,900,000
               Warrants:             $   100,000
               Acquired Shares:      $10,000,000
</TABLE>

     Section 2.06  RIGHTS OF PURCHASERS.  The Purchasers shall have such
rights with respect to the registration of the Warrant Shares and the Acquired
Shares under the Securities Act and state securities laws as are set forth in
the Registration Rights Agreement, which shall be executed by the Seller and the
Purchasers at the Closing.

                                  ARTICLE III
                         SECURITY FOR THE OBLIGATIONS

     Section 3.01  SECURITY.  The Obligations shall be secured by the
Collateral and the Collateral Documents in accordance with the Indenture.

                                  ARTICLE IV
                 REPRESENTATIONS AND WARRANTIES OF THE SELLER

     The Seller represents and warrants to the Purchasers, for the benefit of
each of the holders of the Notes, the holders of the Warrants and the holders of
the Acquired Shares, which representations and warranties shall survive the
execution of any Basic Document, that as of the date of this Agreement:

     Section 4.01  CORPORATE EXISTENCE.  The Seller: (i) is a corporation duly
organized, legally existing and in good standing under the laws of the State of
Delaware; (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 qualifications necessary and where failure
so to qualify would have a Material Adverse Effect.  Brigham, Inc.: (i) is a
corporation duly organized, legally existing and in good standing under the laws
of the State of Nevada; (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 qualifications necessary
and where failure so to qualify would have a Material Adverse Effect.  Each of
Brigham Holdings I, LLC and Brigham Holdings II, LLC:  (i) is a limited
liability company duly organized, legally existing and in good standing under
the laws of the State of Nevada; (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 qualifications 

                                      -12-
<PAGE>
 
necessary and where failure so to qualify would have a Material Adverse Effect.
Brigham Oil & Gas, L.P.: (i) is a limited partnership duly organized, legally
existing and in good standing under the laws of the State of Delaware; (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 qualifications necessary and where failure so to qualify would have a
Material Adverse Effect.

     Section  4.02  FINANCIAL CONDITION.  The audited consolidated balance
sheet of the Seller and its Consolidated Subsidiaries as at December 31, 1997
and the related consolidated statement of income, stockholders' equity and cash
flow of the Seller and its Consolidated Subsidiaries for the fiscal year ended
on said date, with the opinion thereon of Price Waterhouse, heretofore furnished
to the Purchasers and the unaudited consolidated balance sheet of the Seller and
its Consolidated Subsidiaries as at June 30, 1998, and their related
consolidated statements of income, stockholders' equity and cash flow of the
Seller and its Consolidated Subsidiaries for the six-month period ended on such
date heretofore furnished to the Purchasers, are complete and correct and fairly
present the consolidated financial condition of the Seller and its Consolidated
Subsidiaries as at said dates and the results of its operations for the fiscal
year and the six-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 Seller 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 4.02.  Since June 30, 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 Seller or any of the
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 4.03  LITIGATION.  Except as disclosed to the Purchasers in
Schedule 4.03, 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 Seller, threatened against or affecting the Seller or
any Subsidiary which both (a) involves the possibility of any judgment or
liability against the Seller 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 4.04  NO BREACH.  Neither the execution and delivery of the Basic
Documents, nor compliance with the terms and provisions thereof 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 Articles of Incorporation or by-laws
of the Seller, the respective charter, by-laws, partnership agreements or
regulations of any Subsidiary or any Governmental Requirement or any material
agreement or instrument to which the Seller or any Subsidiary is a party or by
which it is bound or to which it or its Properties are subject, 

                                      -13-
<PAGE>
 
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 Seller or any Subsidiary pursuant to the terms of any such agreement or
instrument other than the Liens created by the Loan Documents and the
restrictions contained in the Senior Loan Documents (as amended concurrently
herewith) which limit the circumstances in which BOG can make dividends or
distributions to the Seller and in which the Seller can make cash payments of
interest on the Notes.

     Section 4.05  AUTHORITY.  The Seller and each Subsidiary has all
necessary power and authority to execute, deliver and perform its obligations
under the Basic Documents to which it is a party; and the execution, delivery
and performance by the Seller and each Subsidiary of the Basic Documents to
which it is a party, have been duly authorized by all necessary action on its
part; and the Basic Documents constitute the legal, valid and binding
obligations of the Seller 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 4.06  APPROVALS.  Except for registration of the Securities under
the Securities Act, 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 Seller or any Subsidiary of the Basic
Documents or for the validity or enforceability thereof.

     Section   4.07  USE OF LOANS.  The purchase price of the Notes, the
Warrants and the Acquired Shares shall be used solely to pay principal and
interest outstanding on the Senior Loan.  In no event shall the purchase price
of the Notes, the Warrants or the Acquired Shares be used to finance in whole or
in part any hostile acquisition.  The Seller 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, or 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 purchase price of the Notes, the
Warrants or the Acquired Shares will be used to buy or carry any margin stock.

     Section 4.08  ERISA.

          (a)  The Seller and each ERISA Affiliate have complied in all material
respects with ERISA and, where applicable, the Code regarding such 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 Seller 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 Seller or any ERISA Affiliate
has been or is expected by the Seller or 

                                      -14-
<PAGE>
 
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.

          (e)  Full payment when due has been made of all amounts which the
Seller 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.

          (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
Seller'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 Seller 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
Seller or any ERISA Affiliate in its sole discretion at any time without any
material liability.

          (h)  None of the Seller 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 Seller 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 4.09  TAXES.   Except as set out in Schedule 4.09, the Seller and
each Subsidiary 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
Seller or any such Subsidiary, 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 Seller
and its Subsidiaries in respect of taxes and other governmental charges are, in
the opinion of the Seller, adequate.  No tax lien has been filed and, to the
knowledge of the Seller, 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 4.10  TITLES, ETC.

                                      -15-
<PAGE>
 
          (a)  Subject to the matters set out in Schedule 4.10, each of the
Seller and the Subsidiaries has good and defensible title to (i) the Oil and Gas
Properties that are both (A) evaluated in the most recently delivered Reserve
Report and (B) described in Part One of Exhibit A to the Mortgage, free and
clear of all Liens except Liens permitted by Section 8.02 of the Indenture, and
(ii) to the best of Seller's knowledge, the balance of Seller's material
(individually or in the aggregate) Oil and Gas Properties (and/or those of the
Subsidiaries) that are described in the Mortgage or that are otherwise evaluated
in the most recently delivered Reserve Report, are free and clear (to the best
of Seller's knowledge) of all Liens except Liens permitted by Section 8.02 of
the Indenture.  Except for immaterial divergences, after giving full effect to
the Excepted Liens and the matters set forth in Schedule 4.10, the Seller or its
Subsidiaries own 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 the Mortgage, and the ownership of such Hydrocarbon
Interests shall not in any material respect obligate the Seller or its
Subsidiaries 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 the
Mortgage (without a corresponding increase in net revenue interest).  The Seller
does not believe, based upon information in its possession, that its most
recently delivered Reserve Report materially overstates its (or any
Subsidiaries) 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 and that reserve estimates are affected
by the oil and gas prices used in the preparation thereof.

          (b)  All leases and agreements necessary for the conduct of the
business of the Seller 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 Seller and the Subsidiaries.

          (c)  The Properties presently owned, leased or licensed by the Seller
and the Subsidiaries, including, without limitation, all easements and rights of
way, include all Properties necessary to permit the Seller 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 Seller 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 4.11  NO MATERIAL MISSTATEMENTS.  Taken as a whole, the written
information, statements, exhibits, certificates, documents and reports furnished
to the Purchasers by the Seller 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 Seller or any Guarantor.  As of the Closing
Date, there is no fact peculiar to the Seller or any Guarantor which has a
Material Adverse Effect or in the future is reasonably likely to have 

                                      -16-
<PAGE>
 
(so far as the Seller 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 Purchasers by or on behalf of the Seller or any
Guarantor prior to, or on, the Closing Date in connection with the transactions
contemplated hereby.

     Section 4.12  INVESTMENT COMPANY ACT.  Neither the Seller 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 4.13  PUBLIC UTILITY HOLDING COMPANY ACT.  Neither the Seller
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 4.14  SUBSIDIARIES.  Except as set forth on Schedule 4.14, the
Seller has no Subsidiaries or any direct or indirect ownership interest in any
other Persons.  Schedule 4.14 sets forth the ownership interest of the Seller
(direct or indirect) in and to all such Persons.

     Section 4.15  LOCATION OF BUSINESS AND OFFICES.  As of the Closing Date,
the Seller's principal place of business and chief executive offices are located
at the address stated in Section 12.06.  The principal place of business and
chief executive office of each Subsidiary are located at the addresses stated on
Schedule 4.14.

     Section 4.16  DEFAULTS.  Neither the Seller nor any Subsidiary is 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
Seller or any Subsidiary is a party or by which the Seller or any Subsidiary is
bound which default would have a Material Adverse Effect.  No Default hereunder
has occurred and is continuing.  No "Event of Default" under the Senior Loan
Documents has occurred and is continuing nor has Seller or any of its
Subsidiaries received any notice of a "Default" under the Senior Loan Documents
that has triggered a cure period.

     Section 4.17  ENVIRONMENTAL MATTERS.  Except as provided in Schedule
4.17 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 the Seller 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 the Seller
or any of its Subsidiaries nor the operations currently conducted thereon or, to
the best knowledge of the Seller, by any prior owner or operator of such
Property or operation, are in violation of or subject to any 

                                      -17-
<PAGE>
 
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 Seller or any of its Subsidiaries in
connection with the operation or use of any and all Property of the Seller and
each of its Subsidiaries, including without limitation present, or to the best
of Seller'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 the Seller 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
the Seller and each of its Subsidiaries have in the past, during Seller's or its
Subsidiaries' tenure of ownership and to the best of Seller'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 Seller, 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 Seller 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 the Seller 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 the Seller 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 Seller 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 the Seller 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 4.18  COMPLIANCE WITH THE LAW.  Neither the Seller 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

                                      -18-
<PAGE>
 
asserted by any Person through appropriate action) a Material Adverse 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) of the
Seller and its subsidiaries 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 such 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 such 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 such 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, such Oil and Gas Properties (or in the case of
wells located on properties unitized therewith, such unitized properties).

     Section 4.19  INSURANCE.  Schedule 4.19 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 Seller
and each Subsidiary as of the Closing Date.  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 Seller or any Subsidiary is a party; are valid, outstanding and
enforceable policies; provide adequate insurance coverage in at lease 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
Seller and each Subsidiary; will remain in full force and effect through the
respective dates set forth on Schedule 4.19 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 4.19
identifies all material risks, if any, which the Seller, the Subsidiaries and
their respective board of directors or officers have designated as being self
insured.  Neither the Seller 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 is has carried insurance during the
last three years.

     Section 4.20  HEDGING AGREEMENTS.   Schedule 4.20 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 Seller and each Subsidiary, the material terms thereof
(including the type, term, effective date, termination date and notional amounts
of volumes), the net mark to market value thereof, all credit support agreements
relating thereto (including any margin required or supplied), and the
counterparty to each such agreement.

                                      -19-
<PAGE>
 
     Section 4.21  RESTRICTION ON LIENS.  Neither the Seller nor any
Subsidiary is a party to any agreement or arrangement (other than the Loan
Documents and the Senior Loan Documents), or subject to any order, judgment,
writ or decree, which either restricts or purports to restrict ability to grant
Liens to other Persons on or in respect of their respective assets or
Properties.

     Section 4.22  MATERIAL AGREEMENTS.  Set forth on Schedule 4.22 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 the Senior Loan Documents and Hedging
Agreements) providing for, evidencing, securing or otherwise relating to any
material Debt of the Seller or any Subsidiary, and all obligations of the Seller
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 Seller or any such
Subsidiary, and such list correctly set 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 obligations.

     Section 4.23  GAS IMBALANCES.  As of the Closing Date, except as set
forth in the most recent Reserve Report furnished to the Purchasers or on
Schedule 4.23, on a net basis there are no gas imbalances, take or pay or other
prepayments with respect to the Seller's or any Subsidiary's Hydrocarbon
Interests which would require the Seller or such Subsidiary to deliver five
percent (5%) or more of the monthly production from the Seller'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 4.24  CAPITALIZATION.  The authorized Capital Stock of the
Seller consists of: (a) 30,000,000 shares of Common Stock, par value $.01 per
share and (b) 10,000,000 shares of Preferred Stock, par value $.01 per share, of
which there are issued and outstanding 12,253,574 shares of Common Stock and no
other shares of Capital Stock.  All outstanding shares of Common Stock are
validly issued, fully paid and nonassessable and were issued free of preemptive
rights.  Except as set forth on Schedule 4.24, the Seller is not a party to any
voting trust or other agreement with respect to the voting of its Capital Stock.
Except for the Warrants, there are no (i) outstanding securities convertible or
exchangeable into Capital Stock of the Seller or (ii) warrants, contracts,
commitments, agreements, understandings, or arrangements of any kind to which
the Seller is a party relating to the repurchase or issuance of any Capital
Stock.  Except as set forth on Schedule 4.24 and except as contemplated in the
Equity Documents, the Seller is not a party to or bound by any agreement with
respect to any of its securities which grants registration rights to any Person.

     Section 4.25  ACQUIRED SHARES.  When issued and delivered against
payment therefor in accordance with the terms of this Agreement, the Acquired
Shares will be duly and validly issued, fully paid, nonassessable, free of
preemptive rights and free from all taxes payable by the Seller and Liens
(except any Liens created or suffered to be created by the Purchasers) and will
not be subject to any restriction on the voting or transfer thereof created by
the Seller other than in the Equity Documents and the applicable provisions of
federal and state securities laws.

                                      -20-
<PAGE>
 
     Section 4.26  WARRANT SHARES.  When issued and delivered against
payment therefor in accordance with the terms of the Warrants, the Warrant
Shares issuable upon exercise of the Warrants will be duly and validly issued,
fully paid, nonassessable, free of preemptive rights and free from all taxes
payable by the Seller and Liens (except any Liens created or suffered to be
created by the Purchasers) and will not be subject to any restriction on the
voting or transfer thereof created by the Seller other than in the Equity
Documents and the applicable provisions of federal and state securities laws.
The Seller has duly and validly reserved the Warrant Shares, as of the Closing
Date, for issuance upon conversion of the Warrants.

     Section 4.27  NO RESTRICTIONS.  The Seller currently is not, and in the
future will not, be subject to any agreements that purport to impose
restrictions or limitations on the Purchasers, as affiliates of the Seller or
otherwise, without the prior written consent and authorization of each of the
Purchasers.

     Section 4.28  CERTAIN FEES.  Except for the fees payable to ECT
Securities Corp. and JEDI-II pursuant to the Structuring Fee Agreement, no fees
or commissions will be payable by the Seller to brokers, finders, investment
bankers, or Purchasers with respect to the issuance and sale of any of the
Securities or the consummation of the transaction contemplated by this
Agreement.  The Seller agrees that it will indemnify and hold harmless the
Purchasers from and against any and all claims, demands, or liabilities for
broker's, finders, placement, or other similar fees or commissions incurred by
the Seller or alleged to have been incurred by the Seller in connection with the
issuance or sale of the Securities or the consummation of the transaction
contemplated by this Agreement.

                                   ARTICLE V
               REPRESENTATIONS AND WARRANTIES OF THE PURCHASERS

     The Purchasers each represent and warrant to the Seller, which
representations and warranties shall survive the execution of any Basic
Document, that as of the date of this Agreement:

     Section 5.01  INVESTMENT.  Each Purchaser represents and warrants to, and
covenants and agrees with, the Seller that the Securities are being acquired for
its own account and with no intention of distributing or reselling the Notes,
the Warrants, the Warrant Shares or the Acquired Shares in any transaction which
would be in violation of the securities laws of the United States of America or
any State, without prejudice, however, to Purchaser's right at all times to sell
or otherwise dispose of all or any part of the Notes, the Warrants, the Warrant
Shares or the Acquired Shares under a registration statement under the
Securities Act and applicable state securities laws or under an exemption from
such registration available thereunder (including, without limitation, if
available, Rule 144A promulgated thereunder).  If either Purchaser should in the
future decide to dispose of any of the Notes, the Warrants, the Warrant Shares
or the Acquired Shares, the Purchasers understand and agree (i) that it may do
so only (A) in compliance with the Securities Act and applicable state
securities law, as then in effect, and (B) in the manner contemplated by any
registration statement pursuant to which such securities are being offered, and
(ii) that stop-transfer instructions to that effect will be in effect with
respect to such securities.  The Purchasers agree to 

                                      -21-
<PAGE>
 
the imprinting, so long as appropriate, of a legend on each Note and on each
certificate representing Warrants, Warrant Shares or the Acquired Shares, to the
effect as set forth above.

     Section 5.02  NATURE OF PURCHASERS.  Each Purchaser represents and
warrants to, and covenants and agrees with, the Seller that, (i) it is an
"accredited investor" within the meaning of paragraphs (a)(3) or (8) of Rule 501
under the Securities Act and (ii) by reason of its business and financial
experience it has such knowledge, sophistication and experience in business and
financial matters so as to be capable of evaluating the merits and risks of the
prospective investment in the Securities, is able to bear the economic risk of
such investment and, at the present time, would be able to afford a complete
loss of such investment.

     Section 5.03  RECEIPT OF INFORMATION; AUTHORIZATION.  Each Purchaser
acknowledges that it has been furnished all information that it deems necessary
or desirable to the making of an informed investment decision concerning the
Securities.  Each Purchaser acknowledges that it has had an opportunity to ask
questions of and receive satisfactory answers from designated representatives of
the Seller concerning the terms and conditions pursuant to which the purchase of
the Securities are made.  Each Purchaser acknowledges that it has been afforded
an opportunity to examine such documents and other information which it has
requested for the purpose of verifying the information provided to it and for
the purpose of answering any questions it may have concerning the business
affairs and financial condition of the Seller.  Each Purchaser represents that
it alone or with its advisors has knowledge and experience in the business of
the Seller and the Seller so as to be capable of evaluating the merits and risks
of an investment in the Seller based upon the information furnished to it, its
knowledge of the business and affairs of the Seller, the records, files, and
plans of the Seller (which have been made available to it), such additional
information as it has requested and has received from the Seller, and the
independent inquiries and investigations undertaken by it.  Each Purchaser
represents and warrants that the purchase of the Securities by it has been duly
and properly authorized and this Agreement and each Basic Document to which the
Purchasers are a signatory has been duly executed and delivered by it or on its
behalf.

                                  ARTICLE VI
                        CONDITIONS PRECEDENT TO FUNDING

     Section 6.01  CONDITIONS PRECEDENT TO OBLIGATIONS OF THE PURCHASERS.  The
obligation of the Purchasers to acquire the Securities on the Funding Date is
subject to each of the following:

          (a)  The accuracy as of the Closing Date of each and every
representation and warranty of the Seller, each Guarantor, and the Senior Loan
Agent made in this Agreement or any other Basic Document, or in any certificate
delivered to the Purchasers pursuant to or in connection with this Agreement,
and receipt by the Purchasers of a Certificate executed by a duly Responsible
Officer, dated as of the Funding Date, certifying that each of the
representations and warranties of the Seller and each Guarantor made in this
Agreement or any other Basic Document are true and correct as of the Funding
Date, and that the Seller and each Guarantor has performed to date all of its
respective covenants and agreements under the Basic Documents.

                                      -22-
<PAGE>
 
          (b)  The absence as of the Closing Date and the Funding Date of a
Default or Event of Default hereunder or an "Event of Default" under the Senior
Credit Agreement or any Default hereunder the Senior Loan Documents that has
triggered a cure period.

          (c)  The performance by the Seller of its respective obligations to be
performed hereunder on or before the Funding Date.

          (d)  The satisfaction of each of the following conditions as of or
prior to the Closing Date:

               (i)   The Purchasers (or the Trustee, where appropriate) shall
     have received the following, each in form and substance satisfactory to the
     Purchasers and in sufficient counterparts:

                     (A)   Duly executed counterparts of this Agreement and the
          Indenture signed by all the parties hereto and thereto.

                     (B)   The duly executed Financing Agreement, Structuring
          Fee Agreement, Guaranty Agreements, Subordination Agreement and
          Registration Rights Agreement, dated as of the Closing Date in form
          and substance satisfactory to Purchasers.

                     (C)   Duly executed counterparts of the Collateral
          Documents (including without limitation UCC-1 Financing Statements).

                     (D)   Certificates of good standing as to the Seller and
          each Guarantor issued by the Secretary of State of their respective
          states of incorporation or formation.

                     (E)   The duly executed certificate of the Secretary of the
          Seller setting forth (i) resolutions of its directors in form and
          substance satisfactory to the Purchasers with respect to the
          authorization of this Agreement and the other Basic Documents to which
          it is a party and the transactions contemplated hereby and thereby;
          (ii) the names and true signatures of the officers authorized to sign
          such instruments; and (iii) copies of the articles or certificate of
          incorporation and the bylaws of the Seller.

                     (F)   The duly executed certificate of the Secretary of
          each Guarantor which is a corporation setting forth (i) resolutions of
          its directors in form and substance satisfactory to the Purchasers
          with respect to the authorization of the Guaranty Agreements executed
          by such Guarantors and the transactions contemplated hereby and
          thereby; (ii) the names and true signatures of the officers authorized
          to sign such instruments; and (iii) copies of the articles or
          certificate of incorporation and the bylaws of each Guarantor.

                                      -23-
<PAGE>
 
                     (G)   The duly executed certificate of all the partners of
          each Guarantor that is a Partnership and each member of each Guarantor
          that is a limited liability company, setting forth (i) the
          authorization of the Guaranty Agreements and the transactions
          contemplated hereby and thereby; (ii) the names and title of all
          persons authorized to sign such instruments; and (iii) copies of the
          applicable partnership agreement or other regulating documents of each
          such Guarantor.

                     (H)   Evidence that the insurance required hereunder and
          under the other Basic Documents has been obtained and is in full force
          and effect.

                     (I)   Copies of the Senior Loan Documents.

                     (J)   Any other document which the Purchasers may
          reasonably request, including opinions addressed to Purchasers, dated
          as of the Closing Date, from the counsel for the Seller and each of
          the Guarantors acceptable to each of the Purchasers addressing the
          existence and good standing of the Seller, the authorization of the
          Basic Documents, the enforceability of the Basic Documents, the
          absence of conflicts with law, other material agreements, and court
          orders, the absence of litigation, and such other matters as the
          Purchasers may reasonably request.

               (ii)  The Seller shall have executed (but not delivered) the
     Notes, Warrants and Acquired Shares, each in form and substance
     satisfactory to the Purchasers.

               (iii) The Seller shall have received consents to the Basic
     Documents by the Senior Lenders; and the Senior Loan Documents shall have
     been amended in form and substance reasonably satisfactory to Purchasers to
     permit the transactions contemplated by the Loan Documents, including the
     payment of dividends or other distributions by Subsidiaries to the Seller
     in order for the Seller to meet its debt service obligations to the
     Purchasers under the Notes.

               (iv)  The Purchasers shall have completed a due diligence review
     of the Seller and the Subsidiaries to the satisfaction of the Purchasers in
     their sole discretion.

               (v)   The Purchasers shall have received the latest internally
     prepared consolidated financial statements of the Seller and its
     Subsidiaries which shall be at least through June 30, 1998.  Since June 30,
     1998, there shall have occurred no event which could have a Material
     Adverse Effect.

               (vi)  The Board of Directors of each of the Seller, the
     Guarantors, the Purchasers and Enron Corp. must have approved the
     transactions contemplated under this Agreement and the other Basic
     Documents.

               (vii) All other consents, including without limitation any
     required shareholder approval, and waivers necessary to complete the
     transactions under this 

                                      -24-
<PAGE>
 
     Agreement and the other Basic Documents shall have been obtained by the
     Seller, the Guarantors and the Purchasers.

          (e)  The Warrants Shares and the Acquired Shares shall have been
approved for listing on NASDAQ and the registration statement on Form S-1
registering the Notes, the Warrants, and the Acquired Shares shall have been
declared effective by the Commission and no stop order with respect thereto
shall have been issued.

          (f)  The Seller shall have delivered to the Purchasers the executed
Notes, Warrants and Acquired Shares.

          (g)  The Mortgages shall have been filed in two counties of 
Purchasers's choice.

          (h)  The Seller shall have paid to ECT Securities Corp. and JEDI-II
all payments required under the terms of the Structuring Fee Agreement.

          (i)  If requested in writing by either of the Purchasers, a Designee
of the Purchasers shall have been appointed to the Board of Directors of the
Seller pursuant to Section 7.03.

          (j)  The Seller shall have duly and validly reserved the Warrant
Shares for issuance upon conversion of the Warrants.

          (k)  The issuance of the Securities by the Seller shall not as of the
Funding Date be enjoined (temporarily or permanently) under the laws of any
jurisdiction to which the Seller is subject.

          (l)  Each of the Basic Documents shall have been executed and
delivered by all the respective parties thereto and shall be in full force and
effect.

     Section 6.02  CONDITIONS PRECEDENT TO OBLIGATIONS OF THE SELLER.  The
obligations of the Seller to issue and sell Securities hereunder is subject, on
the Funding Date, to the prior or simultaneous satisfaction or waiver of the
following conditions:

          (a)  The representations and warranties made by the Purchasers herein
shall be true and correct in all respects on and as of the Funding Date with the
same effect as though such representations and warranties had been made on and
as of the Funding Date.

          (b)  The Purchasers shall have accepted delivery of and made payment
for the Securities.

          (c)  The issuance of the Securities by the Seller shall not as of the
Funding Date be enjoined (temporarily or permanently) under the laws of any
jurisdiction to which the Seller is subject.

                                      -25-
<PAGE>
 
          (d)  Each of the Basic Documents shall have been executed and
delivered by all the respective parties thereto and shall be in full force and
effect.

     Section 6.03  CONDITIONS PRECEDENT TO THE OBLIGATIONS OF PURCHASERS AND 
SELLER.  The obligations of the Purchasers and Seller hereunder are contingent
upon the Funding Date  occurring on or before 5:00 p.m., Houston, Texas time on
September 1, 1998.

                                  ARTICLE VII
                             AFFIRMATIVE COVENANTS

     Unless the prior written consent to the contrary is obtained from (i) the
holders of the majority of the Warrants (as to Sections 7.01 and 7.02) and (ii)
ECT (as to Sections 7.03 and 7.04) the Seller will, for the benefit of each of
the holders of the Warrants or Warrant Shares and the holders of the Acquired
Shares, comply with the covenants contained in this Article VII (or cause each
Subsidiary's compliance with the applicable covenants).

     Section 7.01  WARRANTS.  Seller shall at all times during the term of
the Warrants maintain a sufficient number of shares of Common Stock of the
Seller to be issued as Warrant Shares upon the exercise of all or part of the
Warrants.  Seller shall (i) notify the holders of the Warrants promptly after
the exercise of any of the Warrants by a holder or holders thereof, of the
exercise thereof, (ii) provide to the holders of the Warrants such information
or materials in connection therewith as may be reasonably requested by the
holders of the Warrants, and (iii) otherwise provide to all the holders of the
Warrants copies of all notices provided to or from the Seller in connection with
the Warrants.  Seller's obligations under this Section 7.01 shall expire upon
expiration of the term of the Warrants.

     Section 7.02  HART-SCOTT-RODINO COMPLIANCE.  As soon as practicable
after the receipt from any holder of the Warrants or any Seller (the "Notice
Giver") 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 Seller 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 any holder of the Warrants (the "Notice Giver"), request
early termination of the waiting period imposed by the HSR Act, (iii) coordinate
and cooperate with the Notice Giver in responding to formal and informal
requests for additional information and documentary material from the DOJ and
the FTC in connection with such filing, and (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 reasonably necessary and appropriate to permit the issuance to the Notice
Giver of the shares of common stock issuance upon the exercise of the warrants
with respect to which any filing is required under the HSR Act, and (v)
reimburse the holders of the Warrants for the entire amount of any filing fee or
any other costs and expenses incurred by holders of the Warrants in connection
therewith (including legal fees), or as required to be paid under the HSR Act.
Seller's obligations under this Section 7.02 shall expire one (1) year following
the expiration of the term of the Warrants.

                                      -26-
<PAGE>
 
     Section 7.03  BOARD REPRESENTATION.  ECT or its designated Affiliate
(the "Acting Party") shall have the right (a) to designate one member of the
Board of Directors of the Seller or (b) (i) to receive (and Seller covenants and
agrees to deliver to the Acting Party) prior notice of any proposed board action
and to receive (and Seller covenants and agrees to deliver to the Acting Party)
reasonable notice of and a right to attend any meeting of the Seller's Board of
Directors, (ii) to receive (and Seller covenants and agrees to deliver to the
Acting Party), promptly after they are produced, all management reports and
accounts relating to the Seller that are provided to Seller's Board of Directors
or any committee of the Board of Directors and (iii) upon reasonable notice, to
have reasonable access to the books and records of the Seller, including
statutory books, minute books and customer lists.  In the event the Acting Party
elects to designate a person to serve as a member of the Board of Directors of
the Seller (the "Designee"), the Seller shall (x) expand as required the number
of directors constituting the entire board, (y) fill the vacancy created by such
expansion with such Designee and (z) submit the name of such Designee to the
stockholders of the Seller (together with a recommendation of his or her
election) at each meeting of stockholders at which directors are elected, until
requested otherwise by the Acting Party. The obligations of the Seller pursuant
to this Section 7.03 shall continue in full force and effect for so long as the
ECT and JEDI-II and/or their respective Affiliates beneficially own 5% or more
of the outstanding Common Stock of the Seller (including the Warrant Shares
represented by the Warrants, whether exercised or not).  Any Designee shall
agree to resign at the request of the Seller, at any time after the expiration
of the rights of the ECT and any Acting Party pursuant to this Section 7.03.
The rights of ECT under this Section 7.03 shall not be assignable other than to
an Affiliate of ECT.

     Section 7.04  COMMON STOCK; DIVIDENDS; VOTING RIGHTS.  The declaration
of dividends by the Seller shall be solely at the discretion of the Board of
Directors of the Seller.  Except for holders of Common Stock, no other class of
Capital Stock of the Seller shall have any voting rights whatsoever, either
separately or in conjunction with the Common Stock.  Seller's obligations under
this Section 7.04 shall expire upon payment of the Notes in full.


                                 ARTICLE VIII
                        [OMITTED BY THE PARTIES HERETO]


                                  ARTICLE IX
                        [OMITTED BY THE PARTIES HERETO]


                                   ARTICLE X
                        [OMITTED BY THE PARTIES HERETO]


                                  ARTICLE XI
                        [OMITTED BY THE PARTIES HERETO]

                                      -27-
<PAGE>
 
                                  ARTICLE XII
                                 MISCELLANEOUS

     Section 12.01.  INTERPRETATION AND SURVIVAL OF PROVISIONS.  Article,
Section, Schedule, and Exhibit references are to this Agreement, unless
otherwise specified.  All references to instruments, documents, contracts, and
agreements are references to such instruments, documents, contracts, and
agreements as the same may be amended, supplemented, and otherwise modified from
time to time, unless otherwise specified.  The word "including" shall mean
"including but not limited to."  Whenever the Seller has an obligation under the
Basic Documents, the expense of complying with that obligation shall be an
expense of the Seller unless otherwise specified.  Whenever any determination,
consent, or approval is to be made or given by the Purchasers, any holder of the
Warrants or the Acquired Shares, such action shall be in such Person's sole
discretion unless otherwise specified in this Agreement.  If any provision in
the Basic Documents is held to be illegal, invalid, not binding, or
unenforceable, such provision shall be fully severable and the Basic Documents
shall be construed and enforced as if such illegal, invalid, not binding, or
unenforceable provision had never comprised a part of the Basic Documents, and
the remaining provisions shall remain in full force and effect.  The Basic
Documents have been reviewed and negotiated by sophisticated parties with access
to legal counsel and shall not be construed against the drafter.  The
representations, warranties, and covenants made in this Agreement, the Notes or
any other Basic Document shall remain operative and in full force and effect
regardless of (a) any investigation made by or on behalf of the Seller or the
Purchasers or (b) acceptance of any of the Securities and payment therefor and
repayment or repurchase thereof.  All indemnification obligations of the Seller
and the provisions of Section 12.02 shall remain operative and in full force and
effect unless such obligations are expressly terminated in a writing referencing
those individual Sections, regardless of any purported general termination of
this Agreement.

     Section 12.02  COSTS, EXPENSES AND TAXES. 

          (a)   Intentionally Deleted.

          (b)   The Seller agrees to indemnify the Purchasers, and their
respective officers, directors, employees, representatives, agents, attorneys,
and Affiliates (collectively, "Related Parties") from, hold each of them
harmless against and promptly upon demand pay or reimburse each of them for, any
and all actions, suits, proceedings (including any investigations, litigation,
or inquiries), claims, demands, and causes of action by third parties, and, in
connection therewith, all reasonable costs, losses, liabilities, damages, or
expenses of any kind or nature whatsoever (collectively 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 Seller of the
proceeds of any sale of the Securities, (ii) the operations of the business of
the Seller or any Subsidiary, (iii) any bodily injury or death or property
damage occurring in or upon or in the vicinity of any Collateral, (iv) any claim
by any third Person against any Collateral assigned to or paid to any Noteholder
pursuant to any Collateral Document, (v) the failure of the Seller or any
Subsidiary to comply with any Governmental Requirement, or (vi) any other aspect
of this Agreement and the other Basic 

                                      -28-
<PAGE>
 
Documents, 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 INDEMNITEE (but excluding all Indemnity Matters arising solely by reason
of claims between the Purchasers or any Purchaser's shareholders against any
Purchaser or by reason of the gross negligence or wilful misconduct of any
Indemnitee).

          (c)  The Seller agrees to pay and hold the Purchasers harmless from
and against any and all present and future stamp and other similar taxes with
respect to this Agreement and the  Equity Documents and save the Purchasers
harmless from and against any and all liabilities with respect to or resulting
from any delay or omission to pay such taxes, and will indemnify the Purchasers
for the full amount of taxes paid by the Purchasers in respect of payments made
or to be made under this Agreement, any other Equity Document and any liability
(including penalties, interest, and expenses) arising therefrom or with respect
thereto, whether or not such taxes were correctly or legally asserted.

          (d)  In the case of any indemnification hereunder, the Purchaser or
other Person indemnified hereunder shall give notice to the Seller within a
reasonable period of time of any such claim or demand being made against the
Purchaser or other indemnified Person and the Seller, at its sole cost and
expense, shall provide a defense of such claim, provided, however, that, (i) if
the Seller has failed to assume the defense and employ counsel or (ii) if the
defendants in any such action include both the indemnified party and the Seller
or any Subsidiary and counsel to the indemnified party shall have concluded that
there may be reasonable defenses available to the indemnified party that are
different from or additional to those available to the Seller or such Subsidiary
or if the interests of the indemnified party reasonably may be deemed to
conflict with the interest of the Seller or such Subsidiary, then the
indemnified party shall have the right to select a separate counsel and to
assume such legal defense and otherwise to participate in the defense of such
action, with the expenses and fees of such separate counsel and other expenses
related to such participation to be reimbursed by the Seller as incurred.

          (e)  No indemnitee 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
settlement that an indemnitee proposes if the indemnitor does not have the
financial ability to pay all its obligations outstanding and asserted against
the indemnitee at that time, including the maximum potential claims against the
indemnitee to be indemnified pursuant to this Section 12.02.

          (f)  This Section 12.02 shall not apply to actions, suits,
proceedings, investigations, demands, losses, liabilities, claims, damages,
deficiencies, interest, judgements, costs, or expenses relating to any Property
to the extent arising from the acts or omissions of the Agent or any Noteholder
during the period after which such Person, its successors or assigns shall have
acquired possession of such Property (whether through foreclosure or deed in
lieu of foreclosure, as mortgagee in possession or otherwise).

                                      -29-
<PAGE>
 
          (g)  The Seller's obligations under this Section 12.02 shall survive
any termination of this Agreement and the payment of the Obligations.

     Section 12.03  NO WAIVER; MODIFICATIONS IN WRITING. 

          (a)  No failure or delay on the part of the Seller or the Purchasers
in exercising any right, power, or remedy hereunder shall operate as a waiver
thereof, nor shall any single or partial exercise of any such right, power, or
remedy preclude any other or further exercise thereof or the exercise of any
right, power, or remedy.  The remedies provided for herein are cumulative and
are not exclusive of any remedies that may be available to the Seller or the
Purchasers at law or in equity or otherwise.

          (b)  Except as otherwise provided herein, no amendment, waiver,
consent, modification, or termination of any provision of this Agreement, shall
be effective unless signed by the Seller and the holders of more than 50% of the
outstanding principal balance of the Notes and the holders of more than 50% of
the Warrants.  Any amendment, supplement or modification of or to any provision
of this Agreement or any other Equity Document, any waiver of any provision of
this Agreement or any other Equity Document, and any consent to any departure by
the Seller from the terms of any provision of this Agreement or any other Equity
Document, shall be effective only in the specific instance and for the specific
purpose for which made or given.  Except where notice is specifically required
by this Agreement, no notice to or demand on the Seller in any case shall
entitle the Seller to any other or further notice or demand in similar or other
circumstances.

     Section 12.04  BINDING EFFECT; ASSIGNMENT.  This Agreement shall be
binding upon the Seller and the Purchasers, and their respective successors and
permitted assigns. Except as expressly provided in this Agreement, this
Agreement shall not be construed so as to confer any right or benefit upon any
Person other than the parties to this Agreement, and their respective successors
and permitted assigns.  Subject to applicable federal and state securities laws
the rights and obligations of the Purchasers under this Agreement with respect
to the Warrants and the Equity Documents may be sold, assigned or pledged by any
Purchaser, in whole or in part, in accordance with the provisions of the
Warrants, and upon any such assignment, the holders of the Warrants shall
succeed to all of the selling Purchaser's rights and obligations under this
Agreement with respect to the Warrants and the Equity Documents to the extent
assigned and the selling Purchaser shall be automatically released from any
obligations thereunder with respect to the Warrants and the Equity Documents to
the extent assigned.  Subject to applicable federal and state securities laws
the Acquired Shares may be sold, assigned or pledged subject only to the
Registration Rights Agreement and upon any such assignment the holders of the
Acquired Shares shall succeed to the Purchaser's rights and obligations under
the Registration Rights Agreement.  Upon request of any Purchaser in connection
with any transfer of the Warrants or Acquired Shares, the Seller shall execute
and deliver any amendment to this Agreement, the Warrants, and the other Equity
Documents reasonably requested by the Purchaser to reflect the transfer and
delineate the rights of the transferor and the transferee.

     Section 12.05  REPLACEMENT SECURITIES.  Upon receipt of evidence
satisfactory to the Seller of the loss, theft, destruction, or mutilation of any
Warrants, Warrant Shares or Acquired Shares and, 

                                      -30-
<PAGE>
 
in the case of any such loss, theft, or destruction, upon delivery of any
unsecured letter of indemnity reasonably satisfactory to the Seller or, in the
case of any such mutilation, upon surrender or cancellation thereof, the Seller
will issue a new Warrants, Warrant Shares or Acquired Shares, as applicable.

     Section 12.06  COMMUNICATIONS.  All notices and demands provided for
hereunder shall be in writing and shall be given by registered or certified
mail, return receipt requested, telecopy, air courier guaranteeing overnight
delivery or personal delivery to the following addresses:

     If to the Purchasers:

     Enron Capital Management II Limited Partnership
     c/o Enron Capital II Corp.
     1400 Smith Street
     Houston, Texas 77002
     Attention: Shirley Hudler
     Telecopier: (713) 646-8008

     and

     Enron Capital & Trade Resources Corp.
     1400 Smith Street
     Houston, Texas 77002
     Attention: Donna Lowry
     Telecopier: (713) 646-4039

     If to the Seller:

     6300 Bridge Point Parkway
     Building 2, Suite 500
     Austin, Texas 78730
     Attention: Craig M. Fleming
     Telecopier: (512) 472-3400

or to such other address as the Seller or any Purchaser may designate in
writing.  All other communications may be by regular mail.  All notices and
communications shall be deemed to have been duly given:  at the time delivered
by hand, if personally delivered; four days after being sent by certified mail,
return receipt requested, if mailed; when receipt acknowledged, if telecopied;
and on the next Business Day if timely delivered to an air courier guaranteeing
overnight delivery.

     Section 12.07  GOVERNING LAW.  This Agreement will be construed in
accordance with and governed by the laws of the State of Texas without regard to
principles of conflicts of laws.

     Section 12.08  ARBITRATION.

                                      -31-
<PAGE>
 
          (a)  BINDING ARBITRATION.  Subject to the provisions of subparagraph
(e), on the request of either the Seller or any Purchaser, whether made before
or after the institution of any legal proceeding, any action, dispute, claim or
controversy of any kind now existing or hereafter arising between any of the
parties hereto in any way arising out of, pertaining to or in connection with
this Agreement (a "Dispute") shall be resolved by binding arbitration in
accordance with the terms hereof.  Either the Seller or any Purchaser may, by
summary proceedings, bring an action in court to compel arbitration of any
Dispute.

          (b)  GOVERNING RULES.  Any arbitration shall be administered by the
American Arbitration Association (the "AAA") in accordance with the terms of
this Section, the Commercial Arbitration Rules of the AAA, and, to the maximum
extent applicable, the Federal Arbitration Act.  Judgment on any award rendered
by an arbitrator may be entered in any court having jurisdiction.

          (c)  ARBITRATORS.  Any arbitration shall be conducted before a three
person panel of neutral arbitrators. Such panel shall consist of one person from
each of the following categories: (1) an attorney who has practiced in the area
of commercial law for at least 10 years or a retired judge at the Texas or
United States District Court or an appellate court level; (2) a person with at
least 10 years experience in commercial lending; and (3) a person with at least
10 years experience in the energy service industry. The AAA shall submit a list
of persons meeting the criteria outlined above for each category of arbitrator,
and the parties shall select one person from each category in the manner
established by the AAA. If the parties cannot agree on an arbitrator within 30
days after the request for an arbitration, then any party may request the AAA to
select an arbitrator. The arbitrator may engage engineers, accountants or other
consultants that the arbitrator deems necessary to render a conclusion in the
arbitration proceeding.

          (d)  CONDUCT OF ARBITRATION.  To the maximum extent practicable, an
arbitration proceeding hereunder shall be concluded within 180 days of the
filing of the Dispute with the AAA.  Arbitration proceedings shall be conducted
in Houston, Texas.  At the conclusion of any arbitration proceeding, the
arbitrator shall make specific written findings of fact and conclusions of law.
The arbitrator shall have the power to award recovery of all costs and fees to
the prevailing party.  The Seller and the Purchasers each agree to keep all
Disputes and arbitration proceedings strictly confidential except for disclosure
of information required by applicable law.

          (e)  COSTS OF ARBITRATION.  All fees of the arbitrator and any
engineer, accountant or other consultant engaged by the arbitrator, shall be
paid by the Seller (as to 50%) and the Purchasers (as to 50%) unless otherwise
awarded by the arbitrator.

     Section 12.09  EXECUTION IN COUNTERPARTS.  This Agreement may be executed
in any number of counterparts and by different parties hereto in separate
counterparts, each of which counterparts, when so executed and delivered, shall
be deemed to be an original and all of which counterparts, taken together, shall
constitute but one and the same Agreement.

                                      -32-
<PAGE>
 
          IN WITNESS WHEREOF, the parties hereto execute this Agreement,
effective as of the date first above written.

                              BRIGHAM EXPLORATION COMPANY,
                              a Delaware corporation



                              By:
                                  ---------------------------------------------
                                    Craig M. Fleming
                                    Chief Financial Officer

                                      -33-
<PAGE>
 
                              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:
                                             ----------------------------------
                                         Name:
                                               --------------------------------
                                         Title:
                                                -------------------------------


                              ENRON CAPITAL & TRADE RESOURCES
                              CORP., a Delaware corporation



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

                                      -34-

<PAGE>
 
                         REGISTRATION RIGHTS AGREEMENT

     This Registration Rights Agreement (this "Agreement") is made and entered
into as of August 20, 1998, by and among Brigham Exploration Company, a Delaware
corporation (the "Company"), Joint Energy Development Investments II Limited
Partnership, a Delaware limited partnership ("JEDI"), and Enron Capital & Trade
Resources Corp., a Delaware corporation ("ECT").

     This Agreement is made pursuant to the Securities Purchase Agreement.  In
order to induce ECT and JEDI to enter into the Securities Purchase Agreement,
the Company has agreed to provide the registration and other rights set forth in
this Agreement.  Pursuant to the Securities Purchase Agreement, ECT and JEDI
will purchase the Acquired Shares and Warrants.  The execution and delivery of
this Agreement is a condition to the Closing (as defined in the Securities
Purchase Agreement).

     The parties agree as follows:

                                 ARTICLE I

     Section 1.01.  Definitions.  Capitalized terms used herein without
definition shall have the meanings given to them in the Securities Purchase
Agreement.  The terms set forth below are used herein as so defined:

          "Commission" has the meaning specified therefor in Section 1.02 of
this Agreement.

          "Common Stock" means the common stock, par value $0.01 per share, of
the Company.

          "Exchange Act" shall mean the Securities Exchange Act of 1934, as
amended, and the rules and regulations promulgated thereunder.

          "Holder" means the record holder of any Registrable Securities.

          "Inspector" has the meaning specified therefor in Section 2.03 this
Agreement.

          "Losses" has the meaning specified therefor in Section 2.07 of this
Agreement.

          "Other Holders" has the meaning specified therefor in Section 2.01 of
this Agreement.

          "Person" means any individual, corporation, limited liability company,
partnership, joint venture, association, joint-stock company, business trust,
trust or unincorporated entity.

          "Records" has the meaning specified therefor in Section 2.03 of this
Agreement.
<PAGE>
 
          "Registrable Securities" means the Acquired Shares, the Warrants, the
Warrant Shares and any other securities issued upon the exercise of the
Warrants, until such time as such securities cease to be Registrable Securities
pursuant to Section 1.02 hereof.

          "Requesting Holder(s)" has the meaning specified therefor in Section
2.01 of this Agreement.

          "Request Notice" has the meaning specified therefor in Section 2.01 of
this Agreement.

          "Registration Statement" has the meaning specified therefor in Section
2.01 of this Agreement.

          "Securities Act" has the meaning specified therefor in Section 1.02 of
this Agreement.

          "Securities Purchase Agreement" means the Securities Purchase
Agreement, dated as of August 20, 1998, among the Company, ECT and JEDI,
individually and as agent.

          "Selling Holder" means a Holder who is selling Registrable Securities
pursuant to a Registration Statement.

     Section 1.02.  Registrable Securities.  Any Registrable Security will cease
to be a Registrable Security when (i) a Registration Statement covering such
Registrable Security has been declared effective by the Securities and Exchange
Commission (the "Commission") and such Registrable Security has been sold or
disposed of pursuant to such effective Registration Statement; (ii) such
Registrable Security is disposed of pursuant to Rule 144 (or any similar
provision then in force) under the Securities Act of 1933, as amended (the
"Securities Act");  (iii) such Registrable Security is eligible to be, and at
the time of determination can be, disposed of pursuant to paragraph (k) of Rule
144 (or any similar provision then in force) under the Securities Act; or (iv)
such Registrable Security is held by the Company or one of its subsidiaries.

                                 ARTICLE II

     Section 2.01.  Demand Registration. (a) Any time after the Funding Date, as
defined in the Securities Purchase Agreement, (i) any Holder or Holders who
collectively beneficially own at least 25% (twenty-five percent) of the
Registrable Securities may request (a "Request Notice") the Company to register
under the Securities Act (other than pursuant to a shelf registration on Form S-
3) all or any portion of the Registrable Securities that are held by such Holder
or Holders (collectively, the "Requesting Holder") for sale in the manner
specified in the Request Notice and (ii) in the event that the Company is
eligible to file a Registration Statement on Form S-3, any Holders who
collectively beneficially own at least a majority of the Registrable Securities
may submit a Request Notice to the Company to register under Form S-3 all or any
portion of the Registrable Securities that are held by such Requesting Holder(s)
for sale in the manner specified in the Request Notice.

                                       2
<PAGE>
 
          (b) Promptly following receipt of a Request Notice, the Company shall
immediately notify each Holder (except the Requesting Holder) of the receipt of
a Request Notice and shall use its best efforts to file a registration statement
under the Securities Act (each such registration statement is hereinafter
referred to as a "Registration Statement") effecting the registration under the
Securities Act, for public sale in accordance with the method of disposition
specified in such Request Notice, of the Registrable Securities specified in the
Request Notice (and in any notices that the Company receives from other Holders
no later than the 15th day after receipt of the notice sent by the Company)
(such other Holders and the Requesting Holder are hereinafter referred to as the
"Requesting Holders").  If such method of disposition shall be an underwritten
public offering, the Requesting Holders holding a majority of the Registerable
Securities to be registered may designate the managing underwriter of such
offering, subject to the approval of the Company, which approval shall not be
withheld unreasonably.  The Company shall be obligated to register Registrable
Securities pursuant to this Section 2.01 on two occasions only.  A request
pursuant to this Section 2.01 shall be counted ("Counted") only when (i) all the
Registrable Securities requested to be included in any such registration have
been so included, (ii) the corresponding Registration Statement has become
effective under the Securities Act, and (iii) the public offering has been
consummated and the Registrable Securities have been sold on the terms and
conditions specified therein; provided, however, that in the event of a shelf
registration if the Company is then eligible to file a Registration Statement on
Form S-3, the Company shall keep such Registration Statement effective for two
years from the effective date of the Registration Statement.

          (c) The Company may delay the filing or effectiveness of a
Registration Statement after receipt of a Request Notice (i) for up to 90 days
if at the time of such request, the Company is engaged in a firm commitment
underwritten public offering of its securities in which Holders may include
Registrable Securities and for which the Company has delivered the notice to the
Holders required by Section 2.02 or (ii) for up to 60 days if at the time of
such request the Board of Directors of the Company determines in its reasonable
judgment and in good faith that the filing of such a Registration Statement or
the making of any required disclosure in connection therewith would have a
material adverse effect on the Company or substantially interfere with a
significant transaction in which the Company is then engaged; provided that the
Company may not delay the filing of a Registration Statement in reliance on this
clause (ii) more than once during any period of twelve consecutive calendar
months.

          (d) The Company and the parties to the Registration Rights Agreement
with the Company dated February 26, 1997, who are entitled to piggy-back
registration rights as of the Closing Date ("Other Holders") with respect to a
Registration Statement filed pursuant to Section 2.01 may include securities of
the Company in such Registration Statement, but only to the extent that, in the
good faith opinion of the managing underwriter (if such method of disposition
shall be an underwritten public offering) supported by written reasons therefor,
the inclusion of such shares would not raise a substantial doubt as to whether
the proposed offering could successfully be consummated.  Subject to Section
2.01(c) above, except as provided in this subsection (d), the Company will not
effect any other registration of its equity securities (except with respect to
Registration Statements on Form S-4 or S-8 or for purposes permissible under
such forms as of the date hereof), whether for its own account or that of any
Other Holder, from the date of receipt of a 

                                       3
<PAGE>
 
Request Notice related to an underwritten public offering until the completion
of the distribution by the underwriters of all securities thereunder.

          (e) Exercise of the right to convert the Warrants to Warrant Shares
shall at the Holder's sole election and discretion be contingent upon the
registration of the Warrant Shares in accordance with this Agreement and should
such registration not be completed pursuant to the terms hereof, Holder shall
have the right, at its sole discretion, to rescind its election to convert the
Warrants.

          (f) From and after the date of this Agreement and until no Registrable
Securities remain outstanding, the Company shall not grant registration rights
to any Person if such rights would conflict with the provisions of this
Agreement.

          Section 2.02.  Piggy-Back Registration.  If the Company proposes to
register any of its equity securities under the Securities Act for sale to the
public, whether for its own account or for the account of Other Holders or both
(except with respect to Registration Statements on Forms S-4 or S-8 or for
purposes permissible under such forms as of the date hereof), each such time it
will give written notice to all Holders of its intention to do so no less than
20 days prior to the anticipated filing date.  Upon the written request received
by the Company from any Holder no later than the 15th day after receipt by such
Holder of the notice sent by the Company (which request shall state the intended
method of disposition thereof),  the Company will use best efforts to cause the
Registrable Securities as to which registration shall have been so requested to
be included in the securities to be covered by such Registration Statement, all
to the extent requisite to permit the sale or other disposition by each Holder
(in accordance with its written request) of such Registrable Securities so
registered; provided, however, that the Company may at any time prior to the
effectiveness of any such Registration Statement, in its sole discretion and
without the consent of any Holder, abandon any proposed offering by the Company
in which any Holder had requested to participate.  The number of Registrable
Securities to be included in such a registration may be reduced or eliminated if
and to the extent, in the case of an underwritten offering, the managing
underwriter shall advise the Company that such inclusion would materially
jeopardize the successful marketing of the securities (including the Registrable
Securities) proposed to be sold therein; provided, however, that such number of
shares of Registrable Securities shall not be reduced if any securities included
in such registration are included other than for the account of the Company
unless the shares included in the Registration for the account of such Persons
are also reduced on a pro rata basis, provided, in the case of a Registration
Statement filed pursuant to the exercise of demand registration rights of any
Other Holders, priority shall be given first to the Other Holders demanding such
registration.

          Section 2.03.  Registration Procedures.  If and whenever the Company
is required pursuant to this Agreement to effect the registration of any of the
Registrable Securities under the Securities Act, the Company will, as
expeditiously as possible:

          (a) prepare and file with the Commission a Registration Statement, on
a form available to the Company, with respect to such securities (which filing
shall be made (i) as promptly 

                                       4
<PAGE>
 
as possible (but in no event later than 30 days after the receipt by the Company
of a Request Notice) in the case of a shelf registration if the Company is then
eligible to file a Registration Statement on Form S-3 or (ii) as promptly as
possible (but in no event later than 60 days after the receipt by the Company of
a Request Notice) in the case of any underwritten offering or if the Company is
not eligible to file a Registration Statement on Form S-3, provided that in no
event will the Company be obligated to file a Registration Statement pursuant to
(i) or (ii) prior to the Funding Date pursuant to the Securities Purchase
Agreement. The Company shall thereafter use best efforts to cause such
Registration Statement to become and remain effective for the period of the
distribution in order for it to be Counted;

          (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 for
the distribution period to be Counted and as may be necessary to comply with the
provisions of the Securities Act with respect to the disposition of all
securities covered by such Registration Statement in accordance with the Holders
intended method of disposition;

          (c) furnish to each Selling Holder and to each underwriter such number
of copies of the Registration Statement and the prospectus included therein
(including each preliminary prospectus and each document incorporated by
reference therein to the extent then required by the rules and regulations of
the Commission) as such Persons may reasonably request in order to facilitate
the public sale or other disposition of the Registrable Securities covered by
such Registration Statement;

          (d) if applicable, use best efforts to register or qualify the
Registrable Securities covered by such Registration Statement under the
securities or blue sky laws of such jurisdictions as the Selling Holders or, in
the case of an underwritten public offering, the managing underwriter, shall
reasonably request, provided that the Company will not be required to qualify
generally to transact business in any jurisdiction where it is not then required
to so qualify or to take any action that would subject it to general service of
process in any such jurisdiction where it is not then so subject;

          (e) immediately notify each Selling Holder and each underwriter, at
any time when a prospectus relating thereto is required to be delivered under
the Securities Act, of the happening of any event as a result of which the
prospectus contained in such Registration Statement, as then in effect, includes
an untrue statement of a material fact or omits to state any material fact
required to be stated therein or necessary to make the statements therein not
misleading in the light of the circumstances then existing and as promptly as
practicable amend or supplement the prospectus or take other appropriate action
so that the prospectus does not include an untrue statement of a material fact
or omit to state a material fact required to be stated therein or necessary to
make the statements therein not misleading in the light of the circumstances
then existing;

          (f) in the case of an underwritten public offering, furnish upon
request, (i) on the date that Registrable Securities are delivered to the
underwriters for sale pursuant to such 

                                       5
<PAGE>
 
Registration Statement, an opinion of counsel for the Company dated as of such
date and addressed to the underwriters and to the Selling Holders, stating that
such Registration Statement has become effective under the Securities Act and
that (A) to the best knowledge of such counsel, no stop order suspending the
effectiveness thereof has been issued and no proceedings for that purpose have
been instituted or are pending or contemplated under the Securities Act, (B) the
Registration Statement, the related prospectus, and each amendment or supplement
thereof, comply as to form in all material respects with the requirements of the
Securities Act and the applicable rules and regulations thereunder of the
Commission (except that such counsel need express no opinion as to the financial
statements, or any expertized schedule, report or information contained or
incorporated therein) and (C) to such other effects as may reasonably be
requested by counsel for the underwriters, and (ii) on the effective date of the
Registration Statement and on the date that Registrable Securities are delivered
to the underwriters for sale pursuant to such Registration Statement, a letter
dated such dates from the independent accountants retained by the Company,
addressed to the underwriters and, if available, to the Selling Holders, stating
that they are independent public accountants within the meaning of the
Securities Act and that, in the opinion of such accountants, the financial
statements of the Company and the schedules thereto that are included or
incorporated by reference in the Registration Statement or the prospectus, or
any amendment or supplement thereof, comply as to form in all material respects
with the applicable requirements of the Securities Act and the published rules
and regulations thereunder, and such letter shall additionally address such
other financial matters (including information as to the period ending no more
than five business days prior to the date of such letter) included in the
Registration Statement in respect of which such letter is being given as the
underwriters may reasonably request;

          (g) make available for inspection by the Selling Holders designated by
a majority thereof, any underwriter participating in any distribution pursuant
to such Registration Statement, and any attorney, accountant or other agent
retained by such representative of the Selling Holders or underwriter (the
"Inspectors"),  all financial and other records, pertinent corporate documents
and properties of the Company (collectively, the "Records"), and cause the
Company's officers, directors and employees to supply all information reasonably
requested by any such Inspector in connection with such Registration Statement.

          (h) cause the Registerable Securities to be listed on New York Stock
Exchange, American Stock Exchange or on the NASDAQ National Market if the Common
Stock is or becomes so listed;

          (i) use best efforts to keep effective and maintain for the period of
distribution to be Counted, qualification, approval or listing obtained to cover
the Registrable Securities as may be necessary for the Selling Holders to
dispose thereof and shall from time to time amend or supplement any prospectus
used in connection therewith to the extent necessary in order to comply with
applicable law;

          (j) use best efforts to cause the Registrable Securities to be
registered with or approved by such other governmental agencies or authorities
as may be necessary by virtue of the 

                                       6
<PAGE>
 
business and operations of the Company to enable the Selling Holders to
consummate the disposition of such Registrable Securities; and

          (k) take such other actions as are reasonably requested by the Selling
Holders or the underwriters, if any, in order to expedite, facilitate or
consummate the disposition of such Registrable Securities.

     In connection with each registration hereunder with respect to an
underwritten public offering, the Company and each Selling Holder agrees to
enter into a written agreement with the managing underwriter or underwriters
selected in the manner herein provided in such form and containing such
provisions as are customary in the securities business for such an arrangement
between underwriters and companies of the Company's size and investment stature,
provided that such agreement shall not contain any such provision applicable to
the Company or the Selling Holders that is inconsistent with the provisions
hereof; and further provided, that the time and place of the closing under said
agreement shall be as mutually agreed upon among the Company, the Selling
Holders and such managing underwriter.  In connection with each registration
hereunder, each Selling Holder will furnish promptly to the Company in writing
such information with respect to itself and the proposed distribution by it as
shall be necessary in order to ensure compliance with federal and applicable
state securities laws.

     Section 2.04.  Restrictions on Public Sale by Selling Holders of
Registrable Securities.   To the extent not inconsistent with applicable law,
including insurance codes, each Selling Holder whose Registrable Securities are
included in a Registration Statement pursuant to this Agreement agrees not to
effect any public sale or distribution of the issue being registered (or any
securities of the Company convertible into or exchangeable or exercisable for
securities of the same type as the issue being registered) during the 14 days
before, and during the 90-day period beginning on, the effective date of such
Registration Statement (except as part of such registration), but only if and to
the extent requested in writing (with reasonable prior notice) by the managing
underwriter or underwriters in the case of an underwritten public offering by
the Company of securities of the same type as the Registrable Securities,
provided that the duration of the foregoing restrictions shall be no longer than
the duration of the shortest restriction imposed by the underwriters on the
officers or directors or any other stockholder of the Company; and provided
further, that the period of time for which the Company is required to keep such
registration statement which includes Registrable Securities continuously
effective shall be increased by a period equal to such requested holdback
period.

     Section 2.05.  Restrictions on Public Sale by the Company.  To the extent
required by an underwriter in an underwritten public offering, the Company
agrees not to effect on its own behalf any public sale or distribution of any
securities similar to those being registered, or any securities convertible into
or exchangeable or exercisable for such securities, during the 14 days before,
and during the 90-day period beginning on, the effective date of any
registration statement in which the Selling Holders of Registrable Securities
are participating, other than pursuant to such registration statement or a
Registration Statement on Form S-8 or Form S-4.

                                       7
<PAGE>
 
     Section 2.06.  Expenses.

          (a)  "Registration Expenses" means all expenses incident to the
Company's performance under or compliance with this Agreement, including without
limitation, all registration and filing fees, blue sky fees and expenses,
printing expenses, listing fees, fees and disbursements of counsel and
independent public accountants for the Company, fees of the National Association
of Securities Dealers, Inc., transfer taxes, fees of transfer agents and
registrars, costs of insurance and reasonable out-of-pocket expenses (including
without limitation, reasonable legal fees of one counsel for all Selling
Holders), but excluding any Selling Expenses.  "Selling Expenses" means all
underwriting fees, discounts and selling commissions allocable to the sale of
the Registrable Securities.

          (b) The Company will pay all Registration Expenses in connection with
each Registration Statement filed pursuant to this Agreement, whether or not the
Registration Statement becomes effective, and the Selling Holders shall pay all
Selling Expenses in connection with any Registrable Securities registered
pursuant to this Agreement.

     Section 2.07.  Indemnification.  (a)   In the event of a registration of
any Registrable Securities under the Securities Act pursuant to this Agreement,
the Company will indemnify and hold harmless each Selling Holder thereunder and
each underwriter, pursuant to the applicable underwriting agreement with such
underwriter, of Registrable Securities thereunder and each Person, if any, who
controls such Selling Holder or underwriter within the meaning of the Securities
Act and the Exchange Act, against any losses, claims, damages or liabilities
(including reasonable attorneys' fees) ("Losses"), joint or several, to which
such Selling Holder or underwriter or controlling Person may become subject
under the Securities Act, the Exchange Act or otherwise, insofar as such Losses,
(or actions in respect thereof) arise out of or are based upon any untrue
statement or alleged untrue statement of any material fact contained in any
Registration Statement under which such Registrable Securities were registered
under the Securities Act pursuant to this Agreement, any preliminary prospectus
or final prospectus contained therein, or any amendment or supplement thereof,
or arise out of or are based upon the omission or alleged omission to state
therein a material fact required to be stated therein or necessary to make the
statements therein not misleading, and will reimburse each such Selling Holder,
each such underwriter and each such controlling Person for any legal or other
expenses reasonably incurred by them in connection with investigating or
defending any such Loss or actions; provided, however, that the Company will
not be liable in any such case if and to the extent that any such loss, claim,
damage or liability arises out of or is based upon an untrue statement or
alleged untrue statement or omission or alleged omission so made in conformity
with information furnished by such Selling Holder, such underwriter or such
controlling Person in writing specifically for use in such Registration
Statement or prospectus.

          (b) Each Selling Holder agrees to indemnify and hold harmless the
Company, its directors, officers, employees and agents and each Person, if any,
who controls the Company within the meaning of the Securities Act or of the
Exchange Act to the same extent as the foregoing indemnity from the Company to
such Selling Holder, but only with respect to information regarding such Selling
Holder furnished in writing by or on behalf of such Selling Holder expressly for

                                       8
<PAGE>
 
inclusion in any Registration Statement or prospectus relating to the
Registrable Securities, or any amendment or supplement thereto; provided,
however, that the liability of such Selling Holder shall not be greater in
amount than the dollar amount of the proceeds (net of any Selling Expenses)
received by such Selling Holder from the sale of the Registrable Securities
giving rise to such indemnification.

          (c) Promptly after receipt by an indemnified party hereunder of notice
of the commencement of any action, such indemnified party shall, if a claim in
respect thereof is to be made against the indemnifying party hereunder, notify
the indemnifying party in writing thereof, but the omission so to notify the
indemnifying party shall not relieve it from any liability which it may have to
any indemnified party.  In case any such action shall be brought against any
indemnified party and it shall notify the indemnifying party of the commencement
thereof, the indemnifying party shall be entitled to participate in and, to the
extent it shall wish, to assume and undertake the defense thereof with counsel
reasonably satisfactory to such indemnified party and, after notice from the
indemnifying party to such indemnified party of its election so to assume and
undertake the defense thereof, the indemnifying party shall not be liable to
such indemnified party under this Section 2.07 for any legal expenses
subsequently incurred by such indemnified party in connection with the defense
thereof other than reasonable costs of investigation and of liaison with counsel
as so elected; provided, however, that, (i) if the indemnifying party has failed
to assume the defense and employ counsel or (ii) if the defendants in any such
action include both the indemnified party and the indemnifying party and counsel
to the indemnified party shall have concluded that there may be reasonable
defenses available to the indemnified party that are different from or
additional to those available to the indemnifying party or that the interests of
the indemnified party reasonably may be deemed to conflict with the interests of
the indemnifying party, then the indemnified party shall have the right to
select a separate counsel and to assume such legal defense and otherwise to
participate in the defense of such action, with the expenses and fees of such
separate counsel and other expenses related to such participation to be
reimbursed by the indemnifying party as incurred.

          (d) If the indemnification provided for in this Section 2.07 is
unavailable to the Company or the Selling Holders or is insufficient to hold
them harmless in respect of any Losses, then each such 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 as between the
Company on the one hand and each Selling Holder on the other, in such proportion
as is appropriate to reflect the relative fault of the Company on the one hand
and of each Selling Holder on the other in connection with the statements or
omissions which resulted in such Losses, as well as any other relevant equitable
considerations.  The relative fault of the Company on the one hand and each
Selling Holder on the other shall be determined by reference to, among other
things, whether the untrue or alleged untrue statements of a material fact or
the omission or alleged omission to state a material fact has been made by, or
relates to, information supplied by such party, and the parties' relative
intent, knowledge, access to information and opportunity to correct or prevent
such statement or omission.

                                       9
<PAGE>
 
          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 is not guilty of such fraudulent misrepresentation.

                                 ARTICLE III


     Section 3.01  Communications.  All notices and other communications
provided for or permitted hereunder shall be made in writing by telecopy,
courier service or personal delivery:

          (a) if to a Holder, at the most current address given by such Holder
to the Company in accordance with the provisions of this Section 3.01, which
address initially is, with respect to JEDI or ECT, the address set forth in the
Securities Purchase Agreement, and

          (b) if to the Company, initially at its address set forth in the
Securities Purchase Agreement, and

          (c) for each, thereafter at such other address, notice of which is
given in accordance with the provisions of this Section 3.01.

          All such notices and communications shall be deemed to have been
received at the time delivered by hand, if personally delivered; when receipt
acknowledged, if telecopied; and on the next business day if timely delivered to
an air courier guaranteeing overnight delivery.

     Section 3.02.  Successor and Assigns.  This Agreement shall inure to the
benefit of and be binding upon the successors and assigns of each of the
parties, including subsequent holders of Registrable Securities.

     Section 3.03.  Counterparts.  This Agreement may be executed in any number
of counterparts and by different parties hereto in separate counterparts, each
of which counterparts, when so executed and delivered, shall be deemed to be an
original and all of which counterparts, taken together, shall constitute but one
and the same Agreement.

     Section 3.04.  Headings.  The headings in this Agreement are for
convenience of reference only and shall not limit or otherwise affect the
meaning hereof.

     Section 3.05.  Governing Law.  THE LAWS OF THE STATE OF TEXAS SHALL GOVERN
THIS AGREEMENT WITHOUT REGARD TO PRINCIPLES OF CONFLICT OF LAWS.

     Section 3.06.  Severability of Provisions.  Any provision of this Agreement
which is prohibited or unenforceable in any jurisdiction shall, as to such
jurisdiction, be ineffective to the extent of such prohibition or
unenforceability without invalidating the remaining provisions hereof or
affecting or impairing the validity or enforceability of such provision in any
other jurisdiction.

                                       10
<PAGE>
 
     Section 3.07.  Entire Agreement.  This Agreement, together with the
Securities Purchase Agreement and the other Basic Documents (as defined in the
Securities Purchase Agreement) are  intended by the parties as a final
expression of their agreement and intended to be a complete and exclusive
statement of the agreement and understanding of the parties hereto in respect of
the subject matter contained herein.  There are no restrictions, promises,
warranties or undertakings, other than those set forth or referred to herein
with respect to the registration rights granted by the Company with respect to
the securities sold pursuant to the Securities Purchase Agreement.  This
Agreement, the Securities Purchase Agreement and the other Basic Documents
supersede all prior agreements and understandings between the parties with
respect to such subject matter.

     Section 3.08.  Attorneys' Fees.  In any action or proceeding brought to
enforce any provision of this Agreement, the successful party shall be entitled
to recover reasonable attorneys' fees in addition to its costs and expenses and
any other available remedy.

     Section 3.09.  Amendment.  This Agreement may be amended only by means of a
written amendment signed by the Company and by the Holders of a majority of the
Registrable Securities.

     Section 3.10.  Registrable Securities Held by the Company or Its
Affiliates.  In determining whether the Holders of the required amount of
Registrable Securities have concurred in any direction, amendment, supplement,
waiver or consent, Registrable Securities owned by the Company or one of its
Affiliates shall be disregarded.

     Section 3.11.  Assignment of Rights.   The rights of any Holder under this
Agreement may be assigned to any Person who acquires any Registrable Securities.
Any assignment of registration rights pursuant to this Section 3.11 shall be
effective only upon receipt by the Company of written notice from such assigning
Holder stating the name and address of any assignee.  The rights of an assignee
under this Section 3.11 shall be the same rights granted to the assigning Holder
under this Agreement.  In connection with any such assignment, the term "Holder"
as used herein shall, where appropriate to assign the rights and obligations of
the assigning Holder hereunder to such assignee, be deemed to refer to the
assignee.

                                       11
<PAGE>
 
          IN WITNESS WHEREOF, the parties have executed this Agreement as of the
date first written above.

      
                             BRIGHAM EXPLORATION COMPANY
      
      
      
                             By:
                                ------------------------------------
                                  Craig M. Fleming
                                  Chief Financial Officer
      
      
      
                             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:
                                     -------------------------------
      
      
      
                             ENRON CAPITAL & TRADE RESOURCES CORP.
      
      
                                  By:
                                     -------------------------------
                                  Name:
                                     -------------------------------
                                  Title:
                                     -------------------------------

                                       12

<PAGE>
 
                              WARRANT CERTIFICATE


Number of Warrants: 250,000                                      Warrant No. A-1

     This warrant certificate ("Warrant Certificate") certifies that, for value
received,

                     ENRON CAPITAL & TRADE RESOURCES 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 the initial Issuance Date,
1.6402% 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.

     "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 $10.45.

     "Expiration Date" means August 22, 2005.

     "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.

     "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.
<PAGE>
 
     "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 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.

     "Securities Purchase Agreement" means the Securities Purchase Agreement,
dated as of August 20, 1998, among the Company, Enron Capital & Trade Resources
Corp. and Joint Energy Development Investments II Limited Partnership,
individually and as agent.

     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, 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 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) 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-
<PAGE>
 
     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 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

                                      -3-
<PAGE>
 
     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

          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 

                                      -4-
<PAGE>
 
     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).

     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.

                                      -5-
<PAGE>
 
          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 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.

                                      -6-
<PAGE>
 
     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.

     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

                                      -7-
<PAGE>
 
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.

     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 

                                      -8-
<PAGE>
 
(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 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:

          Enron Capital & Trade Resources 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:  Craig M. Fleming
          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.

                                      -9-
<PAGE>
 
     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.


     IN WITNESS WHEREOF, the Company has caused this Warrant Certificate to be
executed this 20th day of August, 1998 by the undersigned, thereunto duly
authorized.

                              BRIGHAM EXPLORATION COMPANY


                              By:
                                 ------------------------------
                                 Craig M. Fleming
                                 Chief Financial Officer

                                      -10-
<PAGE>
 
                                   EXHIBIT A

                             ELECTION TO EXERCISE
        [To be executed on exercise of the Warrants evidenced by this 
                             Warrant Certificate]

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 ________________________ ($______) 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 ___________________________.

     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.

                                      -11-
<PAGE>
 
                                   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 _________________________________ 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.

                                      -12-

<PAGE>
 
                              WARRANT CERTIFICATE


Number of Warrants: 750,000                                      Warrant No. A-2

     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 the initial Issuance Date,
4.9206% 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.

     "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 $10.45.

     "Expiration Date" means August 22, 2005.

     "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.

     "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.
<PAGE>
 
     "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 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.

     "Securities Purchase Agreement" means the Securities Purchase Agreement,
dated as of August 20, 1998, among the Company, Enron Capital & Trade Resources
Corp. and Joint Energy Development Investments II Limited Partnership,
individually and as agent.

     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, 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 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) 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 

                                      -2-
<PAGE>
 
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 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 

                                      -3-
<PAGE>
 
(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

               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 

                                      -4-
<PAGE>
 
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).

          (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 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.

                                      -5-
<PAGE>
 
               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.

          (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.

                                      -6-
<PAGE>
 
     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.

     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.

                                      -7-
<PAGE>
 
          (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 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.

                                      -8-
<PAGE>
 
     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:

          Enron Capital & Trade Resources 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: Craig M. Fleming
          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.  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.

                                      -9-
<PAGE>
 
     IN WITNESS WHEREOF, the Company has caused this Warrant Certificate to be
executed this 20th day of August, 1998 by the undersigned, thereunto duly
authorized.

                              BRIGHAM EXPLORATION COMPANY


                              By:_________________________
                                    Craig M. Fleming
                                    Chief Financial Officer

                                      -10-
<PAGE>
 
                                   EXHIBIT A

                             ELECTION TO EXERCISE
                 [To be executed on exercise of the Warrants 
                    evidenced by this Warrant Certificate]

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 ______________ ($________) 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 ______________________.

     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.

                                      -11-
<PAGE>
 
                                   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 ______________________________________________________  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.

                                      -12-

<PAGE>
 
- --------------------------------------------------------------------------------


                          BRIGHAM EXPLORATION COMPANY

                                   Borrower

                                      AND

                   CHASE BANK OF TEXAS, NATIONAL ASSOCIATION

                                    Trustee



                                _______________



                               I N D E N T U R E

                          Dated as of August 20, 1998



                                _______________



                                  $50,000,000
                  Senior Subordinated Secured Notes due 2003
<PAGE>
 
                               TABLE OF CONTENTS
 
PRELIMINARY STATEMENT......................................................... 1
 
ARTICLE I
     DEFINITIONS.............................................................. 1
     Section 1.01  Definitions................................................ 1
     Section 1.02  Accounting Procedures and Interpretation...................16
 
ARTICLE II
     ISSUE, DESCRIPTION, FORM, EXECUTION, REGISTRATION 
     OF TRANSFER AND EXCHANGE OF NOTES........................................17
     Section 2.01  Form and Dating............................................17
     Section 2.02  Execution and Authentication...............................17
     Section 2.03  Denomination of Notes and Record Date......................17
     Section 2.04  Manual Execution...........................................18
     Section 2.05  Transfer and Exchange......................................18
     Section 2.06  Replacement Notes..........................................19
     Section 2.07  Cancellation of Notes......................................20
     Section 2.08  No Third Party Benefit.....................................20
 
ARTICLE III
     SUBORDINATION............................................................20
 
ARTICLE IV
     SECURITY FOR THE OBLIGATIONS.............................................20
     Section 4.01  Security...................................................20
 
ARTICLE V
     [RESERVED]...............................................................22
 
ARTICLE VI
     [RESERVED]...............................................................22
 
ARTICLE VII
     AFFIRMATIVE COVENANTS....................................................22
     Section 7.01  Financial Statements and Reports...........................22
     Section 7.02  Litigation.................................................24
     Section 7.03  Maintenance, Etc...........................................24
     Section 7.04  Environmental Matters......................................25
     Section 7.05  Further Assurances.........................................25
     Section 7.06  Performance of Obligations.................................26
     Section 7.07  Engineering Reports........................................26
     Section 7.08  Intentionally Omitted......................................27

                                      -i-
<PAGE>
 
     Section 7.09  Additional Collateral......................................27
     Section 7.10  ERISA Information and Compliance...........................28
     Section 7.11  Subsidiary Security........................................28
 
ARTICLE VIII
     NEGATIVE COVENANTS.......................................................29
     Section 8.01  Debt.......................................................29
     Section 8.02  Liens......................................................30
     Section 8.03  Investments, Loans and Advances............................30
     Section 8.04  Dividends, Distributions and Redemptions...................31
     Section 8.05  Sales and Leasebacks.......................................32
     Section 8.06  Nature of Business.........................................32
     Section 8.07  Mergers, Etc...............................................32
     Section 8.08  Proceeds of Notes..........................................32
     Section 8.09  ERISA Compliance...........................................32
     Section 8.10  Sale of Oil and Gas Properties.............................33
     Section 8.11  Environmental Matters......................................34
     Section 8.12  Transactions with Affiliates...............................34
     Section 8.13  Negative Pledge Agreements.................................34
     Section 8.14  Gas Imbalances, Take-or-Pay Prepayments....................34
     Section 8.15  Borrower as Operator.......................................34
     Section 8.16  Consolidated Interest Coverage Ratio.......................35
     Section 8.17  Current Ratio..............................................35
 
ARTICLE IX
     PAYMENT OF THE NOTES.....................................................35
     Section 9.01  Repayment..................................................35
     Section 9.02  Interest...................................................35
     Section 9.03  Payments and Computations..................................38
 
ARTICLE X
     DEFAULT AND REMEDIES.....................................................39
     Section 10.01  Events of Default.........................................39
     Section 10.02  Remedies..................................................41
     Section 10.03  Production and Proceeds...................................42
     Section 10.04  Set-Off...................................................42
 
ARTICLE XI
     THE AGENT................................................................42
     Section 11.01  Authorization and Action..................................42
     Section 11.02  Agent's Reliance, Etc.....................................43
     Section 11.03  The Agent and Its Affiliates..............................43
     Section 11.04  Noteholders Loan Decision.................................43
     Section 11.05  Indemnification...........................................44
     Section 11.06  Successor Agent...........................................44
 

                                      -ii-
<PAGE>
 
ARTICLE XII
     TRUSTEE..................................................................45
     Section 12.01  Duties of Trustee.........................................45
     Section 12.02  Rights of Trustee.........................................46
     Section 12.03  Individual Rights of Trustee..............................47
     Section 12.04  Trustee's Disclaimer......................................47
     Section 12.05  Notice of Defaults........................................47
     Section 12.06  Reports by Trustee to Noteholders.........................47
     Section 12.07  Compensation and Indemnity................................48
     Section 12.08  Replacement of Trustee....................................49
     Section 12.09  Successor Trustee by Merger, etc..........................50
     Section 12.10  Eligibility, Disqualification.............................50
     Section 12.11  Preferential Collection of Claims Against Borrower........50
     Section 12.12  Appointment of Co-Trustee.................................50
     Section 12.13  No Conflict...............................................51
 
ARTICLE XIII
     MISCELLANEOUS............................................................51
     Section 13.01  Interpretation and Survival of Provisions.................51
     Section 13.02  Costs, Expenses and Taxes.................................52
     Section 13.03  No Waiver; Modifications in Writing.......................54
     Section 13.04  Binding Effect; Assignment................................54
     Section 13.05  Communications............................................55
     Section 13.06  Governing Law.............................................56
     Section 13.07  Arbitration...............................................56
     Section 13.08  Confidentiality...........................................57
     Section 13.09  Execution in Counterparts.................................58
     Section 13.10  Trust Indenture Act Controls..............................58
     Section 13.11  Communication by Noteholders with Other Noteholders.......58
     Section 13.12  Certificate and Opinion as to Conditions Precedent........58
     Section 13.13  Statements Required in Certificate or Opinion.............59
     Section 13.14  Rules by Trustee and Agents...............................59
     Section 13.15  Legal Holidays............................................59

EXHIBITS

     Exhibit A  Form of Note
     Exhibit B  Form of Guaranty Agreement
     Exhibit C  Form of Subordination Agreement
     Exhibit D  Form of Security Agreement
     Exhibit E  Form of Security Agreement
     Exhibit F  Form of Mortgage, Deed of Trust, Assignment of Production,
                    Security Agreement and Financing Statement
     Exhibit G  Acceptance of Appointment

                                     -iii-
<PAGE>
 
     INDENTURE, dated as of August 20, 1998, between BRIGHAM EXPLORATION
COMPANY, a corporation duly organized and existing under the laws of the State
of Delaware (hereinafter sometimes referred to as the "Borrower"), and CHASE
BANK OF TEXAS, NATIONAL ASSOCIATION, a national banking association existing
under the laws of the United States (hereinafter sometimes referred to as the
"Trustee").

                             PRELIMINARY STATEMENT

     All covenants and agreements made by the Borrower herein are for the
benefit and security of the holders of the Borrower's Senior Subordinated
Secured Notes due 2003.


                                   ARTICLE I
                                  DEFINITIONS

     Section 1.01  Definitions.

     "Acquired Shares" means 1,052,632 shares of Common Stock acquired by the
Noteholders on the Funding Date in accordance with Section 2.01 of the
Securities Purchase Agreement and any additional shares of Common Stock of the
Borrower issued to the Noteholders after the Funding Date in accordance with
Section 2.01(ii) of the Securities Purchase Agreement.

     "Adjusted Consolidated Net Tangible Assets" or "ACNTA" means (without
duplication), as of the date of determination, (a) the sum of (i) the discounted
future net revenue from proved crude oil and natural gas reserves of the
Borrower and its Consolidated Subsidiaries calculated in accordance with
Commission guidelines before any state or federal income taxes, as estimated in
the most current Reserve Report, as increased by, as of the date of
determination, the discounted future net revenue of (A) estimated proved crude
oil and natural gas reserves of the Borrower and its Consolidated Subsidiaries
attributable to acquisitions consummated since the date of such Reserve Report,
and (B) estimated proved crude oil and natural gas reserves of the Borrower and
its Consolidated Subsidiaries attributable to extensions, discoveries and other
additions and upward determinations of estimates of proved crude oil and natural
gas reserves due to exploration, development or exploitation, production or
other activities which reserves were not reflected in the most current Reserve
Report which would, in the case of determination made pursuant to clauses (A)
and (B), in accordance with standard industry practice, result in such
determinations, in each case calculated in accordance with Commission guidelines
(utilizing the Commission guideline prices utilized in the most current Reserve
Report), and decreased by, as of the date of determination, the discounted
future net revenue attributable to (C) estimated proved crude oil and natural
gas reserves of the Borrower and its Consolidated Subsidiaries reflected in the
most current Reserve Report produced or disposed of since the date of such
Reserve Report and (D) reductions in the estimated proved crude oil and natural
gas reserves of the Borrower and its Consolidated Subsidiaries reflected in such
Reserve Report since the date of such Reserve Report attributable to downward
determinations of estimates of proved crude oil and natural gas reserves due to
exploration, development or exploitation, production

                                      -1-
<PAGE>

or other activities conducted or otherwise occurring since the date of the most
current Reserve Report which would, in the case of determinations made pursuant
to clauses (C) and (D), in accordance with standard industry practice, result in
such determinations, in each case calculated in accordance with Commission
guidelines (utilizing the Commission guideline prices utilized in the most
current Reserve Report); provided, however, that, in the case of each of the
determinations made pursuant to clauses (A) through (D), such increases and
decreases shall be as estimated by the Borrower's engineers, except that if as a
result of such acquisitions, dispositions, discoveries, extensions or revisions,
there is a net increase in the ACNTA which exceeds $10,000,000, the Agent shall
have the right to require that such increases and decreases in the discounted
future net revenue be confirmed in writing by an independent petroleum engineer,
at the Borrower's expense, (ii) the capitalized costs that are attributable to
seismic and undeveloped oil and gas leases of the Borrower and its Consolidated
Subsidiaries to which no proved crude oil and natural gas reserves are
attributed, based on the Borrower's books and records as of a date no earlier
than the date of the Borrower's latest annual or quarterly financial statements,
(iii) the Net Working Capital on a date no earlier than the date of the
Borrower's latest annual or quarterly financial statements and (iv) the greater
of (I) the net book value on a date no earlier than the date of the Borrower's
latest annual or quarterly financial statements and (II) the appraised value, as
estimated by independent appraisers reasonably acceptable to the Agent, of other
tangible assets of the Borrower and its Consolidated Subsidiaries as of a date
no earlier than the date of the Borrower's latest audited financial statements,
minus (b) to the extent not otherwise taken into account in the immediately
preceding clause (a), the sum of (i) minority interests, (ii) any natural gas
balancing liabilities and credits of the Borrower and its Consolidated
Subsidiaries reflected in the Borrower's latest audited financial statements,
(iii) the discounted future net revenue, calculated in accordance with
Commission guidelines (utilizing the Commission guideline prices utilized in the
Borrower's most current Reserve Report), attributable to reserves subject to
participation interests, overriding royalty interests or other interests of
third parties, pursuant to participation, partnership, vendor financing or other
agreements then in effect, or which otherwise are required to be delivered to
third parties, (iv) the discounted future net revenue, calculated in accordance
with Commission guidelines (utilizing the Commission guideline prices utilized
in the Borrower's most current Reserve Report), attributable to reserves that
are required to be delivered to third parties to fully satisfy the obligations
of the Borrower and its Consolidated Subsidiaries with respect to volumetric
production payments and (v) the discounted future net revenue, calculated in
accordance with Commission guidelines, attributable to reserves subject to
dollar-denominated production payments that, based on the estimates of
production included in determining the discounted future net revenue specified
in the immediately preceding clause (a) (i) (utilizing the Commission guideline
prices utilized in the Borrower's most current Reserve Report), would be
necessary to satisfy fully the obligations of the Borrower and its Consolidated
Subsidiaries with respect to dollar-denominated production payments.

     "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 

                                      -2-
<PAGE>
 
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" means JEDI-II in its capacity as agent pursuant to Article XI and
includes any successor agent pursuant to Section 11.06.

     "Agent's Account" shall have the meaning specified in Section 9.03.

     "Average Share Price" means $9.50.

     "Basic Documents" means, collectively, this Indenture, the Securities
Purchase Agreement and the other Loan Documents.

     "Board of Directors" means the Board of Directors of the Borrower.

     "BOG" means Brigham Oil & Gas, L.P., a Delaware limited partnership.

     "Business Day" means any day other than a Saturday, Sunday, or a legal
holiday for commercial banks in Houston, Texas, or New York, New York.

     "Business Opportunities Agreement" means the Corporate Shareholders'
Agreement dated as of even date herewith between the Purchasers and the
Borrower.

     "Capital Stock" of any Person means any and all shares, interests,
participations, or other equivalents (however designated) of, or rights,
warrants, or options to purchase, corporate stock, partnership interests, or any
other equity interest (however designated) of or in such Person.

     "Change in Control" means (i) a transaction, including any merger or
consolidation of Borrower with any other Person, in which the shareholders of
the Borrower immediately prior to such transaction (treating the holders of the
Warrants as holders of voting shares) do not own at least fifty-one percent
(51.0%) of the voting shares of stock of the Borrower (or the surviving 
entity in the case of a merger or consolidation) immediately following the
consummation of such transaction, or (ii) a transaction, including any merger or
consolidation of Borrower with any other Person, in which the members of the
Board of Directors immediately prior to such transaction do not comprise at
least a majority of the board of directors of the Borrower (or the surviving
entity in the case of a merger or consolidation) for a period of twelve (12)
months immediately following the consummation of such transaction, or (iii) an
event, including any merger or consolidation of Borrower with any other Person,
such that Mr. Ben Brigham no longer manages the Borrower (or the surviving

                                      -3-
<PAGE>
 
entity in the case of a merger or consolidation), other than as a result of his
death or disability.

     "Closing" has the meaning provided therefor in Section 2.02 of the
Securities Purchase Agreement.

     "Closing Date" means the date upon which the Closing occurs as provided in
Section 2.02 of the Securities Purchase Agreement.

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

     "Collateral" means the properties, property interests and rights described
in Section 4.01 hereof, or otherwise covered by the Collateral Documents, as
security for the Obligations.

     "Collateral Documents" means collectively the documents required by the
Agent or the Noteholders to obtain the security interests in the Collateral, as
described in Section 4.01 hereof, and all other agreements, documents and
instruments required in Section 4.01, as the same may from time to time be
amended or supplemented.

     "Commission" means the United States Securities and Exchange Commission.

     "Common Stock" means the common stock, par value $0.01 per share, of the
Borrower or such other class of securities as shall, after the date of this
Indenture, constitute the common equity of the Borrower.

     "Consolidated Indebtedness" means all Debt of the Borrower and its
Consolidated Subsidiaries.

     "Consolidated Interest Coverage Ratio" means, as of the date of
determination, the ratio of (i) EBITDA for the preceding four calendar quarters
to (ii) Interest Expense for the same four calendar quarters.

     "Consolidated Net Income" means with respect to the Borrower and its
Consolidated Subsidiaries, for any period, the aggregate of the net income (or
loss) of the Borrower and its Consolidated Subsidiaries after allowance 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 Borrower 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 Borrower 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
the Borrower 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 

                                      -4-
<PAGE>
 
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 Subsidiaries" shall mean each Subsidiary of the Borrower
(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 the Borrower in accordance with GAAP.

     "corporate trust office" of the Trustee means the office of the Trustee at
the address set out in Section 13.05 or at any other office or agency so
designated by the Trustee.

     "Debt" means, 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
and earned but unpaid issuance fees); (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 but including Schedule 8.02
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
(or $500,000 in the aggregate) 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 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 

                                      -5-
<PAGE>
 
of which such Person directly or indirectly received payment; and (xiv) all
obligations of such Person under Hedging Agreements, provided that "Debt" shall
not include (a) interest or fees (other than earned but unpaid issuance fees) on
any of the foregoing, (b) obligations associated with bid, performance, surety
or appeal bonds (including those required by Governmental Requirements in
connection with Oil and Gas Properties), (c) gas balancing obligations (whether
volumetric or dollar denominated), (d) intercompany obligations among the
Borrower and its Consolidated Subsidiaries, (e) indemnity obligations which have
not matured into fixed liabilities, and (f) purchase price adjustments and
similar post-closing obligations (but excluding the deferred payment of any
purchase price) incurred in connection with the permitted purchase and sale of
Property or stock, and which is to be determined and payable no later than 180
days following the closing of such purchase and sale.

     "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.

     "Default Rate" means, for any applicable period, an interest rate equal to
the then applicable rate of interest on the Notes (for cash payments of
interest) plus 4.00% per annum, but in no event shall the Default Rate exceed
the Maximum Rate.

     "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 non-cash charges, minus all non-cash income added to
Consolidated Net Income in such period.

     "ECT" means Enron Capital & Trade Resources Corp., a Delaware corporation.

     "Effective Date" means the date this Indenture is executed by all the
parties hereto.

     "Employee Plan" means any employee benefit plan, program or policy with
respect to which the Borrower or any ERISA Affiliate may have any liability or
any obligation to contribute, other than a Plan or a Multiemployer Plan.

     "Environmental Laws" means 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"), as amended, 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 

                                      -6-
<PAGE>
 
Laws, the term "oil" has 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 Documents" means the Warrants, the stock certificates representing
the Acquired Shares, the Registration Rights Agreement and the Business
Opportunities Agreement.

     "ERISA" means 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.

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

     "Excepted Liens" means (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 workman'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 the 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, 

                                      -7-
<PAGE>
 
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 for which such 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; and (vii) Liens permitted by the
Loan Documents.

     "Federal Funds Rate" means, for any day, a fluctuating interest 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
members of the Federal Reserve System arranged by federal funds brokers on such
day, as published for such day (or, if such day is not a Business Day, for the
next preceding Business Day) by the Federal Reserve Bank of New York, or, if
such rate is not so published for any day which is a Business Day, the average
of the quotations for any such day on such transactions received by the Agent
from three federal funds brokers of recognized standing selected by it.

     "Financial Statements" means the financial statement or statements
described or referred to in Section 4.02 of the Securities Purchase Agreement.

     "First Reserve Report" shall have the meaning set out in Section 7.07(a).

     "Funding Date" means the first Business Day following the date all of the
conditions precedent to funding in Article VI of the Securities Purchase
Agreement have been satisfied.

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

     "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 or any
Noteholder.

     "Guarantors" means Brigham, Inc., Brigham Holdings I, LLC, Brigham Holdings
II, LLC, BOG and any other Person who becomes party to a Guaranty Agreement
pursuant to the terms of Section 7.11.

                                      -8-
<PAGE>
 
     "Guaranty Agreements" means the agreements executed by the Guarantors
substantially in the form of Exhibit B guarantying, unconditionally, payment of
the Obligations, as the same may be amended, modified or supplemented from time
to time.

     "Hedging Agreements" means 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.

     "Hydrocarbon Interests" means 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" means oil, gas, casinghead gas, drip gasoline, natural
gasoline, condensate, distillate, liquid hydrocarbons, gaseous hydrocarbons and
all products refined or separated therefrom.

     "Indenture" means this instrument as originally executed, or, if amended or
supplemented as herein provided, as so amended or supplemented.

          "Initial Reserve Report" means the report of Cawley, Gillespie &
Associates with respect to the Oil and Gas Properties of BOG as of November 30,
1997, a copy of which has been delivered to Agent.

    "Interest Expense" means, for each applicable period for which EBITDA is to
be calculated, the sum of all required cash payments of interest during such
period on borrowed money.  Interest on the Notes, for purposes of this
definition, shall be deemed cash payments, calculated at the cash interest rate,
whether paid in cash or in kind, except that if a payment of interest is made in
kind on any Interest Payment Date, an amount equal to the cash payment of
interest that would have been due on such Interest Payment Date if payment in
kind had not been made shall be deemed subtracted from Interest Expense for the
four quarter period ending on the last day of the fiscal quarter preceding such
Interest Payment Date (but not for any other four quarter period for which
Interest Expense is calculated).

    "Interest Payment Date" means each November 20, February 20, May 20, and
August 20 following the Funding Date until and including the Maturity Date.

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

     "Lien" means 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, 

                                      -9-
<PAGE>
 
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 purpose of this Indenture, 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" means this Indenture, the Notes, the Structuring Fee
Agreement, the Collateral Documents, 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 (other than the Equity Documents and any
assignments, participation or similar agreements between any Noteholder and any
other lender or creditor with respect to any Obligations pursuant to this
Indenture) in connection with, or as security for the payment or performance of,
the Notes or this Indenture, as such agreements may be amended, supplemented or
restated from time to time.

     "Majority Noteholders" means, at any time, the Noteholders holding more
than 50% of the outstanding principal balance of the Notes.

     "Material Adverse Effect" means any material and adverse effect on (i) the
assets, liabilities, financial condition, business, operations or affairs of 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 at the time made, or (ii) the ability of the Borrower and its
Subsidiaries taken as a whole to carry out their business as of the Closing Date
or as proposed as of the Closing Date to be conducted or to meet their
obligations under the Loan Documents on a timely basis.

     "Maturity Date" means August 20, 2003, or in the event of an acceleration
of the Obligations, such earlier date as the Obligations become due and payable
in full.

     "Maximum Rate" means at any particular time in question, the maximum
nonusurious rate of interest, if any, which under applicable law may then be
charged on the Notes. If such maximum rate changes after the date hereof, the
Maximum Rate shall be automatically increased or decreased, as the case may be,
without notice to the Borrower from time to time as the effective date of each
change in such maximum rate.

     "Mortgage" means the "Mortgage" referred to in Section 4.01(c) or
4.01(f)(ii) and any other mortgages executed pursuant to Section 7.09 hereof.

     "Mortgaged Property" means the Property owned by the Borrower and its
Subsidiaries which is subject to the Liens existing and to exist under the Loan
Documents.

                                      -10-
<PAGE>
 
     "Multiemployer Plan" means a Plan defined as such in Section 3(37) or
4001(a)(3) of ERISA.

     "NASDAQ" means  the National Association of Securities Dealers Automated
Quotation System.

     "Net Working Capital" means, for any Person or group of Persons and as of
any date of its determination, the difference (shown on the balance sheets of
such Person or group as of the end of the most recent fiscal quarter of such
Person or group for which internal financial statements are available) between
(i) all current assets of such Person or group and (ii) all current liabilities
of such Person or group, except the current portion of long-term Debt.

     "Notes" means the Senior Subordinated Secured Notes issued pursuant to
Section 2.03 of the Securities Purchase Agreement, in the aggregate face amount
of $50,000,000, dated as of the date hereof, made by the Borrower and payable to
the order of the Noteholders in their respective Participations.

     "Noteholders" means ECT and JEDI-II and/or, to the extent then applicable,
each assignee of ECT or JEDI-II or their respective successors or assigns in
whose name a Note may be registered in the Note Register kept for that purpose.

     "Noteholder's Account" means for any Noteholder, the account specified by
such Noteholder as its Noteholder's Account by notice in writing to the Agent.

     "Note Register" and "Note Registrar" have the respective meanings specified
in Section 2.05.

     "Obligations" means any and all amounts, liabilities and obligations owing
from time to time by Borrower to the Agent or the Noteholders, pursuant to any
of the Basic Documents and all renewals, extensions and/or rearrangements
thereof, whether such amounts, liabilities or obligations be liquidated or
unliquidated, now existing or hereafter arising, absolute or contingent.

     "Officers' Certificate" means a certificate signed by the Chairman of the
Board, the President or any Vice President and by the Treasurer or any Assistant
Treasurer or the Secretary or any Assistant Secretary of the Borrower. Each such
certificate shall include the statements provided for in Section 13.13, if and
to the extent required by the provisions thereof.

     "Oil and Gas Properties" means 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; 

                                      -11-
<PAGE>
 
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 hereafter
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 rights, automotive equipment or other personal
property which may be on such premises for the purpose of drilling a well or
other similar temporary use) 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.

     "Opinion of Counsel" means an opinion in writing signed by legal counsel
who shall be reasonably satisfactory to the Trustee and may be counsel to the
Borrower. Each such opinion shall include the statements provided for in Section
13.13, if and to the extent required by the provisions thereof.

     "outstanding", when used with reference to Notes, means, as of any
particular time, all Notes authenticated and delivered by the Trustee under this
Indenture, except

          (a) Notes that have been canceled by the Trustee or delivered to the
     Trustee for cancellation;

          (b) Notes for which monies in the necessary amount for payment or
     redemption shall have been deposited in trust with the Trustee or with any
     paying agent (other than the Borrower), provided that, if such Notes are to
     be redeemed, notice of such redemption shall have been given as provided in
     Article IV or provision satisfactory to the Trustee shall have been made
     for giving such notice; and

          (c) Notes in lieu of or in substitution for which other Notes shall
     have been authenticated and delivered pursuant to the terms of Section
     2.06.

     "Participation" means, for each Noteholder, such Noteholder's proportionate
share of the Obligations and the Warrants.  As of the Effective Date, ECT's
Participation shall be 25% and JEDI-II's Participation shall be 75%.

                                      -12-
<PAGE>
 
     "PBGC" means the Pension Benefit Guaranty Corporation or any entity
succeeding to any or all of its functions.

     "Permitted Debt" means:

          (a) The Senior Loan, up to the lesser of $75,000,000 or the "Borrowing
     Base" under the Senior Credit Agreement;

          (b) The Notes or other Obligations arising under the Loan Documents or
     any guaranty of or suretyship arrangement for the Notes or other
     Obligations arising under the Loan Documents;

          (c) Debt of the Borrower which is existing on the Closing Date and is
     reflected in the Financial Statements or which constitutes Schedule 8.02
     Payables, and any renewals or extensions (but not increases) thereof;

          (d) 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 invoice
     or billing date, are being contested in good faith by appropriate
     proceedings if reserves adequate under GAAP shall have been established
     therefor;

          (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 with a Senior Lender
     or another investment grade counterparty the notional amounts on which do
     not exceed 75% of Borrower's anticipated oil and/or gas production to be
     produced during the term of such Hedging Agreements 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; and

          (g) Debt of the Borrower not described in clauses (a) through (f)
     which, in the aggregate, does not exceed $1,000,000 at any one time
     outstanding.

     "Person" means 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" means 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 

                                      -13-
<PAGE>
 
six calendar years sponsored, maintained or contributed to, by the Borrower, any
Subsidiary or an ERISA Affiliate.

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

     "Registration Rights Agreement" means the Registration Rights Agreement
dated as of the date hereof, made by the Borrower relating to the Warrants, the
Warrant Shares and the Acquired Shares.

     "Reportable Event" means an event described in Section 4043(c) of ERISA
with respect to a Plan, other than an event described in paragraphs (1) through
(8) as to which the 30 day notice requirement has been waived by the PBGC.

     "Reserve Report" means a report, in form satisfactory to the Senior Loan
Agent (or if there is no Senior Loan or requirement for a Reserve Report under
the Senior Loan, the Agent), setting forth, as of the dates set forth in
Sections 7.07(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 Commission reporting requirements
at the time and (ii) such other information as the Senior Loan Agent (or, if
there is no Senior Loan, or requirement for a Reserve Report under the Senior
Loan, the Agent) may reasonably request.  The term "Reserve Report" shall also
include the Initial Reserve Report, the First Reserve Report, the supplemental
Reserve Reports described in Section 7.07(b), and the information to be provided
by the Borrower each year pursuant to Section 7.07(d).

     "Responsible Officer" means, as to any Person, the Chief Executive Officer,
the President, any Vice President or 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.  "Responsible Officer" when used
with respect to the Trustee means the chairman or the vice-chairman of the board
of directors, the chairman of the executive committee of the board of directors,
the president, any vice president, any second or assistant vice president, the
cashier, any assistant cashier, the secretary, any assistant secretary, the
treasurer, any assistant treasurer, any senior trust officer or trust officer,
or any other officer or assistant officer of the Trustee customarily performing
functions similar to those performed by the persons who at the time shall be
such officers, respectively, or to whom any corporate trust matter is referred
because of his knowledge of and familiarity with the particular subject.

     "Schedule 8.02 Payables" means payables owing under the agreements listed
on Schedule 8.02 which are outstanding more than 75 days after they become fixed
and owing, provided that the aggregate amounts of such payables under each such
agreement do not exceed the amount set forth for each such agreement on such
schedule.

                                      -14-
<PAGE>
 
     "Scheduled Redetermination Date"  means the last Business Day of each
September and  March during the term of the Notes, commencing September 1999.

     "Securities" means the Notes, the Warrants and the Acquired Shares.

     "Securities Act" means the Securities Act of 1933, as amended from time to
time, and the rules and regulations of the Commission promulgated thereunder.

     "Securities Purchase Agreement" means the Securities Purchase Agreement
dated of even date herewith between the Noteholders and the Borrower.

     "Senior Credit Agreement" means the Credit Agreement dated as of January
26, 1998, among BOG, the Senior Loan Agent, and the Senior Lenders, as it may
from time to time be amended, modified or supplemented from time to time, and
any Credit Agreement or similar agreement executed with banks or other financial
institutions in connection with any refinancing of the Senior Loan permitted
hereunder and under the Subordination Agreement.

     "Senior Loan Agent" means the agent or agents designated under the Senior
Credit Agreement.  Bank of Montreal is the Senior Loan Agent as of the date
hereof.

     "Senior Lenders" means each of the lenders from time to time under the
Senior Credit Agreement.

     "Senior Loan" shall mean, collectively, any advance or advances of
principal made by the Senior Lenders to BOG or the Borrower under the Senior
Credit Agreement and the other Senior Loan Documents.

     "Senior Loan Documents" means the Senior Credit Agreement and all
promissory notes, collateral documents and other agreements, documents and
instruments executed or delivered in connection therewith, as such agreements
may be amended, modified or supplemented from time to time.

     "Special Entity" means 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).

     "Structuring Fee Agreement" means the agreement between the Borrower and
ECT Securities Corp. dated as of the date hereof.

                                      -15-
<PAGE>
 
     "Subordination Agreement" means the Intercreditor and Subordination
Agreement dated as of even date herewith, by and among the Trustee, the Senior
Loan Agent, the Senior Lenders, the Agent, the Noteholders, the Borrower and
certain Subsidiaries, substantially in the form of Exhibit C as the same may be
supplemented or amended from time to time.

     "Subsidiary" means (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.

     "TIA" (except as herein otherwise expressly provided or unless the context
otherwise requires) means the Trust Indenture Act of 1939, as amended, as in
force at the date of this Indenture as originally executed.

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

     "Trustee" means Chase Bank of Texas, National Association, and, subject to
the provisions of Article XII, shall also include its successors and assigns.

     "Warrants" means the Warrants issued by the Borrower to ECT and JEDI-II in
their respective Participations pursuant to Section 2.03 of the Securities
Purchase Agreement, for the purchase of an aggregate of 1,000,000 shares of
Common Stock, and any Warrants issued upon the transfer thereof or in
substitution therefore, pursuant to the Warrant Certificate to be issued to ECT
and JEDI-II, forms of which are attached to the Securities Purchase Agreement as
Exhibit A.

     "Warrant Shares" means the shares of Common Stock and other securities
receivable upon exercise of the Warrants.


     Section 1.02  Accounting Procedures and Interpretation .  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 Noteholders (including ACNTA
calculations) hereunder shall be prepared, in accordance with GAAP, applied on a
basis consistent with the Financial Statements (except for changes concurred
with by the Borrower's independent public accountants).

                                      -16-
<PAGE>
 
                                  ARTICLE II
               ISSUE, DESCRIPTION, FORM, EXECUTION, REGISTRATION
                       OF TRANSFER AND EXCHANGE OF NOTES

     Section 2.01  Form and Dating.  The Notes and the Trustee's certificate of
authentication are to be substantially in the form of Exhibit A, with such
appropriate insertions, omissions, substitutions, amendments, changes and other
variations as are required or permitted by this Indenture, and may have such
letters, numbers or other marks of identification and such legends or
endorsements placed thereon as may be required to comply with the rules of any
securities exchange on which the Notes may be listed or as may, consistently
herewith, be determined by the officers executing such Notes as evidenced by
their execution of the Notes.

     The terms and provisions contained in the Notes and each Guaranty Agreement
shall constitute, and are hereby expressly made, a part of this Indenture and,
to the extent applicable, the Borrower and the Guarantors, by their execution
and delivery of this Indenture and each Guaranty Agreement, expressly agree to
such terms and provisions and to be bound thereby.

     The definitive Notes shall be printed or produced in any manner as may be
determined by the officers executing such Notes, as evidenced by their execution
of such Notes.

     Section 2.02  Execution and Authentication.  The Notes and each Guaranty
Agreement shall be executed by the Borrower and Guarantors, respectively, and be
delivered to the Trustee for authentication, and the Trustee shall thereupon, or
from time to time thereafter, authenticate and deliver said Notes and each
Guaranty Agreement to and upon the written order of the Borrower, signed by its
President or a Vice President and by its Treasurer, Assistant Treasurer,
Secretary or Assistant Secretary, without any further action by the Borrower.

     Section 2.03  Denomination of Notes and Record Date.  The Notes shall be
issuable as registered Notes without coupons in denominations of $1,000 and any
integral multiple thereof.  Each Note shall be dated the date of its
authentication.

     The person in whose name any Note is registered at the close of business on
any record date (as hereinafter defined) with respect to any interest payment
date shall be entitled to receive the interest payable on such interest payment
date. The term "record date" as used with respect to any Interest Payment Date
shall mean the day of the calendar month preceding the day on which such
Interest Payment Date falls.  The principal of, and premium, if any, and
interest on, the Notes shall be payable at the principal office of the Borrower
and any other office or agency of the Borrower designated for that purpose;
provided, however, that principal and interest may be payable at the option of
the Noteholders to the Agent's Account.

                                      -17-
<PAGE>
 
     Section 2.04  Manual Execution.  The Notes and Guaranty Agreements shall be
signed manually or by facsimile signature on behalf of the Borrower by its
President or a Vice President attested by the manual or facsimile signature of
its Secretary or an Assistant Secretary.

     Only such Notes as shall bear thereon a certificate of authentication
substantially in the form recited in Exhibit A, manually executed by the
Trustee, shall be entitled to the benefits of this Indenture or be valid or
obligatory for any purpose. Such certificate by the Trustee upon any Note
executed by the Borrower shall be conclusive evidence that the Note so
authenticated has been duly authenticated and delivered hereunder.

     In case any officer of the Borrower who shall have signed any of the Notes
shall cease to be such officer before the Notes so signed shall have been
authenticated and delivered by the Trustee, or disposed of by the Borrower, such
Notes nevertheless may be authenticated and delivered or disposed of as though
the person who signed such Notes had not ceased to be such officer of the
Borrower; and any Note may be signed on behalf of the Borrower by such persons
as, at the actual date of the execution of such Note, shall be the proper
officers of the Borrower, although at the date of the execution of this
Indenture any such person was not an officer.

     Section 2.05  Transfer and Exchange.  The Notes may be exchanged for a like
aggregate principal amount of Notes of other authorized denominations.  Notes to
be exchanged shall be surrendered at the Borrower's principal office, and the
Borrower shall execute and the Trustee shall authenticate and deliver in
exchange therefor the Note or Notes which the Noteholder making the exchange
shall be entitled to receive.

     The Borrower shall keep or cause to be maintained at said office or agency
a register (herein sometimes referred to as the "Note Register") in which,
subject to such reasonable regulations as it may prescribe, the Borrower shall
register Notes and shall register the transfer of Notes as in this Article II
provided. For the purposes of registration, exchange, registration of transfer,
redemption or conversion of Notes, the Trustee is hereby appointed Note
Registrar. Upon surrender for registration of transfer of any Note at said
office or agency, the Borrower shall execute and the Trustee shall authenticate
and deliver in the name of the transferee or transferees a new Note or Notes in
a like aggregate principal amount. At all reasonable times the Note Register
shall be open for inspection by the Trustee. No transfer of any Note shall be
valid unless made at said office or agency.

     All Notes presented or surrendered for registration of transfer, exchange,
conversion or payment shall (if so required by the Borrower or the Trustee) be
accompanied by a written instrument or instruments of transfer, in form
satisfactory to the Borrower and the Trustee, duly executed by the registered
Noteholder or his attorney duly authorized in writing.

     No service charge shall be made for any exchange or registration of
transfer of Notes, or issue of new Notes in case of partial prepayment or
conversion, but the Borrower may 

                                      -18-
<PAGE>
 
require payment of a sum sufficient to cover any tax or other governmental
charge that may be imposed in relation thereto.

     The Borrower shall not be required (i) to issue, register the transfer of,
or exchange any Note during a period beginning at the opening of business 15
days before the mailing of a notice of redemption of the Notes selected for
redemption and ending on the day of such mailing, or (ii) to register the
transfer of or exchange any Note so selected for redemption in whole or in part,
except the unredeemed portions of Notes being redeemed in part.

     Section 2.06  Replacement Notes.  In case any Note shall become mutilated
or be destroyed, lost or stolen, the Borrower shall execute, and the Trustee
shall authenticate and deliver, a new Note, in exchange and substitution for the
mutilated Note or in lieu of and substitution for the Note destroyed, lost or
stolen. In every case, the applicant for a substituted Note shall furnish to the
Borrower and the Trustee such security or indemnity as may be required by them
to hold each of them harmless, and, in every case of destruction, loss or theft,
the applicant shall also furnish to the Borrower and to the Trustee evidence to
their satisfaction of the destruction, loss or theft of such Note and of the
ownership thereof. The Trustee may authenticate any such substituted Note and
deliver the same upon the request or authorization of the Borrower.  Upon the
issuance of any substituted Note, the Borrower may require the payment of a sum
sufficient to cover any tax or other governmental charge that may be imposed in
relation thereto and any other expenses connected therewith, including fees and
expenses of the Trustee. In case any Note which has matured or is about to
mature or has been called for prepayment or has been presented for conversion
shall become mutilated or be destroyed, lost or stolen, the Borrower may,
instead of issuing a substitute Note, pay or authorize the payment of the same
(without surrender thereof except in the case of a mutilated Note) if the
applicant for such payment shall furnish the Borrower and the Trustee with such
security or indemnity as may be required by them to hold each of them harmless,
and, in case of destruction, loss or theft, evidence to the satisfaction of the
Borrower and the Trustee of the destruction, loss or theft of such Note and of
the ownership thereof.

     If, after the delivery of such replacement Note, a bona fide purchaser of
the original Note in lieu of which such replacement Note was issued presents for
payment or registration such original Note, the Trustee shall be entitled to
recover such replacement Note from the person to whom it was delivered or any
person taking therefrom, except a bona fide purchaser, and shall be entitled to
recover upon the security or indemnity provided therefor to the extent of any
loss, damage, cost or expense incurred by the borrower or Trustee in connection
therewith.

     Every substituted Note issued pursuant to the provisions of this Section
2.06 upon evidence that any Note is destroyed, lost or stolen shall, with
respect to such Note, constitute an additional contractual obligation of the
Borrower, whether or not the destroyed, lost or stolen Note shall be found at
any time, and shall be entitled to all the benefits of this Indenture equally
and proportionately with any and all other Notes duly issued hereunder. 

                                      -19-
<PAGE>
 
All Notes shall be held and owned upon the express condition that the foregoing
provisions are exclusive with respect to the replacement or payment of
mutilated, destroyed, lost or stolen Notes, and shall preclude any and all other
rights or remedies, notwithstanding any law or statute existing or hereafter
enacted to the contrary with respect to the replacement or payment of negotiable
instruments or other securities without their surrender.

     Section 2.07  Cancellation of Notes.  All Notes surrendered for payment,
conversion, registration of transfer or exchange shall, if surrendered to the
Borrower or any paying agent, be delivered to the Trustee for cancellation, or,
if surrendered to the Trustee, shall be canceled by it, and no Notes shall be
issued in lieu thereof except as expressly permitted by any of the provisions of
this Indenture. On request of the Borrower, the Trustee shall deliver to the
Borrower canceled Notes held by the Trustee; provided, however, that the Trustee
may at any time destroy any canceled Notes and deliver to the Borrower a
certificate of such destruction.  If the Borrower shall acquire any of the
Notes, however, such acquisition shall not operate as a redemption or
satisfaction of the indebtedness represented by such Notes unless and until the
same are delivered to the Trustee or surrendered to the Trustee for
cancellation.

     Section 2.08  No Third Party Benefit.  Subject to the terms of the
Subordination Agreement, nothing in this Indenture or in the Notes, expressed or
implied, shall give or be construed to give to any person, firm or corporation,
other than the parties hereto and the Noteholders, any legal or equitable right,
remedy or claim under or in respect of this Indenture, or under any covenant,
condition or provision herein contained; all its covenants, conditions and
provisions being for the sole benefit of the parties hereto and of the
Noteholders.


                                  ARTICLE III
                                 SUBORDINATION

     The Notes shall be subject to the Subordination Agreement.


                                  ARTICLE IV
                         SECURITY FOR THE OBLIGATIONS

     Section 4.01  Security.  The Obligations shall be secured by the following
which, in each case shall be subordinate in priority only to those liens,
security interests or rights granted in the same collateral to secure the
performance of Borrower under the Senior Loan Documents, in accordance with, but
subject to, the terms of the Subordination Agreement:

          (a) (i)  A Security Agreement substantially in the form of Exhibit D
duly executed by the Borrower in favor of the Trustee for the ratable benefit of
the Noteholders granting a security interest in all of the Borrower's right,
title and interest in and to the Capital Stock of Brigham, Inc. and Brigham
Holdings I, LLC, together with proper UCC-1 

                                      -20-
<PAGE>
 
Financing Statements duly filed in Texas, (ii) a Security Agreement
substantially in the form of Exhibit D duly executed by Brigham, Inc. in favor
of the Trustee for the ratable benefit of the Noteholders granting a security
interest in all of Brigham, Inc.'s right, title and interest in and to the
Capital Stock of Brigham Holdings II, LLC and BOG, together with proper UCC-1
Financing Statements duly filed in Texas, (iii) a Security Agreement
substantially in the form of Exhibit D duly executed by Brigham Holdings II, LLC
in favor of the Trustee for the ratable benefit of the Noteholders granting a
security interest in all of Brigham Holdings II, LLC's, right, title and
interest in and to the Capital Stock of BOG, together with proper UCC-1
Financing Statements duly filed in Texas and (iv) a Security Agreement
substantially in the form of Exhibit D duly executed by Brigham Holdings I, LLC
in favor of the Trustee for the ratable benefit of the Noteholders granting a
security interest in all of Brigham Holdings I, LLC's right, title and interest
in and to the Capital Stock of BOG, together with proper UCC-1 Financing
Statements duly filed in Texas.

          (b) A Security Agreement, substantially in the form of Exhibit E duly
executed by BOG in favor of the Trustee, as collateral agent for the ratable
benefit of the Noteholders granting a security interest in all of BOG's right,
title and interest in and to all accounts, general intangibles, equipment and
inventory of BOG subject to Liens under the Senior Loan Documents.

          (c) A Mortgage, Deed of Trust, Assignment of Production, Security
Agreement and Financing Statement substantially in the form of Exhibit F
executed by BOG in favor of the Trustee, as collateral agent for the ratable
benefit of the Noteholders covering all of the Property of BOG subject to Liens
under the Senior Loan Documents.

          (d) A Guaranty Agreement duly executed by each of BOG, Brigham, Inc.,
Brigham Holdings I, LLC and Brigham Holdings II, LLC in favor of the Trustee for
the ratable benefit of the Noteholders guarantying the payment and performance
of the Obligations.

          (e)  Stock Powers executed by the Borrower and related stock
certificates of Brigham, Inc.

          (f) (i) Guaranty Agreements from each and every Person now or
hereafter guaranteeing all or any portion of the Senior Loan, (ii) Mortgages
covering any and all real property (including Oil and Gas Property) now or
hereafter pledged as collateral for all or any portion of the Senior Loan, (iii)
security agreements covering any and all Property (other than real property
subject to a Mortgage) now or hereafter pledged as collateral for all or any
portion of the Senior Loan, and (iv) financing statements, stock pledges or
other agreements necessary or appropriate to perfect the liens and/or security
interests granted pursuant to any of the foregoing.  Each of the foregoing
instruments shall be in substantially the same form and substance as those
executed of even date herewith or otherwise.

                                      -21-
<PAGE>
 
                                   ARTICLE V
                                  [RESERVED]


                                  ARTICLE VI
                                  [RESERVED]


                                  ARTICLE VII
                             AFFIRMATIVE COVENANTS

     Unless the Agent's prior written consent to the contrary is obtained, the
Borrower will, for the benefit of each of the Noteholders, at all times comply
with the covenants contained in this Article VII (or cause each Subsidiary's
compliance with the applicable covenants), from the date hereof and for so long
as any part of the Obligations is outstanding.

     Section 7.01  Financial Statements and Reports. The Borrower shall
deliver, or shall cause to be delivered, to the Agent with sufficient copies for
each of the Noteholders:

          (a) Annual Financial Statements.  As soon as available and in any
event within 90 days after the end of each fiscal year of the Borrower, the
audited consolidated statements of income, stockholders' equity, changes in
financial position and cash flow of the Borrower and its Consolidated
Subsidiaries for such fiscal year, and the related consolidated and unaudited
consolidating balance sheets of the Borrower 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 Senior Loan Agent (or in the absence of a Senior
Loan, the Agent) which opinion shall state that said financial statements fairly
present the consolidated financial condition and results of operations of the
Borrower 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 60 days after the end of each of the first three fiscal quarterly
periods of each fiscal year of the Borrower, consolidated statements of income,
stockholders' equity, changes in financial position and cash flow of the
Borrower 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, 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 

                                      -22-
<PAGE>
 
the consolidated financial condition and results of operations of the Borrower
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) 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.

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

          (e) SEC Filings, Etc.  Promptly upon its becoming available, each
financial statement, report, notice or proxy statement sent by the Borrower 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 the Borrower with or received by the Borrower in
connection therewith from any securities exchange or the Commission or any
successor agency.

          (f) 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, other than this Indenture and not otherwise required to be furnished
to the Agent or the Trustee pursuant to any other provision of this Section
7.01.

          (g) 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 (including, without limitation,
any Plan or Multiemployer Plan and any reports or other information required to
be filed under ERISA) as may be requested by and provided to the Senior Lender
or Senior Loan Agent.

          (h) Annual Budgets.  Concurrent with the First Reserve Report and each
January 1 Reserve Report thereafter, a one-year financial projection for the
Borrower and its Subsidiaries in form acceptable to the Senior Loan Agent (or in
the absence of a Senior Loan or Senior Loan Agent, the Agent), which projection
shall include revenues, expenses and capital expenditures.

          (i) Monthly Operating Statements.  As soon as available and in any
event within 30 days after the end of each month, monthly operating statements
of BOG 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 

                                      -23-
<PAGE>
 
operating costs which have accrued to BOG's accounts in such period, and such
other information with respect thereto as the Senior Loan Agent (or in the
absence of a Senior Loan or Senior Loan Agent, the Agent) may require.

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 to the Senior Credit Agreement 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 the Borrower is in compliance with Sections 8.01 and 8.16 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).

     Section 7.02  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 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 7.03  Maintenance, Etc.

          (a) The Borrower shall and shall cause each Subsidiary to: upon
reasonable notice, permit representatives of 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 required by the Agent; 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; and, where failure to do so
would have a Material Adverse Effect: preserve and maintain its corporate
existence and all of its material attendant rights, privileges and franchises,
keep appropriate books of record and account in relation to its business and
activities, comply with all Governmental Requirements, 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, except for any such tax,
assessment, charge or levy the payment of which is being contested in 

                                      -24-
<PAGE>
 
good faith and by proper proceedings and against which adequate reserves are
being maintained.

          (b) Contemporaneously with the delivery of the financial statements
required by Section 7.01(a) to be delivered for each year, the Borrower will
furnish or cause to be furnished to the Agent a certificate of insurance
coverage from the insurer in form and scope reasonably satisfactory to the Agent
and, if required by the Agent, will furnish the Agent copies of the applicable
policies.

          (c) The Borrower will and will cause each Subsidiary to maintain and
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 maintained and operated in all material respects
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 7.03(c) shall not apply to insignificant
Properties unless a failure of such covenant could have a Material Adverse
Effect.

     Section 7.04  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
necessary to periodically determine and assure that all Oil and Gas Properties
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, where failure of the
foregoing would have a Material Adverse Effect.

          (b) The Borrower will promptly notify the Agent 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 correction action.

     Section 7.05  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 Basic 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
further evidence and more fully describe the collateral intended as security for
the Notes, or to correct any omissions in the Basic Documents, or to state more
fully the security obligations set out herein or in any of the Basic Documents,
or to perfect, protect or preserve any Liens created pursuant to any of the
Basic Documents, or to make any recordings, to file any notices or obtain any
consents, all as may be necessary or appropriate in connection therewith.

                                      -25-
<PAGE>
 
     Section 7.06  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 Basic Documents, at
the time and times and in the manner specified.

     Section 7.07  Engineering Reports.

          (a) Not less than 30 days prior to the First Borrowing Base
Determination Date, the Borrower shall furnish to the Agent a Reserve Report
prepared as of December 1, 1998 or later (the "First Reserve Report") and as
provided in clause 7.07(b) below.

          (b) On January 31, 1999 and not less than 30 days prior to each
Scheduled Redetermination Date thereafter, commencing with the Scheduled
Redetermination Date to occur on September 30, 1999, the Borrower shall furnish
to the Agent a Reserve Report.  The Reserve Report furnished for the September
30 Scheduled Redetermination Date shall be prepared as of the preceding July 1
and the Reserve Report furnished for the March Scheduled Redetermination Date
(as well as the Reserve Report furnished on January 31, 1999) shall be prepared
as of the preceding January 1.  The Reserve Report furnished on January 31, 1999
and the January 1 Reserve Report of each year beginning January 1, 2000 shall be
prepared by certified independent petroleum engineers or other independent
petroleum consultant(s) acceptable to the Agent and the First Reserve Report and
the July 1 Reserve Report 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 First Reserve
Report or January 1 Reserve Report, as appropriate.  At Borrower's option, the
July 1 Reserve Report 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 on.

          (c) In addition, the Borrower shall furnish to the Agent copies of any
additional Reserve Reports (other than those specified in Sections 7.07(a) and
(b) above) that Borrower or any of its Subsidiaries deliver to the Senior Loan
Agent or Senior Lenders pursuant to the Senior Loan Documents.

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

              (i)    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

                                      -26-
<PAGE>
 
     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 8.14, (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 Agent, (iv)
     attached to the certificate is a list of its proved Hydrocarbon Interests
     added to and deleted from the immediately prior Reserve Report 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 the proved Hydrocarbon
     Interests evaluated by such Reserve Report are Mortgaged Property; and

              (ii)   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 4.10 are true and correct and
     apply to the Hydrocarbon Interests evaluated in the Reserve Report that are
     described in the 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 Mortgage, conducted
     overall title due diligence that, in all material respects, equals or
     exceeds industry standards given the applicable facts and circumstances.

          (e) In addition to the foregoing, on August 30, 1998, the Borrower
shall furnish to the Agent a Reserve Report prepared as of July 1, 1998, 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 Initial Reserve
Report.

          (f) Notwithstanding the foregoing, so long as there is a Senior Credit
Agreement in effect which requires the semi-annual delivery to the Senior
Lenders of reserve reports evaluating the Borrower's and its Subsidiaries' Oil
and Gas Properties, delivering the Agent and Noteholders with a copy of each
such reserve report and any accompanying officer's certificate (certified to
Agent and the Noteholders) required thereunder shall satisfy the Borrower's
obligations under this Section 7.07, so long as such reserve report includes a
calculation of reserve value based upon pricing assumptions consistent with
Commission reporting requirements at the time.

     Section 7.08  Intentionally Omitted.

     Section 7.09  Additional Collateral.

          (a) Should any of the Borrower's or any Subsidiary's Properties which
are not Mortgaged Property be pledged as collateral for the payment of all or
any portion of the 

                                      -27-
<PAGE>
 
Senior Loan Obligations, the Borrower will simultaneously with such pledge in
favor of the Senior Lenders (or Senior Loan Agent) grant or cause such
Subsidiary to grant to the Trustee as security for the Obligations a second-
priority Lien interest (subject only to Excepted Liens, the matters set out on
Schedule 4.10 of the Securities Purchase Agreement, and any additional
qualifications and exceptions accepted by the Senior Lenders under any mortgage
of such Property to the Senior Agent) in the Borrower's or the Subsidiary's
interest in such Properties not already subject to a Lien of the Basic
Documents, 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 Basic Documents, all in form substantially the same as the previous
Collateral Documents and in sufficient executed (and acknowledged where
necessary or appropriate) counterparts for recording purposes.

          (b) Concurrently with the granting of the Lien or other action
referred to in Section 7.09(a) above, the Borrower will provide to the Agent all
title information provided to the Senior Lenders or Senior Loan Agent in
connection therewith and any legal opinion (addressed to the Agent as well)
provided to the Seniors Lenders or Senior Loan Agent in connection therewith.

     Section 7.10  ERISA Information and Compliance.  Immediately after any
Responsible Officer of the Borrower knows or has reason to know any of the
following items are true, the Borrower will deliver to the Agent a certificate
of a Responsible Officer of the Borrower setting forth details as to such
occurrence and such action, if any, the Borrower or any ERISA Affiliate is
required or proposes to take, together with any notices required or proposed to
be given to or filed with or by the Borrower or its ERISA Affiliate with respect
thereto: that a Reportable Event has occurred or that an application may be or
has been made to the Secretary of the Treasury for a waiver or modification of
the minimum funding standard; that a Multiemployer Plan has been or may be
terminated, reorganized, partitioned or declared insolvent under Title IV of
ERISA; that any required contribution which is material to a Plan, Multiemployer
Plan or Employee Plan has not been or may not be timely made; that proceedings
may be or have been instituted under Section 4069(a) of ERISA to impose
liability on the Borrower or an ERISA Affiliate or under Section 4042 of ERISA
to terminate a Plan or appoint a trustee to administer a Plan; that the Borrower
or any ERISA Affiliate has incurred or may incur any liability (including any
contingent or secondary liability) on account of the termination of or
withdrawal from a Plan or a Multiemployer Plan; and that the Borrower or any
ERISA Affiliate may be required to provide security to a Plan under Section
401(a)(29) of the Code; or any other condition(s) exist(s) or may occur with
respect to one or more Plans, Employee Plans and/or Multiemployer Plans which
would reasonably be expected to result, individually or in the aggregate, in a
Material Adverse Effect.

     Section 7.11  Subsidiary Security.  Should the Borrower grant to the
Senior Loan Agent for the benefit of the Senior Lenders, or to the Senior
Lenders, a security interest and pledge of the Capital Stock of any Subsidiary
(whether existing as of the Closing Date or created or acquired thereafter), the
Borrower will, simultaneously with such pledge in favor of the Senior Loan Agent
or Senior Lenders, grant to the Trustee for the benefit of the Noteholders, a
second in priority security interest and pledge of such Capital Stock in form

                                      -28-
<PAGE>
 
and substance satisfactory to the Agent and if any Subsidiary should guaranty
all or any portion of the Senior Loan, the Borrower will cause such Subsidiary
to enter into a Guaranty Agreement of the Obligations in substantially the same
form as the Guaranty Agreement given by Brigham, Inc. on the Closing Date or
otherwise in form and substance satisfactory to the Agent.  The delivery of such
security and guaranty shall be accompanied by such back up corporate authority
and opinions of counsel (addressed to the Agent as well as the Senior Loan
Agent) as are provided to the Senior Loan Agent.


                                 ARTICLE VIII
                              NEGATIVE COVENANTS

     Unless the Agent's prior written consent to the contrary is obtained, for
the benefit of each of the Noteholders, the Borrower will at all times comply
with the covenants contained in this Article VIII (or cause each Subsidiary's
compliance with the applicable covenants), from the date hereof and for so long
as any part of the Obligations is outstanding.

     Section 8.01  Debt.  Neither the Borrower nor any Subsidiary will:

          (a) Incur, create or assume any Debt, other than Permitted Debt, such
that the ratio of the Borrower's Adjusted Consolidated Net Tangible Assets (as
at the end of the immediately preceding calendar quarter) to the sum of (i)
Borrower's Consolidated Indebtedness (after such incurrence, creation or
assumption of additional Debt other than Permitted Debt) plus (ii) past due
interest on Debt, is less than 1.5 to 1.0.  This covenant shall also apply to
any such Debt incurred or assumed as a result of a merger or consolidation with
any other Person.  Any such Debt so incurred, created or assumed (without
violation of this Section 8.01) must be fully subordinated to the Obligations
unless the Agent agrees otherwise, provided that, so long as ECT has been given
a first look and right to make a proposal for any future subordinated
indebtedness, up to $25,000,000 (less the maximum potential balance at the time
in question of the Schedule 8.02 Payables) in the aggregate of such Debt may be
incurred that is pari passu in right of payment with the Notes.  Notwithstanding
the foregoing, in the event of any refinancing of the Senior Loan, which
refinancing does not violate, on a proforma basis for the four fiscal quarters
of the Borrower after the refinancing, the interest coverage test of Section
8.16, the current ratio test of Section 8.17, or, provided the amount of such
refinanced Senior Loan is more than $75,000,000, the covenant in the first
sentence of this subsection (a), the refinanced Senior Loan shall remain senior
to (and shall not be subordinate to) the Obligations; or

          (b) Incur, create, suffer or assume any accounts payable for the
deferred purchase price of Property or services or any Trade Payables which are
more than 75 days past the invoice or billing date, unless such accounts payable
are either (i) being contested in good faith by appropriate proceedings and
reserves as required under GAAP shall have been established therefor, or (ii)
Schedule 8.02 Payables which are not past due.

                                      -29-
<PAGE>
 
Notwithstanding the foregoing, if at any time the ratio of the Borrower's
Adjusted Consolidated Net  Tangible Assets to the sum of (a) Borrower's
Consolidated Indebtedness plus (b) past due interest on Debt, is less than 1.5
to 1.0, the Agent shall have the right to require, and the Borrower covenants
and agrees to convey (or cause to be conveyed) to the Trustee or the Agent for
the benefit of the Agent and the Noteholders, such additional Potential
Collateral as the Agent shall require (subject to the Senior Lenders' rights to
a first and prior lien in such Potential Collateral).  Such conveyance shall be
made within 30 days following receipt of written notice from the Agent and shall
be deemed a pledge of additional Collateral in accordance with Section 7.09.  As
used in this paragraph, "Potential Collateral" means any of Borrower's or any
Subsidiary's Oil and Gas Properties (which are not already Collateral) which are
identified as containing proved Hydrocarbon reserves, whether currently existing
or hereafter acquired.

     Section 8.02  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 Senior Loan; provided the Trustee or the Agent
is granted a second Lien in such Property securing the payment of the
Obligations;

          (b) Liens securing the payment of the Obligations;

          (c) Excepted Liens;

          (d) Liens securing leases allowed under clause (e) of the definition
of Excepted Liens but only on the Property under lease;

          (e) Liens disclosed on Schedule 8.02; and

          (f) Any Permitted Encumbrances as described in the Mortgage.

     Section 8.03  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 Noteholders in Schedule 8.03;

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

          (c) 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;

                                      -30-
<PAGE>
 
          (d) 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) deposits maturing within one year from the date of creation
thereof with, including certificates of deposit issued by any office located in
the United States, Canada, or England of, any bank or trust company which is
organized under the laws of the United States, Canada, England or any state or
province thereof, which has capital, surplus and undivided profits aggregating
at least $100,000,000.00 (as of the date of such 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. (or their successors),
respectively;

          (f) deposits in money market funds investing exclusively in
investments described in Section 8.03(c), 8.03(d) or 8.03(e);

          (g) investments of up to $400,000 in the aggregate in Quest Resources
L.L.C.;

          (h) (i) investments, distributions, loans and advances by the Borrower
in or to any Subsidiary of the Borrower which is a Guarantor, (ii) investments,
distributions, loans and advances by the Borrower in or to any Subsidiary of the
Borrower which is not a Guarantor, provided that such Subsidiary has direct or
indirect ownership interests in Oil and Gas Properties or gas gathering systems,
gas plants, and similar assets related thereto and the aggregate outstanding
amount of such investments, distributions, loans and advances under this clause
(ii) shall not exceed $1,000,000 at any time, or (iii) investments in equity
interests in any Person (other than a Subsidiary as provided in clauses (i) or
(ii)) whose business is the acquisition, exploration and development of Oil and
Gas Properties, gas gathering systems, gas plants, or any line of business which
is closely related thereto, provided that the aggregate outstanding amount of
any such investments under this clause (iii) shall not exceed $1,000,000 at any
time;

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

          (j) extensions of credit to purchasers, working interest owners,
employees and other persons in the ordinary course of business, up to an
aggregate of $1,000,000 at any one time.

     Section 8.04  Dividends, Distributions and Redemptions.  Neither the
Borrower or any Subsidiary will 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 to the Borrower or any Subsidiary.

                                      -31-
<PAGE>
 
     Section 8.05  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 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 8.06  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.

     Section 8.07  Mergers, Etc.  The Borrower will not and will not permit
any Subsidiary to merge into or with or consolidate with any other Person (other
than the Borrower or a Subsidiary) 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 (other than the Borrower or a
Subsidiary) unless (i) no Default or Event of Default exists and after giving
effect to such merger, no Default or Event of Default shall exist, (ii) after
giving effect to such merger or consolidation, the surviving entity (as the
Borrower hereunder), or in the event of a merger or consolidation of a
Subsidiary, the Borrower, would be able to incur at least $1 in additional Debt
(other than Permitted Indebtedness), and (iii) the surviving entity ratifies and
confirms its Obligations under the Basic Documents and the Notes to the
reasonable satisfaction of the Agent and each Guarantor whose Guaranty Agreement
is in full force and effect ratifies and confirms its Guaranty Agreement to the
reasonable satisfaction of the Agent.

     Section 8.08  Proceeds of Notes.  The Borrower will not permit proceeds
of the Notes to be used for any purpose other than the partial payment of the
Senior Loan.  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 Basic
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 8.09  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 (l) of ERISA or a tax imposed by Chapter 43 of Subtitle D of the Code, which
could reasonably be expected to have a Material Adverse Effect;

          (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 

                                      -32-
<PAGE>
 
expected to result in any liability of the Borrower or any ERISA Affiliate to
the PBGC, which could have a Material Adverse Effect;

          (c) Permit to exist, or allow any ERISA Affiliate to permit to exist,
any accumulated funding deficiency within the meaning of Section 302 of ERISA or
section 412 of the Code, whether or not waived, with respect to any Plan which,
if funded, could reasonably be expected to have a Material Adverse Effect;

          (d) 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 which could, if such benefits become payable,
reasonably be expected to have a Material Adverse Effect.  The term "actuarial
present value of the benefit liabilities" shall have the meaning specified in
section 4041 of ERISA;

          (e) 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;

          (f) 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 liabilities, could reasonably be expected
to have a Material Adverse Effect;

          (g) 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

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

     Section 8.10  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; (ii) assignments, farmouts, and
other disposition of Hydrocarbon Interests which do not contain identified
proved Hydrocarbon reserves, provided such assignments, farmouts, and other
dispositions are in the normal course of business (e.g., in bringing in
participants or disposing of unattractive prospects); (iii) 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 

                                      -33-
<PAGE>
 
of at least comparable value and use and (iv) during any consecutive four fiscal
quarters, sales of Hydrocarbon Interests containing identified proved
Hydrocarbon reserves which, when taken together with the proceeds of any
permitted sales of Subsidiaries during such four quarters under the next
sentence of this Section 8.10, shall not exceed $3,000,000 in the aggregate. The
Borrower will not sell, and will not permit the sale of, any interest in any
Subsidiary unless all or substantially all of the Borrower's interest in such
Subsidiary is sold and, during any consecutive four fiscal quarters, the
proceeds of any such sale taken together with the proceeds of any sale of
Hydrocarbon Interests permitted under clause (iv) of this Section 8.10 does not
exceed $3,000,000.

     Section 8.11  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 8.12  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 (other than the Borrower or a Subsidiary) unless
such transaction (a) is otherwise not in violation of this Indenture, and (b)
unless approved by a majority of the disinterested members of the Board of
Directors, is in the ordinary course of its business and is 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 8.13  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 Basic Documents) which in
any way prohibits or restricts any Subsidiary from paying dividends or making
any other distribution to the Borrower or which requires the consent of a notice
to other Persons in connection with any of the foregoing, other than the
restrictions contained in the Senior Loan Documents as they exist on the day
hereof.

     Section 8.14  Gas Imbalances, Take-or-Pay 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 8.15  Borrower as Operator.  The Borrower will not and will not
allow any of its Subsidiaries to voluntarily resign as operator of more than
twenty-five percent (25%) of their currently operated Oil and Gas Properties,
unless a substitute operator is appointed 

                                      -34-
<PAGE>
 
that is another Subsidiary of the Borrower or is otherwise acceptable to the
Majority Noteholders, approval of such substitute operator not to be
unreasonably withheld.

     Section 8.16  Consolidated Interest Coverage Ratio.  As of the last day
of each fiscal quarter, the Borrower will not permit the Consolidated Interest
Coverage Ratio to be less than (i) 1.5 to 1.0 as of the end of the first four
(4) fiscal quarters following the Closing Date and (ii) 2.0 to 1.0 as of the end
of each fiscal quarter thereafter.

     Section 8.17  Current Ratio.  The Borrower will not permit its ratio of
(i) consolidated current assets of the Borrower and its Consolidated
Subsidiaries (including, without limitation, any unused and available
commitments under the Senior Credit Agreement) to (ii) their consolidated
current liabilities (excluding any principal or interest payments due on the
Senior Loan or the Notes), to be less than .8 to 1.0 at any time.

                                  ARTICLE IX
                             PAYMENT OF THE NOTES

     Section 9.01  Repayment.  The Borrower shall pay to the Noteholders on the
Maturity Date an amount equal to the outstanding principal amount of the Notes
plus the accrued and unpaid interest on the outstanding principal amount of the
Notes.  The Borrower may prepay the Obligations at any time in whole or in part
without penalty or premium.

     Section 9.02  Interest.

          (a) Subject to the provisions of Section 9.02(b), the outstanding
principal amount of the Notes shall bear interest at the following rates per
annum:

                Period                               Rate

          Funding Date through August 20, 2001        12%

          August 21, 2001 through August 20, 2002     13%

          August 21, 2002 through Maturity Date       14%

The foregoing rates shall apply only to interest which is paid in cash.  In the
event the Borrower should elect to make any interest payments in kind as
permitted by Section 9.02(b), the rates applicable to such payments shall be as
set forth in Section 9.02(b).

          (b) So long as there exists no Event of Default, if on any Interest
Payment Date either (i) there exists a "Borrowing Base Deficiency" under the
Senior Credit Agreement or (ii) the payment in cash of interest accrued on the
Notes would cause the Borrower to be in violation of any covenant or other
restriction set forth in the Senior Loan Documents or any Basic Document, the
Borrower may pay such interest in kind, as provided in this Section 9.02(b).  In
such event the accrued interest due on such Interest Payment 

                                      -35-
<PAGE>
 
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 under the Notes and, as of the Interest
Payment Date, shall be added to the outstanding principal balance of the Notes
(notwithstanding that the outstanding principal balance may exceed, in the
aggregate, the face amount of the Notes). In order to exercise its option to pay
interest in kind under this Section 9.02(b), the Borrower shall, on or before
the applicable Interest Payment Date, deliver written notice to the Agent
executed by a Responsible Officer specifying the applicable covenant or
restriction of the Senior Loan Documents or the Basic Documents that will be
violated by payment of accrued interest in cash and notifying Agent of its
election to pay interest in kind. Any such election must be made as to all
Notes. 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 cash and any subsequent failure to do so in a timely fashion
(subject to the thirty (30) day grace period provided in Section 10.01(a)) shall
constitute an Event of Default hereunder. Notwithstanding anything contained
herein to the contrary, the Borrower may not pay interest in kind over the term
of the Notes for more than six (6) calendar quarters. In the event the Borrower
elects to pay interest in kind, such interest to be paid shall be calculated at
the following rates commencing on the immediately preceding Interest Payment
Date:

                 Period                              Rate

          Funding Date through August 20, 2001        13%

          August 21, 2001 through August 20, 2002     14%

          August 21, 2002 through Maturity Date       15%

          (c) In the event any sum due and payable hereunder is not paid when
due such past due amount shall accrue interest at the Default Rate from the date
due until paid.  Should an Event of Default occur hereunder, interest on the
Obligations shall accrue at the Default Rate from the date of occurrence of the
Default to which such Event of Default is attributable, until such Event of
Default is cured or waived.

          (d) Interest shall be computed based on a year of 360 days and twelve
30-day months (pro-rated appropriately for the period from the Funding Date
until the first Interest Payment Date and for any period of less than three
months for which interest may be due as a result of the prepayment or
acceleration of the Notes).  The rates of interest applicable to the Notes
provided in Sections 9.02(a) and (b) shall commence on the first day immediately
following the Funding Date or the applicable anniversary of the Funding Date and
remain in effect through the next succeeding anniversary of the Funding Date, or
the Maturity Date, as applicable.

          (e) Accrued interest on the Notes shall be due and payable in cash or,
if permitted by Section 9.02(b), in kind, quarterly on each Interest Payment
Date (including the 

                                      -36-
<PAGE>
 
Maturity Date) or, in the event the maturity of the Notes is accelerated
pursuant to the terms of the Basic Documents, such earlier date as the Notes
become due and payable, or the date the Notes are paid in full, whichever first
occurs. If any Interest Payment Date is not a Business Day, the interest payment
that would be due thereon shall instead be due on the next following Business
Day.

          (f) Notwithstanding anything herein or in the other Basic Documents to
the contrary, it is the intention of the parties hereto to conform strictly to
usury laws applicable to this transaction.  Accordingly, if the transactions
contemplated hereby would be usurious under applicable law, then, in that event,
notwithstanding anything to the contrary in the Notes, this Indenture or in any
other Basic Document or agreement entered into in connection with or as security
for the Notes, it is agreed as follows:  (a) the aggregate of all consideration
which constitutes interest under law applicable to the Noteholders that is
contracted for, taken, reserved, charged or received under the Notes, this
Indenture or under any of the other Basic Documents or agreements or otherwise
in connection with this transaction shall under no circumstances exceed the
maximum amount allowed by such applicable law, and any excess shall be canceled
automatically and, if already paid, shall be credited by the Noteholders on the
principal amount of the Obligations (or, to the extent that the principal amount
of the Obligations shall have been or would thereby be paid in full, refunded to
the Borrower); and (b) in the event that the maturity of the Notes is
accelerated by reason of any Event of Default under this Indenture or otherwise,
or in the event of any required or permitted prepayment, then such consideration
that constitutes interest under law applicable to this transaction may never
include more than the maximum amount allowed by such applicable law, and (c)
excess interest, if any, provided for in this Indenture or otherwise in
connection with the Notes shall be canceled automatically and, if already paid,
shall be credited by the Noteholders on the principal amount of the Obligations
(or, to the extent that the principal amount of the Obligations shall have been
or would thereby be paid in full, refunded by the Noteholders to the Borrower).
All sums paid or agreed to be paid to the Noteholders for the use, forbearance
or detention of sums included in the Obligations shall, to the extent permitted
by applicable law, be amortized, prorated, allocated and spread throughout the
full term of the Notes until payment in full so that the rate or amount of
interest on account of the Obligations does not exceed the applicable usury
ceiling, if any.  As used in this Section 9.02(f), the term "applicable law"
shall mean the laws which govern this Indenture as described in Section 12.07
(or the law of any other jurisdiction whose laws may be mandatorily applicable
notwithstanding other provisions of this Indenture), or law of the United States
of America applicable to the Noteholders and the Notes which would permit the
Noteholders to contract for, charge, take, reserve or receive a greater amount
of interest than under any other applicable law.  If the stated rate of interest
under this Indenture ever exceeds the Maximum Rate, then the outstanding
principal amount of the Notes made hereunder shall bear interest at the Maximum
Rate until the difference between the interest which would have been due at the
stated rates of interest and the amount due at the Maximum Rate (the "Lost
Interest") has been recaptured by the Noteholders.  If the Notes are repaid in
full and the Lost Interest has not been fully recaptured by the Noteholders
pursuant to the preceding sentence, then the Notes shall be deemed to have
accrued interest at the Maximum Rate since the date the initial advance under
the Notes was 

                                      -37-
<PAGE>
 
made to the extent necessary to recapture the Lost Interest not recaptured
pursuant to the preceding sentence and, to the extent allowed by law, the
Borrower shall pay to the Noteholders the amount of the Lost Interest remaining
to be recaptured by the Noteholders.

     Section 9.03  Payments and Computations.

          (a) All payments and obligations by Borrower under the Notes or any
other Basic Document shall be made to the Agent, without any presentment and
without any notation of such payment being made on the Notes (i) by wire
transfer in immediately available funds to such account as the Agent may
designate from time to time by written notice to the Borrower (the "Agent's
Account") or (ii) in such other manner as may be designated in writing to the
Borrower by the Agent.

          (b) The Borrower shall make each payment under this Indenture and
under the Notes not later than 2:00 p.m. (Houston, Texas time) on the day when
due in U.S. Dollars to the Agent at the location specified in paragraph (a)
above in immediately available funds. All payments by the Borrower hereunder
shall be made without any offset, abatement, withholding, or reduction.

          (c) Whenever any payment under the Basic Documents shall be stated to
be due on a day other than a Business Day, such payment shall be made on the
next succeeding Business Day, and (other than an interest payment subject to
Section 9.02(e) above) such extension of time shall in such case be included in
the computation of payment of interest.  If the time for payment for an amount
payable is not specified in the Basic Documents, or in any other document, the
payment shall be due and payable ten days after the date on which the Agent or
any Noteholder demands payment therefor.

          (d) Following receipt of payment in cash of any obligations due under
the Notes or any other Basic Document the Agent will promptly thereafter cause
to be distributed like funds relating to the payment of principal, interest or
fees ratably to the Noteholders at their respective Noteholder's Account.  If
and to the extent that the Agent receives any payment or prepayment from the
Borrower and fails to distribute such payment or prepayment to the Noteholders
ratably on the basis of their respective Participations on the day the Agent
receives such payment or prepayment (if received prior to 1:00 P.M. (Houston,
Texas time) on such day) or the next Business Day (if received after 1:00 P.M.
(Houston, Texas time) on such day), then the Agent shall pay to each Noteholder
such Noteholder's Participation of such payment or prepayment together with
interest thereon at the Federal Funds Rate for each day from the date such
amount should have been distributed by the Agent until such payment or
prepayment is actually distributed to the Noteholders.  All payments and
prepayments received shall be applied first to accrued interest and second to
the reduction of principal.

          (e) Unless the Agent shall have received written notice from the
Borrower prior to the date on which any payment is due to the Noteholders that
the Borrower will not make such payment in full or will make such payment in
kind pursuant to Section 9.02(b), 

                                      -38-
<PAGE>
 
the Agent may assume that the Borrower has made such payment in full, in cash,
to the Agent on such date and the Agent may, in reliance upon such assumption,
cause to be distributed to each Noteholder on such date an amount equal to the
amount then due such Noteholder. If and to the extent the Borrower shall not
have so made such payment in full, in cash, to the Agent, each Noteholder shall
repay to the Agent forthwith on demand such amount distributed to such
Noteholder, together with interest, for each day from the date such amount is
distributed to such Noteholder until the date such Noteholder repays such amount
to the Agent, at the Federal Funds Rate for such day.


                                   ARTICLE X
                             DEFAULT AND REMEDIES

     Section 10.01  Events of Default.  The occurrence of any of the following
shall be an "Event of Default" for the purposes of this Indenture and the Notes:

          (a) the Borrower shall default in the payment or prepayment when due
of any Obligations, 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 thirty (30) days after such Obligations become due,
in the case of interest, or thirty (30) days after the Borrower receives notice
from the Agent that such Obligations are due, in the case of Obligations other
than principal or interest; or

          (b) (i) The Borrower or any Guarantor shall, as to any Debt (other
than the Obligations and the Senior Loan) aggregating more than $2,000,000
default in the payment when due of any principal of or interest thereon, 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 (ii) as to the Senior Loan, there shall have 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

          (c) any representation, warranty or certification made or deemed made
herein or in any other Basic Document by the Borrower or any Guarantor, or any
certificate furnished by the Borrower or any Guarantor to the Trustee, any
Noteholder or the Agent pursuant to the provisions hereof or any other Basic
Document, shall prove to have been false or misleading as of the time made or
furnished in any material and adverse respect and such default shall continue
unremedied for a period of forty-five (45) days after notice thereof to the
Borrower by the Agent; or

          (d) the Borrower shall default in the performance of any of its
obligations under Article VIII which are not capable of being cured, or under
Sections 8.01, 8.16, 8.17  or 7.01(c); or the Borrower shall default in the
performance of any of its obligations under 

                                      -39-
<PAGE>
 
Article VIII which are capable of being cured (other than Sections 8.01, 8.16
and 8.17) or any other Article of this Indenture (other than 7.01(c)) or under
any other Basic 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 forty-five (45) days after notice thereof to
the Borrower by the Agent; or

          (e) any Guarantor shall default in the performance of its obligation
to pay the Liabilities (as defined in the Guaranty Agreement) at maturity, 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 forty-five (45) days after notice thereof to the Guarantor by 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 a 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) file 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 debt; (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, judgement 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
$2,000,000 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 forty-
five (45) days from the date of entry thereof and the Borrower shall not, within
said period of 45 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

                                      -40-
<PAGE>
 
          (j) any of the Basic 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 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 Indenture, or the Borrower or any Guarantor shall so state in writing, and
such Default shall continue unremedied for a period of forty-five (45) days
after notice thereof to the Borrower by the Agent; or

          (k) 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, and such Default shall continue unremedied for a
period of forty-five (45) days after notice thereof to the Guarantor by the
Agent; or

          (l) there occurs a Change in Control; or

          (m) any annual audited financial statement delivered to Agent pursuant
to Section 7.01(a) is qualified (as to going concern or similar qualifications).

     Section 10.02  Remedies.

          (a) At any time during the continuance of any Event of Default
specified in Section 10.01 (other than clauses (f), (g) or (h) of Section
10.01), or in clause (k) as it relates to clauses (f), (g) or (h) thereof, the
Agent may by written notice to the Borrower declare the entire principal amount
of all Obligations then outstanding, including interest accrued thereon, to be
immediately due and payable without presentment, demand, protest, notice of
protest or dishonor, notice of intent to accelerate,  or other notice of default
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 Trustee, Agent or Noteholders with respect thereto without the express
written consent of the Agent.

          (b) Upon the happening of any Event of Default specified in clauses
(f), (g) or (h) of Section 10.01, or clause (k) as it relates to clauses (f),
(g) or (h), the entire principal amount of all Obligations then outstanding,
including interest accrued thereon, shall, without notice or action by the
Trustee, the Agent or the Noteholders be immediately due and payable without
presentment, demand, protest, notice of protest or dishonor, notice of intent to
accelerate or other notice of default of any kind, all of which are hereby
expressly waived by the Borrower.

          (c) In addition to the foregoing, upon the happening of any of the
events described in subsections (a) and (b) above, the Trustee, at the direction
of the Agent may 

                                      -41-
<PAGE>
 
exercise any of the rights or remedies provided in the Collateral Documents and
other Basic Documents or avail itself of any rights or remedies provided by
applicable law.

          (d) 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 Basic Documents; second to accrued interest
on the Notes; third to fees; fourth pro rata to principal outstanding on the
Notes and other Obligations; 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 Basic Documents, the Borrower and any other
mortgagors are and will be assigning to the Trustee 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 Basic 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 an Event
of Default, however, the Trustee at the direction of the Agent may (subject to
all rights of the Senior Loan Agent and the Senior Lenders under the Senior Loan
Documents) exercise its rights and remedies granted under the Mortgages and the
other Basic Documents, including the rights and remedies granted under the
Mortgages and the other Basic 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 and Proceeds.  In no case shall any failure by the Trustee to collect
directly any such Production and Proceeds constitute in any way a release of any
of its or the Agent's rights under the Basic Documents.

     Section 10.04 Set-Off.  Upon the occurrence of any Event of Default, any
Noteholder shall have the right to set-off any funds of the Borrower in the
possession of the Noteholder against any Debt (or accrued interest on Debt) then
due by the Borrower to the Noteholder.  The Borrower agrees that any holder of
Notes or a participation in the Notes may exercise any and all rights of
counter-claim, set-off, banker's lien and other liens with respect to any and
all monies owing by the Borrower to such holder as fully as if such holder of a
participation were a holder of a Note in the amount of such participation.

                                  ARTICLE XI
                                   THE AGENT

     Section 11.01  Authorization and Action.  Each Noteholder hereby appoints
and authorizes the Agent to take such action on behalf of such Noteholder and to
exercise such powers under this Indenture as are delegated to the Agent by the
terms hereof and of the other Basic Documents, together with such powers as are
reasonably incidental thereto.  As 

                                      -42-
<PAGE>
 
to any matters not expressly provided for by this Indenture or any other Basic
Document (including, without limitation, enforcement or collection of the
Notes), the Agent shall not be required to exercise any discretion or take any
action, but shall be required to act or to refrain from acting (and shall be
fully protected in so acting or refraining from acting) only upon the
instructions of the Majority Noteholders, and such instructions shall be binding
upon Noteholders; provided, however, that the Agent shall not be required to
take any action which exposes the Agent to personal liability or which is
contrary to this Indenture, any other Basic Document, or applicable law.

     Section 11.02  Agent's Reliance, Etc.  Neither the Agent nor any of the
Agent's directors, officers, agents or employees shall be liable for any action
taken or omitted to be taken (including the Agent's own negligence) by it or
them under or in connection with this Indenture or the other Basic Documents,
except for its or their own gross negligence or willful misconduct.  Without
limitation of the generality of the foregoing, the Agent:  (a) may treat the
payee of any Note as the holder thereof until the Agent receives written notice
of the assignment or transfer thereof signed by such payee and in form
satisfactory to the Agent; (b) may consult with legal counsel (including counsel
for the Borrower), independent public accountants and other experts selected by
it and shall not be liable for any action taken or omitted to be taken in good
faith by it in accordance with the advice of such counsel, accountants or
experts; (c) makes no warranty or representation to any Noteholder and shall not
be responsible to any Noteholder for any statements, warranties or
representations made in or in connection with this Indenture or the other Basic
Documents; (d) shall not have any duty to ascertain or to inquire as to the
performance or observance of any of the terms, covenants or conditions of this
Indenture or any other Basic Document on the part of the Borrower or any
Subsidiary or to inspect the Property (including the books and records) of such
Persons; (e) shall not be responsible to any Noteholder for the due execution,
legality, validity, enforceability, genuineness, sufficiency or value of this
Indenture or any other Basic Document; and (f) shall incur no liability under or
in respect of this Indenture or any other Basic Document by acting upon any
notice, consent, certificate or other instrument or writing (which may be by
telecopy) reasonably believed by it to be genuine and signed or sent by the
proper party or parties.

     Section 11.03  The Agent and Its Affiliates.  With respect to its
Participation, and the Note issued to it, the Agent shall have the same rights
and powers under this Indenture as any other Noteholder and may exercise the
same as though it were not an Agent hereunder.  The term "Noteholder" or
"Noteholders" shall, unless otherwise expressly indicated, include the Agent in
its individual capacity.  The Agent and its Affiliates may accept deposits from,
lend money to, act as trustee under indentures of, and generally engage in any
kind of business with, the Borrower or any Subsidiary, and any Person who may do
business with or own securities of the Borrower, or any Subsidiary, all as if
the Agent were not an agent hereunder and without any duty to account therefor
to the Noteholders.

     Section 11.04 Noteholders Loan Decision. Each Noteholder acknowledges that
it has, independently and without reliance upon the Agent or any other
Noteholder and based on the Financial Statements and such other documents and
information as it has deemed

                                      -43-
<PAGE>
 
appropriate, made its own credit analysis and decision to enter into the Basic
Documents. Each Noteholder also acknowledges that it will, independently and
without reliance upon the Agent or any other Noteholder and based on such
documents and information as it shall deem appropriate at the time, continue to
make its own credit decisions in taking or not taking action under this
Indenture.

     Section 10.05  Indemnification.  The Noteholders severally agree to
indemnify the Agent and each Affiliate thereof and their respective directors,
officers, employees and agents (to the extent not reimbursed by the Borrower),
according to their respective Participations from and against any and all
liabilities, obligations, losses, damages, penalties, actions, judgments, suits,
costs, expenses or disbursements of any kind or nature whatsoever which may be
imposed on, incurred by, or asserted against the Agent in any way relating to or
arising out of this Indenture or any action taken or omitted by the Agent under
this Indenture or any other Basic Document (INCLUDING THE AGENT'S OWN
NEGLIGENCE), provided that no Noteholder shall be liable for any portion of such
liabilities, obligations, losses, damages, penalties, actions, judgments, suits,
costs, expenses or disbursements resulting from the Agent's gross negligence or
willful misconduct.  Without limitation of the foregoing, each Noteholder agrees
to reimburse the Agent promptly upon demand for its ratable share of any out-of-
pocket expenses (including counsel fees) incurred by the Agent in connection
with the preparation, execution, delivery, administration, modification,
amendment or enforcement (whether through negotiations, legal proceedings or
otherwise) of, or legal advice in respect of rights or responsibilities under,
this Indenture or any other Basic Document, to the extent that the Agent is not
reimbursed for such expenses by the Borrower.

     Section 11.06 Successor Agent. The Agent may resign at any time by giving
written notice thereof to the Noteholders and the Borrower and may be removed at
any time with cause by the Majority Noteholders upon receipt of written notice
from the Majority Noteholders to such effect. Upon receipt of notice of any such
resignation or removal, the Majority Noteholders shall have the right to appoint
a successor Agent with, if no Default exists, the consent of the Borrower, which
consent shall not be unreasonably withheld. If no successor Agent shall have
been so appointed by the Majority Noteholders with the consent of the Borrower,
if required, and shall have accepted such appointment, within 30 days after the
retiring Agent's giving of notice of resignation or the Majority Noteholders,
removal of the retiring Agent, then the retiring Agent may, on behalf of the
Noteholders and the Borrower, appoint a successor Agent. Upon the acceptance of
any appointment as Agent 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 under this Indenture and the other Basic
Documents. After any retiring Agent's resignation or removal hereunder as Agent,
the provisions of this Article XI shall inure to its benefit as to any actions
taken or omitted to be taken by it while it was Agent this Indenture and the
other Basic Documents.

                                      -44-
<PAGE>
 
                                  ARTICLE XII
                                    TRUSTEE

     Section 12.01  Duties of Trustee.

          (a) If an Event of Default has occurred and is continuing, the Trustee
shall exercise such rights and powers vested in it by this Indenture and use the
same degree of care and skill in such exercise as a prudent person would
exercise or use under the circumstances in the conduct of such person's own
affairs.

          (b) Except during the continuance of an Event of Default:

              (i)    The Trustee need perform only those duties that are
     specifically set forth (or incorporated by reference) in this Indenture and
     no others.

              (ii)   In the absence of bad faith on its part, the Trustee may
     conclusively rely, as to the truth of the statements and the correctness of
     the opinions expressed therein, upon certificates or opinions furnished to
     the Trustee and conforming to the requirements of this Indenture.  However,
     in the case of any such certificates or opinions which by any provision
     hereof are specifically required to be furnished to the Trustee, the
     Trustee shall be under a duty to examine the same to determine whether or
     not they conform to the requirements of this Indenture (but need not
     confirm or investigate the accuracy of mathematical calculations or other
     facts stated therein).

          (c) The Trustee may not be relieved from liability for its own
negligent action, its own negligent failure to act, or its own willful
misconduct, except that:

              (i)    This paragraph (c) does not limit the effect of paragraph
     (b) of this Section.

              (ii)   The Trustee shall not be liable for any error of judgment
     made in good faith by an officer of the Trustee, unless it is proved that
     the Trustee was negligent in ascertaining the pertinent facts.

               (iii) The Trustee shall not be liable with respect to action it
     takes or omits to take in good faith in accordance with a direction
     received by it from the Agent, and the Trustee shall be entitled from time
     to time to request such a direction.

          (d) Every provision of this Indenture and each Collateral Document
that in any way relates to the Trustee is subject to paragraphs (a), (b) and (c)
of this Section.

          (e) The Trustee shall be under no obligation and may refuse to perform
any duty or exercise any right or power unless it receives indemnity
satisfactory to it against any loss, liability or expense.  No provision of this
Indenture or any Collateral Document shall 

                                      -45-
<PAGE>
 
require the Trustee to expend or risk its own funds or otherwise incur financial
liability in the performance of any of its duties hereunder or in the exercise
of any of its rights or powers, if it shall have reasonable grounds to believe
that repayment of such funds or adequate indemnity against such risk or
liability is not reasonably assured to it.

          (f) The Trustee shall not be liable for interest on any money received
by it except as the Trustee may agree in writing with the Borrower.  Money held
in trust by the Trustee need not be segregated from other funds except to the
extent required by law.

          (g) The Trustee shall not be required to take notice, and shall not be
deemed to have notice, of any Default or Event of Default hereunder, unless the
Trustee shall be notified specifically of the Default or Event of Default in a
written instrument or document delivered to it by the Borrower or any Guarantor,
or by the Agent or the Majority Noteholders.  In the absence of delivery of a
notice satisfying those requirements, the Trustee may assume that there is no
Default or Event of Default, except as noted above.

     Section 12.02  Rights of Trustee.

          (a) The Trustee may conclusively rely on and shall be fully protected
in acting or refraining from acting upon any document believed by it to be
genuine and to have been signed or presented by the proper person.  The Trustee
shall not be bound to make any investigation into the facts or matters stated in
any resolution, certificate, statement, instrument, opinion, report, notice,
request, direction, consent, order, bond, debenture or other paper or document,
but the Trustee, in its discretion, may make such further inquiry or
investigation into such facts or matters as it may see fit, and, if the Trustee
shall determine to make such further inquiry or investigation, it shall be
entitled to examine the books, records and premises of the Borrower, personally
or by agent or attorney, to the extent reasonably required by such inquiry or
investigation at the sole expense of the Borrower and shall incur no liability
or additional liability of any kind by reason of such inquiry or investigation.

          (b) Before the Trustee acts or refrains from acting, it may require an
Officers, Certificate or an Opinion of Counsel.  The Trustee shall not be liable
for any action it takes or omits to take in good faith in reliance on such
certificate or opinion.

          (c) The Trustee may act through agents and shall not be responsible
for the misconduct or negligence of any agent appointed with due care.

          (d) The Trustee shall not be liable for any action it takes or omits
to take in good faith which it believes to be authorized or within its rights or
powers.

          (e) The Trustee may consult with counsel of its selection and the
advice of such counsel or any Opinion of Counsel shall be full and complete
authorization and protection in respect of any action taken, suffered or omitted
by it hereunder in good faith and in reliance thereon.

                                      -46-
<PAGE>
 
          (f) The Trustee will not, without the consent of the Agent, give any
consent, waiver or approval required under the Collateral Documents or by the
terms hereof with respect to the Collateral or agree to any amendment or
modification of the Collateral Documents.

          (g) The Trustee may settle or compromise at any time any and all
claims against it which may be asserted by any governmental body or private
party for the alleged violation of any Environmental Laws affecting any of the
Collateral, and may disclaim (as to itself, but not as to the Indenture or any
successor Trustee) any power (including, without limitation, the power to sell
the Collateral) granted by the Indenture, the Collateral Documents or any
statute or rule of law, the exercise of which power may, in the sole discretion
of the Trustee, as advised by counsel, cause the Trustee to incur corporate or
personal lability under any Environmental Laws.

     Section 12.03  Individual Rights of Trustee.  The Trustee in its individual
or any other capacity may become the owner or pledgee of Notes and may otherwise
deal with the Borrower or its Subsidiaries or Affiliates with the same rights it
would have if it were not Trustee.  The provision of this Section shall extend
to Affiliates of the Trustee.  Any Agent may do the same with like rights.
However, the Trustee must comply with Sections 12.10 and 12.11.

     Section 12.04  Trustee's Disclaimer.

     The Trustee makes no representation as to the value or condition of the
Collateral or any part thereof, or as to the title of the Borrower or any
Subsidiary thereto, or as to the security afforded thereby or hereby, or as to
the validity or genuineness of any Collateral pledged and deposited with the
Trustee, or the validity or adequacy of this Indenture or the Notes, it shall
not be accountable for the Borrower's use of the proceeds from the Notes or any
offering memorandum or solicitation documents, and it shall not be responsible
for any statement in the Basic Documents other than its certificate of
authentication.

     Section 12.05  Notice of Defaults.

     If a Default occurs and is continuing and if it is actually known to a
Responsible Officer of the Trustee pursuant to Section 12.01(g), the Trustee
shall mail to each Noteholder and the Agent pursuant to Section 13.05 a notice
of the Default within 90 days after it occurs.  Except in the case of a Default
in any payment on any Note, the Trustee may withhold the notice if and so long
as the board of directors, executive committee or a trust committee of officers
in good faith determines that withholding the notice is in the interests of the
Noteholders.

     Section 12.06  Reports by Trustee to Noteholders.

     Within 60 days after each November 15, beginning with the November 15
following the date of this Indenture, the Trustee shall mail to each Noteholder
a brief report dated as 

                                      -47-
<PAGE>
 
of such November 15, that complies with TIA (S)313(a), but only if such report
is required in any year under TIA (S)313(a). The Trustee also shall comply with
TIA (SS)313(b) and 313(c).

     A copy of each report at the time of its mailing to Noteholders shall be
filed with the SEC and each stock exchange on which the Notes are listed.  The
Borrower shall promptly notify the Trustee in writing when the Notes become
listed on any national securities exchange or of any delisting thereof.

     Section 12.07  Compensation and Indemnity.

     The Borrower and the Guarantors jointly and severally agree to pay the
Trustee from time to time such compensation as shall be agreed in writing
between the Borrower and the Trustee for its services (which compensation shall
not be limited by any provision of law in regard to the compensation of a
trustee of an express trust).  The Borrower and the Guarantors jointly and
severally agree to reimburse the Trustee upon request for all reasonable out-of-
pocket expenses, disbursements and advances incurred by. it.  Such expenses
shall include when applicable the reasonable compensation and expenses of the
Trustee's agents and counsel.

     The Borrower and the Guarantors jointly and severally agree to indemnify
each of the Trustee and any predecessor Trustee against any and all loss,
liability, damage, claim or expenses, including taxes (other than taxes based on
the income of the Trustee) incurred by it arising out of or in connection with
the acceptance and administration of the trust and its duties hereunder as
Trustee and/or Note Registrar, including the costs and expenses of enforcing
this Indenture against the Borrower (including with respect to this Section
12.07) and of defending itself against any claim or liability in connection with
the exercise or performance of any of its powers or duties hereunder.  The
Trustee shall notify the Borrower and the Guarantors of any claim for which it
may seek indemnity; however, unless the position of the Borrower is materially
prejudiced by such failure, the failure of the Trustee to promptly notify the
Borrower shall not limit its right to indemnification.  The Borrower shall
defend each such claim and the Trustee shall cooperate in the defense.  The
Trustee may retain separate counsel and the Borrower shall reimburse the Trustee
for the reasonable fees and expenses of such counsel if the Borrower is advised
by an Opinion of Counsel that the Trustee has separate defenses and that
separate representation is appropriate or if the Trustee reasonably determines
that such joint defense would otherwise involve a conflict of interest.  The
Borrower need not pay for any settlement made without its consent.

     Neither the Borrower nor the Guarantors shall be obligated to reimburse any
expense or indemnify against any loss or liability incurred by the Trustee
through the Trustee's breach of the applicable standard of care for its conduct
under Section 12.01.

     When the Trustee incurs expenses or renders services after the occurrence
of any Event of Default specified in Sections 10.01(f), (g) or (h), the expenses
and the compensation 

                                      -48-
<PAGE>
 
for the services are intended to constitute expenses of administration under any
Bankruptcy Law.

     The provisions of this Section 12.07 shall survive the satisfaction and
discharge or other termination of this Indenture.

     Section 12.08  Replacement of Trustee.

     The Trustee may resign by so notifying the Borrower and the Guarantors.
The Agent may remove the Trustee by so notifying the Trustee, in writing.  The
Borrower may remove the Trustee if.

          (a) the Trustee fails to comply with Section 12.10;

          (b) the Trustee is adjudged a bankrupt or an insolvent;

          (c) a receiver or other public officer takes charge of the Trustee or
its property; or

          (d) the Trustee becomes incapable of acting as Trustee hereunder.

     If the Trustee resigns or is removed or if a vacancy exists in the office
of Trustee for any reason, the Borrower shall promptly appoint a successor
Trustee.  Within one year after the successor Trustee takes office, the Agent
may appoint a successor Trustee to replace the successor Trustee appointed by
the Borrower.

     A successor Trustee shall deliver a written acceptance of its appointment
to the retiring Trustee and to the Borrower and the Guarantors.  Immediately
after that, the retiring Trustee shall transfer all property held by it as
Trustee to the successor Trustee the resignation or removal of the retiring
Trustee shall become effective, and the successor Trustee shall have all the
rights, powers and duties of the Trustee under this Indenture.  A successor
Trustee shall mail notice of its succession to each Noteholder.

     If a successor Trustee does not take office within 30 days after the
retiring Trustee resigns or is removed, the retiring Trustee, the Borrower or
the Agent may petition, at the expense of the Borrower, any court of competent
jurisdiction for the appointment of a successor Trustee.

     If the Trustee fails to comply with Section 12.10, the Agent may petition
any court of competent jurisdiction for the removal of the Trustee and the
appointment of a successor Trustee.  Any successor Trustee shall comply with TIA
(S)310(a)(5).

                                      -49-
<PAGE>
 
     Section 12.09  Successor Trustee by Merger, etc.

     If the Trustee consolidates, merges or converts into, or transfers all or
substantially all of its corporate trust business to, another corporation, the
successor corporation without any further act shall be the successor Trustee;
provided such corporation or association shall be otherwise eligible and
qualified under this Article.

     Section 12.10  Eligibility, Disqualification.

     This Indenture shall always have a Trustee which satisfies the requirements
of TIA (S)310(a)(1) and (5). The Trustee shall always have a combined capital
and surplus of at least $50,000,000 as set forth in its most recent published
annual report of condition. The Trustee shall also comply with TIA (S)310(b).

     Section 12.11  Preferential Collection of Claims Against Borrower.

     The Trustee shall comply with TIA (S)311(a), excluding any creditor
relationship listed in TIA (S)311(b). A Trustee who has resigned or been removed
shall be subject to TIA (S)311(a) to the extent indicated therein.

     Section 12.12  Appointment of Co-Trustee.

     If the Trustee deems it necessary or desirable in connection with the
Collateral and/or the enforcement of the Collateral Documents, the Trustee may
appoint a co-Trustee with such powers of the Trustee as may be designated by the
Trustee at the time of such appointment (including acting as separate trustee of
any Collateral), and the Borrower shall, on request, execute and deliver to such
co-Trustee any deeds, conveyances or other instruments required by such co-
Trustee so appointed by the Trustee to more fully and certainly vest in and
confirm to such co-Trustee its rights, powers, trusts, duties and obligations
hereunder.

     All rights (including rights to indemnification hereunder), powers, duties
and obligations conferred or imposed upon the Trustee shall be conferred or
imposed upon and exercised or performed by the Trustee or jointly by the Trustee
and such co-Trustees, except to the extent that under any law of any
jurisdiction in which any particular act or acts are to be performed the Trustee
shall be incompetent or unqualified to perform such act or acts, in which event
such rights, powers, duties and obligations shall be exercised and performed by
such co-Trustees.  No Trustee or co-Trustee shall be personally liable by reason
of any act or omission of any other Trustee or co-Trustee hereunder.  Any co-
Trustee appointed pursuant to this Section 12.12 may be removed by the Trustee
pursuant to the terms of this Indenture and may be removed and may resign
pursuant to the provisions of the applicable Collateral Document and of this
Indenture.

     A co-Trustee shall not be responsible for and makes no representation as to
the value or condition of the Collateral or any part thereof, or as to the title
of the Borrower thereto, or as to the security afforded thereby or hereby, or as
to the validity or genuineness of any 

                                      -50-
<PAGE>
 
Collateral pledged and deposited with such co-Trustee, or the validity or
adequacy of this Indenture or the Notes; a co-Trustee shall not be accountable
for the Borrower's use of the proceeds from the Notes, and it shall not be
responsible for any statement of the Borrower in this Indenture or any document
issued in connection with the sale of the Notes or any statement in the Notes. A
co-Trustee makes no representations with respect to the effectiveness or
adequacy of this Indenture or any Basic Document or the validity or perfection,
if any, of Liens granted under this Indenture or the Collateral Documents. A co-
Trustee shall not be responsible for independently ascertaining or maintaining
such validity or perfection, if any, and shall be fully protected in relying
upon certificates and opinions delivered to it in accordance with the terms of
this Indenture or the Collateral Documents.

     Section 12.13 No Conflict.

     It is the purpose of this section of the Indenture to remove any potential
conflict of interest in the instance in which Chase Bank of Texas, National
Association ("Chase") is acting as Trustee and, in its commercial banking
capacity, has or may develop a lending relationship with the Borrower or any of
its Subsidiary Guarantors.  Accordingly, in the event that Chase, in its
commercial banking capacity, has or may develop a lending relationship with the
Borrower or any of Subsidiary Guarantors, Chase may, but is not obligated to,
resign as Trustee, such resignation to be effective automatically upon receipt
by the Trustee of notice from the successor Trustee evidencing its assumption of
the duties of Trustee hereunder, without notice to and without prior approval of
any party.  In the event Chase resigns as trustee pursuant to this Section
12.13, First Union National Bank, a national banking association duly organized
and existing under the laws of the United States of America with a corporate
trust office in Jacksonville, Florida, or any successor appointed pursuant to
the "Acceptance of Appointment" attached hereto as Exhibit G, has agreed to and
shall automatically become successor Trustee hereunder for all purposes.  Chase
shall give notice of its resignation in writing to the Borrower, the Agent and
the Noteholders as soon as possible but in any event not less than forty-five
(45) days after its resignation, provided that failure to give such notice shall
not impair the effectiveness of such resignation.  The provisions of this
section shall extend to Affiliates of Chase.


                                 ARTICLE XIII
                                 MISCELLANEOUS

     Section 13.01  Interpretation and Survival of Provisions.  Article,
Section, Schedule, and Exhibit references are to this Indenture, unless
otherwise specified.  All references to instruments, documents, contracts, and
agreements are references to such instruments, documents, contracts, and
agreements as the same may be amended, supplemented, and otherwise modified from
time to time, unless otherwise specified.  The word "including" shall mean
"including but not limited to."  Whenever the Borrower has an obligation under
the Basic Documents, the expense of complying with that obligation shall be an
expense of the Borrower unless otherwise specified.  Whenever any determination,
consent, or approval is to be made or given by the Noteholders, such action
shall be in the Noteholders' sole discretion unless 

                                      -51-
<PAGE>
 
otherwise specified in this Indenture. If any provision in the Basic Documents
is held to be illegal, invalid, not binding, or unenforceable, such provision
shall be fully severable and the Basic Documents shall be construed and enforced
as if such illegal, invalid, not binding, or unenforceable provision had never
comprised a part of the Basic Documents, and the remaining provisions shall
remain in full force and effect. The Basic Documents have been reviewed and
negotiated by sophisticated parties with access to legal counsel and shall not
be construed against the drafter. The representations, warranties, and covenants
made in this Indenture, the Notes or any other Basic Document shall remain
operative and in full force and effect regardless of (a) any investigation made
by or on behalf of the Borrower or the Noteholders or (b) acceptance of any of
the Notes and payment therefor and repayment or repurchase thereof. All
indemnification obligations of the Borrower and the provisions of Section 13.02
shall remain operative and in full force and effect unless such obligations are
expressly terminated in a writing referencing those individual Sections,
regardless of any purported general termination of this Indenture or any other
Basic Document.

     Section 13.02  Costs, Expenses and Taxes.

          (a) Intentionally Deleted.

          (b) The Borrower agrees to indemnify the Agent and the Noteholders,
and their respective officers, directors, employees, representatives, agents,
attorneys, and Affiliates (collectively, "Related Parties") from, hold each of
them harmless against and promptly upon demand pay or reimburse each of them
for, any and all actions, suits, proceedings (including any investigations,
litigation, or inquiries), claims, demands, and causes of action, and, in
connection therewith, all reasonable costs, losses, liabilities, damages, or
expenses of any kind or nature whatsoever (collectively 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 sale of the Notes, (ii) the operations of the business of the
Borrower or any Subsidiary, (iii) any bodily injury or death or property damage
occurring in or upon or in the vicinity of any Collateral, (iv) any claim by any
third Person against any Collateral assigned to or paid to any Noteholder
pursuant to any Collateral Document, (v) the failure of the Borrower or any
Subsidiary to comply with any Governmental Requirement, or (vi) any other aspect
of this Indenture and the other Basic Documents, 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 INDEMNITEE (but excluding all
Indemnity Matters arising solely by reason of claims between the Noteholders or
any Noteholder and the Agent or any Noteholder's shareholders against the Agent
or any Noteholder or by reason of the gross negligence or wilful misconduct of
any Indemnitee).

          (c) The Borrower agrees to pay and hold the Noteholders harmless from
and against any and all present and future stamp and other similar taxes with
respect to this 

                                      -52-
<PAGE>
 
Indenture and Basic Documents and save the Noteholders harmless from and against
any and all liabilities with respect to or resulting from any delay or omission
to pay such taxes, and will indemnify the Noteholders for the full amount of
taxes paid by the Noteholders in respect of payments made or to be made under
this Indenture, any Note, or any other Basic Document and any liability
(including penalties, interest, and expenses) arising therefrom or with respect
thereto, whether or not such taxes were correctly or legally asserted.

          (d) The Borrower agrees to indemnify and hold harmless from time to
time the Noteholders, and their respective Related Parties, together with the
Trustee, 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, any Subsidiary, or any of their respective Properties, (ii) as a
result of the breach or non-compliance by the Borrower or any Subsidiary with
any Environmental Law applicable to the Borrower or any Subsidiary, or any of
their respective Properties, (iii) due to the ownership by the Borrower or any
Subsidiary of their respective Properties or any activity on any of their
respective Properties, or any past activity on any of their respective
Properties which, though lawful and fully permissible at the time, could result
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 any Subsidiary, or (v) any other environmental,
health, or safety condition in connection with this Indenture or any other Basic
Document.

          (e) In the case of any indemnification hereunder, the Noteholder or
other Person indemnified hereunder shall give notice to the Borrower within a
reasonable period of time of any such claim or demand being made against the
Noteholder or other indemnified Person and the Borrower at its sole cost and
expense shall provide a defense of such claim, provided, however, that (i) if
the Borrower has failed to assume the defense and employ counsel or (ii) if the
defendants in any such action include both the indemnified party and the
Borrower or any Subsidiary and counsel to the indemnified party shall  have
concluded that there may be reasonable defenses available to the indemnified
party that are different from or additional to those available to the Borrower
or such Subsidiary or if the interests of the indemnified party reasonably may
be deemed to conflict with the interests of the  Borrower or such Subsidiary,
then the indemnified party shall have the right to select a separate counsel and
to assume such legal defense and otherwise to participate in the defense of such
action, with the expenses and fees of such separate counsel and other expenses
related to such participation to be reimbursed by the Borrower as incurred.

          (f) No indemnitee 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
settlement that an indemnitee proposes if the indemnitor does not have the
financial ability to pay all its obligations outstanding and asserted against
the indemnitee at that time, including the maximum potential claims against the
indemnitee to be indemnified pursuant to this Section 13.02.

                                      -53-
<PAGE>
 
          (g) This Section 13.02 shall not apply to actions, suits, proceedings,
investigations, demands, losses, liabilities, claims, damages, deficiencies,
interest, judgments, costs, or expenses relating to any Property to the extent
arising from the acts or omissions of the Agent or any Noteholder during the
period after which such Person, its successors or assigns shall have acquired
possession of such Property (whether through foreclosure or deed in lieu of
foreclosure, as mortgagee in possession or otherwise).

          (h) The Borrower's obligations under this Section 13.02 shall survive
any termination of this Indenture and the payment of the Obligations.

     Section 13.03  No Waiver; Modifications in Writing.

          (a) No failure or delay on the part of the Trustee, the Borrower, the
Agent or the Noteholders in exercising any right, power, or remedy hereunder
shall operate as a waiver thereof, nor shall any single or partial exercise of
any such right, power, or remedy preclude any other or further exercise thereof
or the exercise of any right, power, or remedy.  The remedies provided for
herein are cumulative and are not exclusive of any remedies that may be
available to the Borrower, the Trustee, the Agent or the Noteholders at law or
in equity or otherwise.

          (b) Except as otherwise provided herein, no amendment, waiver,
consent, modification, or termination of any provision of this Indenture, the
Notes or any other Basic Document, shall be effective unless signed by the
Borrower and the Majority Noteholders.  The Noteholders have all rights to take
such actions under this Indenture and the other Basic Documents without the
consent or joinder of any holder of the Acquired Shares or Warrants. Any
amendment, supplement or modification of or to any provision of this Indenture
or the Notes or any other Basic Document, any waiver of any provision of this
Indenture, the Notes or any other Basic Document, and any consent to any
departure by the Borrower from the terms of any provision of this Indenture, the
Notes or any other Basic Document, shall be effective only in the specific
instance and for the specific purpose for which made or given.  Except where
notice is specifically required by this Indenture, no notice to or demand on the
Borrower in any case shall entitle the Borrower to any other or further notice
or demand in similar or other circumstances.

     Section 13.04  Binding Effect; Assignment.  This Indenture shall be
binding upon the Borrower, the Trustee, the Agent and the Noteholders, and their
respective successors and permitted assigns. Except as expressly provided in
this Indenture, this Indenture shall not be construed so as to confer any right
or benefit upon any Person other than the Borrower, Trustee, Agent and
Noteholders, and their respective successors and permitted assigns.  Subject to
applicable federal law and state securities law, all or any portion of the
rights and obligations of the Noteholders under this Indenture with respect to
the Basic Documents may be sold, assigned or pledged by any Noteholder.  Upon
any assignment of the Basic Documents, the acquiring Noteholder shall succeed to
all of the selling Noteholder's rights and obligations under the Basic Documents
to the extent assigned and the selling Noteholder 

                                      -54-
<PAGE>
 
shall be automatically released from any such obligations hereunder with respect
to the Basic Documents to the extent assigned.

     Section 13.05  Communications.  All notices and demands provided for
hereunder shall be in writing and shall be given by registered or certified
mail, return receipt requested, telecopy, air courier guaranteeing overnight
delivery or personal delivery to the following addresses:

     If to the Trustee:

     Chase Bank of Texas, National Association
     Global Trust Services
     600 Travis Street, Suite 1150
     Houston, Texas  77002
     Attention:  Mauri J. Cowen
     Telephone:  (713) 216-6686
     Telecopier: (713) 216-5474


     If to the Agent:

     Enron Capital Management II Limited Partnership
     c/o Enron Capital II Corp.
     1400 Smith Street
     Houston, Texas  77002
     Attention:  Shirley Hudler
     Telecopier: (713) 646-8008

     and

     Attention:  Donna Lowry
     Telecopier: (713) 646-4039

     If to the Noteholders:

     Enron Capital Management II Limited Partnership
     c/o Enron Capital II Corp.
     1400 Smith Street
     Houston, Texas  77002
     Attention:  Shirley Hudler
     Telecopier: (713) 646-8008

     and

                                      -55-
<PAGE>
 
     Enron Capital & Trade Resources Corp.
     1400 Smith Street
     Houston, Texas  77002
     Attention:  Donna Lowry
     Telecopier: (713) 646-4039

     If to the Borrower:

     6300 Bridge Point Parkway
     Building 2, Suite 500
     Austin, Texas 78730
     Attention:  Craig M. Fleming
     Telecopier: (512) 472-3400

or to such other address as the Borrower, Agent or any Noteholder may designate
in writing.  All other communications may be by regular mail.  All notices and
communications shall be deemed to have been duly given:  at the time delivered
by hand, if personally delivered; four days after being sent by certified mail,
return receipt requested, if mailed; when receipt acknowledged, if telecopied;
and on the next Business Day if timely delivered to an air courier guaranteeing
overnight delivery.  Notwithstanding the foregoing, notices to the Trustee shall
be effective only upon receipt.

     Section 13.06  Governing Law.  This Indenture will be construed in
accordance with and governed by the laws of the State of Texas without regard to
principles of conflicts of laws.

     Section 13.07  Arbitration.

          (a) Binding Arbitration.  Subject to the provisions of subparagraph
(e), on the request of either the Borrower, the Agent or any Noteholder, whether
made before or after the institution of any legal proceeding, any action,
dispute, claim or controversy of any kind now existing or hereafter arising
between any of the parties hereto in any way arising out of, pertaining to or in
connection with this Indenture (a "Dispute") shall be resolved by binding
arbitration in accordance with the terms hereof.  Either the Borrower, the Agent
or any Noteholder may, by summary proceedings, bring an action in court to
compel arbitration of any Dispute.

          (b) Governing Rules.  Any arbitration shall be administered by the
American Arbitration Association (the "AAA") in accordance with the terms of
this Section, the Commercial Arbitration Rules of the AAA, and, to the maximum
extent applicable, the Federal Arbitration Act.  Judgment on any award rendered
by an arbitrator may be entered in any court having jurisdiction.

          (c) Arbitrators.  Any arbitration shall be conducted before a three
person panel of neutral arbitrators.  Such panel shall consist of one person
from each of the 

                                      -56-
<PAGE>
 
following categories: (1) an attorney who has practiced in the area of
commercial law for at least 10 years or a retired judge at the Texas or United
States District Court or an appellate court level; (2) a person with at least 10
years experience in commercial lending; and (3) a person with at least 10 years
experience in the energy service industry. The AAA shall submit a list of
persons meeting the criteria outlined above for each category of arbitrator, and
the parties shall select one person from each category in the manner established
by the AAA. If the parties cannot agree on an arbitrator within 30 days after
the request for an arbitration, then any party may request the AAA to select an
arbitrator. The arbitrator may engage engineers, accountants or other
consultants that the arbitrator deems necessary to render a conclusion in the
arbitration proceeding.

          (d) Conduct of Arbitration.  To the maximum extent practicable, an
arbitration proceeding hereunder shall be concluded within 180 days of the
filing of the Dispute with the AAA.  Arbitration proceedings shall be conducted
in Houston, Texas.  At the conclusion of any arbitration proceeding, the
arbitrator shall make specific written findings of fact and conclusions of law.
The arbitrator shall have the power to award recovery of all costs and fees to
the prevailing party.  The Borrower, the Agent and the Noteholders each agree to
keep all Disputes and arbitration proceedings strictly confidential except for
disclosure of information required by applicable law.

          (e) Parties' Rights.  Nothing in the preceding paragraph shall require
arbitration prior to the Agent's or the Noteholders' exercise of any rights and
remedies under Article X.  In addition, nothing in this Section 13.07, nor the
exercise of any right to arbitrate thereunder, shall limit the right of the
Borrower, the Agent, the Trustee or any Noteholder: (a) to foreclose against any
Collateral by the exercise of the power of sale under, or to secure direct
payment of the proceeds of any Collateral as provided under, any deed of trust,
mortgage, or other security agreement or instrument or applicable law; (b) to
exercise self-help remedies such as setoff or repossession; or (c) to obtain
provisional or ancillary remedies or relief such as replevin, injunctive relief,
attachment or appointment of a receiver from a court having jurisdiction,
before, during or after the pendency of any arbitration proceeding.  Any
foreclosure action, or the institution and maintenance of any action for such
judicial relief, or pursuit of provisional or ancillary remedies, or exercise of
self-help remedies shall not constitute a waiver of the right of the exercising
party to submit any claim or dispute to arbitration.

          (f) Costs of Arbitration.  All fees of the arbitrator and any
engineer, accountant or other consultant engaged by the arbitrator, shall be
paid by the Borrower (as to 50%) and the Noteholders (as to 50%) unless
otherwise awarded by the arbitrator.

     Section 13.08  Confidentiality.  In the event that the Borrower or any
Guarantor (hereinafter called the "Subject Entities") provides to the Agent or
the Noteholders written confidential information or, if communicated as
confidential, oral confidential information belonging to any Subject Entity, the
Agent and the Noteholders 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 

                                      -57-
<PAGE>
 
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
Noteholders breaching their obligation of confidence to any Subject Entity,
(iii) are previously known by the Agent or the Noteholders from some source
other than any Subject Entity, (iv) are hereafter developed by the Agent or the
Noteholders without using a Subject Entity's information, (v) are hereafter
obtained by or available to the Agent or the Noteholders 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 Noteholders, or (viii) may be
required to be disclosed by law or regulation or order of any Governmental
Authority in any judicial, arbitration or governmental proceeding. Further, the
Agent or a Noteholder may disclose any such information to any other Noteholder,
any independent petroleum engineers or consultants, any independent certified
public accounts, any legal counsel employed by such Person in connection with
this Indenture or any other Basic Document, including without limitation, the
enforcement or exercise of all rights and remedies thereunder, or, subject to
Section 13.04, any assignee or participant (including prospective assignees and
participants) in the Obligations; provided, however, that the Agent or the
Noteholders 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 Noteholders 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 (3)
year period, to maintain the confidentiality of such information for an
additional three year period.

     Section 13.09  Execution in Counterparts.  This Indenture may be executed
in any number of counterparts and by different parties hereto in separate
counterparts, each of which counterparts, when so executed and delivered, shall
be deemed to be an original and all of which counterparts, taken together, shall
constitute but one and the same Agreement.

     Section 13.10 Trust Indenture Act Controls. Whether prior to or following
the qualification of this Indenture under the TIA, if any provision of this
Indenture limits, qualifies, or conflicts with the duties imposed by operation
of TIA (S)318(c) upon an Indenture qualified under the TIA, the imposed duties
shall control under this Indenture.

     Section 13.11 Communication by Noteholders with Other Noteholders.
Noteholders may communicate pursuant to TIA (S)312(b) with other Noteholders
with respect to their rights under this Indenture or the Notes. The Company, the
Guarantors, the Trustee, the Registrar and anyone else shall have the protection
of TIA (S)312(c).

     Section 13.12  Certificate and Opinion as to Conditions Precedent.  Upon
any request or application by the Borrower or any Guarantor to the Trustee to
take any action under this Indenture, the Borrower or such Guarantor, as the
case may be, shall furnish to the Trustee:

                                      -58-
<PAGE>
 
          (a) an Officers' Certificate (which shall include the statements set
forth in Section 13.13) stating that, in the opinion of the signers, the
conditions precedent, if any, provided for in this Indenture relating to the
proposed action have been complied with;

          (b) an Opinion of Counsel stating that, in the opinion of such
counsel, such conditions precedent have been complied with; and

          (c) any Opinion of Counsel may assume the existence of non-existence
of facts necessary to support such Opinion unless such counsel has actual
knowledge that such assumption would be contrary to the actual facts.

     Section 13.13  Statements Required in Certificate or Opinion.  Each
certificate or opinion with respect to compliance with a condition or covenant
provided for in this Indenture shall include:

          (a) a statement that each person making such certificate or opinion
has read such covenant or condition;

          (b) a brief statement as to the nature and scope of the examination or
investigation upon which the statements or opinions contained in such
certificate or opinion are based;

          (c) a statement that, in the opinion of each such person, he has made
such examination or investigation as is necessary to enable him to express an
informed opinion as to whether or not such covenant or condition has been
complied with; and

          (d) a statement as to whether or not, in the opinion of each such
person, such covenant or condition has been complied with.

     Section 13.14  Rules by Trustee and Agents.  The Trustee may make
reasonable rules for action by or a meeting of the Noteholders.  The Note
Registrar may make reasonable rules for its functions.

     Section 13.15  Legal Holidays.  A "Legal Holiday" is a Saturday, a
Sunday, or a day on which banks and trust companies in the City of New York are
not required by law or executive order to be open.  If a payment date is a Legal
Holiday at a place of payment, payment may be made at the place on the next
succeeding day that is not a Legal Holiday, without additional interest.

                                      -59-
<PAGE>
 
     IN WITNESS WHEREOF, BRIGHAM EXPLORATION COMPANY has caused this Indenture
to be signed by its President or one of its Vice Presidents, and CHASE BANK OF
TEXAS, NATIONAL ASSOCIATION has caused this Indenture to be signed by one of its
duly authorized trust officers, all as of the day and year first above written.

                              BRIGHAM EXPLORATION COMPANY


                              By:
                                 --------------------------------
                                 Craig M. Fleming
                                 Vice President and Chief Financial Officer



                              CHASE BANK OF TEXAS, NATIONAL
                              ASSOCIATION, as Trustee


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

                                      -60-
<PAGE>
 
STATE OF TEXAS      (S)
                    (S)
COUNTY OF HARRIS    (S)

     BEFORE ME, the undersigned authority, a Notary Public in and for said
state, on this day personally appeared Craig M. Fleming known to me to be the
person and officer whose name is subscribed to the foregoing instrument and
acknowledged to me that the same was the act of the said BRIGHAM EXPLORATION
COMPANY, a Delaware corporation, and that he executed the same as the act of
said corporation for the purposes and consideration therein expressed, and in
the capacity therein stated.

     GIVEN UNDER MY HAND AND SEAL OF OFFICE, this 20th day of August, 1998.


                              -------------------------------------------
                              Notary Public in and for the State of Texas

My commission expires:

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

STATE OF TEXAS      (S)
                    (S)
COUNTY OF HARRIS    (S)

     BEFORE ME, the undersigned authority, a Notary Public in and for said
state, on this day personally appeared __________________, known to me to be the
person and officer whose names are subscribed to the foregoing instrument and
acknowledged to me that the same was the act of the said CHASE BANK OF TEXAS,
NATIONAL ASSOCIATION, a national banking association, and that she executed the
same as the act of said national banking association for the purposes and
consideration therein expressed, and in the capacity therein stated.

     GIVEN UNDER MY HAND AND SEAL OF OFFICE, this 20th day of August, 1998.


                              ------------------------------------------- 
                              Notary Public in and for the State of Texas
My commission expires:

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

                                      -61-
<PAGE>
 
                                   EXHIBIT G

                               Re:  $50,000,000
                          Brigham Exploration Company
                  Senior Subordinated Secured Notes due 2003
                                 (the "Notes")

                           ACCEPTANCE OF APPOINTMENT

     FOR GOOD AND VALUABLE CONSIDERATION, the receipt and sufficiency of which
is hereby acknowledged, First Union  National Bank, a national banking
association (the "Successor Trustee"), does hereby accept its appointment upon
the terms specified in Section 12.13 of the Indenture securing the referenced
Notes, and does hereby irrevocably agree (subject to its rights of resignation
described below) to assume the responsibilities, rights, powers and obligations
of the Trustee for the Notes immediately upon its receipt of notice from any
person of the resignation of Chase Bank of Texas, National Association as
Trustee, pursuant to Section 12.13 of the Indenture.  Promptly upon receipt of
such notice, the Successor Trustee will notify the resigning Trustee, the Agent
and the Noteholders of its assumption of the duties of Trustee.

     The Successor Trustee hereby reserves the right to resign, and does hereby
acknowledge that it may be removed, in the same manner as is provided for the
resignation and removal of the Trustee pursuant to Section 12.08 of the
Indenture; provided that no such resignation or removal shall become effective
until a successor to the Successor Trustee shall have been appointed and shall
have accepted its appointment in the manner described in Section 12.08 of the
Indenture.

     IN WITNESS WHEREOF, the Successor Trustee has caused this Acceptance of
Appointment to be executed by its duly authorized officer as of the _____ day of
August, 1998.


                                    FIRST UNION NATIONAL BANK



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

Address of Successor Trustee:

225 Water Street, 3rd Floor
Jacksonville, Florida 32202-0122
Telephone:  (904) 361-3174
Telecopy:    (904) 36107735

<PAGE>
 
     The undersigned each agree that (i) the Statement on Schedule 13D relating
to the Common Stock, $.01 par value, of Brigham Exploration Company is adopted
and filed on behalf on each of them, (ii) all future amendments to such
Statement on Schedule 13D will, unless written notice to the contrary is
delivered as described below, be jointly filed on behalf of each of them, and
(iii) the provisions of Rule 13d-1(k) under the Securities Exchange Act of 1934
apply to each of them.  This agreement may be terminated with respect to the
obligation to jointly file future amendments to such Statement on Schedule 13D
as to any of the undersigned upon such person giving written notice thereof to
each of the other persons signatory hereto, at the principal office thereof.

     IN WITNESS WHEREOF, the undersigned hereby execute this Joint Filing
Agreement as of the date set forth below.

Dated: September 2, 1998.      ENRON CAPITAL & TRADE RESOURCES CORP.



                               By: /s/ Peggy B. Menchaca
                                   --------------------------------
                               Name: Peggy B. Menchaca
                               Title: Vice President and Secretary


Dated: September 2, 1998       ENRON CORP.

                               By: /s/ Peggy B. Menchaca
                                   --------------------------------
                               Name: Peggy B. Menchaca
                               Title: Vice President and Secretary


Dated: September 2, 1998       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: /s/ Peggy B. Menchaca
                                   -------------------------------
                               Name: Peggy B. Menchaca
                               Title: Vice President and Secretary


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