BRIGHAM EXPLORATION CO
PRES14A, 2000-11-30
CRUDE PETROLEUM & NATURAL GAS
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<PAGE>

                                 SCHEDULE 14A

          Proxy Statement Pursuant to Section 14(a) of the Securities
                    Exchange Act of 1934 (Amendment No.  )

Filed by the Registrant [X]

Filed by a Party other than the Registrant [_]

Check the appropriate box:

[X]  Preliminary Proxy Statement

[_]  Confidential, for Use of the
     Commission Only (as permitted by
     Rule 14a-6(e)(2))

[_]  Definitive Proxy Statement

[_]  Definitive Additional Materials

[_]  Soliciting Material Pursuant to (S) 240.14a-11(c) or (S) 240.14a-12

                          BRIGHAM EXPLORATION COMPANY
--------------------------------------------------------------------------------
               (Name of Registrant as Specified in its Charter)


--------------------------------------------------------------------------------
   (Name of Person(s) Filing Proxy Statement, if other than the Registrant)


Payment of Filing Fee (Check the appropriate box):

[X]  No fee required.

[_]  Fee computed on table below per Exchange Act Rules 14a-6(i)(I) and 0-11.


     (1) Title of each class of securities to which transaction applies:

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


     (2) Aggregate number of securities to which transaction applies:

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


     (3) Per unit price or other underlying value of transaction computed
         pursuant to Exchange Act Rule 0-11 (set forth the amount on which
         the filing fee is calculated and state how it was determined):

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


     (4) Proposed maximum aggregate value of transaction:

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


     (5) Total fee paid:

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

[_]  Fee paid previously with preliminary materials.

[_]  Check box if any part of the fee is offset as provided by Exchange Act
     Rule 0-11(a)(2) and identify the filing for which the offsetting fee was
     paid previously. Identify the previous filing by registration statement
     number, or the Form or Schedule and the date of its filing.

     (1) Amount Previously Paid:

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


     (2) Form, Schedule or Registration Statement No.:

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


     (3) Filing Party:

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


     (4) Date Filed:

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

<PAGE>

                                                              PRELIMINARY COPIES

                          BRIGHAM EXPLORATION COMPANY

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

                   NOTICE OF SPECIAL MEETING OF STOCKHOLDERS

                         To Be Held on January 9, 2001

To the Common Stockholders of
 BRIGHAM EXPLORATION COMPANY:

     Notice is hereby given that a Special  Meeting of Stockholders of Brigham
Exploration Company, a Delaware corporation (the "Company"), will be held on
Tuesday, January 9, 2001, at 1:00 p.m., local time, at the Company's offices at
6300 Bridge Point Parkway, Building Two, Suite 500, Austin, Texas, for the
following purposes:

     1.   To consider and vote upon a proposal to approve and ratify the
          warrants issued by the Company in November 2000 to affiliates of
          Credit Suisse First Boston (USA), Inc. (formerly named Donaldson,
          Lufkin & Jenrette, Inc.), and to approve any future adjustments to the
          exercise price of such warrants pursuant to the terms of such
          warrants;

     2.   To consider and vote upon an amendment to the Company's Certificate of
          Incorporation to effect a one-for-________ reverse stock split of all
          issued shares of the Company's common stock, subject to the discretion
          of the Board of Directors to delay filing the amendment or not to file
          the amendment; and

     3.   To transact such other business as may properly come before the
          meeting or any adjournment(s) thereof.

     Only common stockholders of record at the close of business on November 20,
2000 are entitled to notice of, and to vote at, the meeting or any
adjournment(s) thereof.

     You are cordially invited and urged to attend the meeting, but if you are
unable to attend, please sign and date the enclosed proxy and return it promptly
in the enclosed self-addressed stamped envelope.  A prompt response will be
appreciated.  If you attend the meeting, you may vote in person, if you wish,
whether or not you have returned your proxy.  In any event, a proxy may be
revoked at any time before it is exercised.

                                   BY ORDER OF THE BOARD OF DIRECTORS



                                   DAVID T. BRIGHAM
                                   Secretary


December ____, 2000
Austin, Texas
<PAGE>

                                                              PRELIMINARY COPIES

                          Brigham Exploration Company
                           6300 Bridge Point Parkway
                            Building Two, Suite 500
                              Austin, Texas 78730

                                PROXY STATEMENT
                                      For
                        SPECIAL MEETING OF STOCKHOLDERS
                         To Be Held on January 9, 2001

                            SOLICITATION OF PROXIES


                                    GENERAL

Solicitation and Revocability of Proxies

   This proxy statement is furnished to holders of Brigham Exploration Company
("Brigham" or the "Company") common stock, $0.01 par value ("Common Stock"), in
connection with the solicitation of proxies on behalf of the Board of Directors
of Brigham for use at a Special Meeting of Stockholders of Brigham to be held on
Tuesday, January 9, 2001, at 1:00 p.m., local time, at Brigham's offices at 6300
Bridge Point Parkway, Building Two, Suite 500, Austin, Texas, and at any
adjournment(s) thereof, for the purposes set forth in the accompanying Notice of
Special Meeting of Stockholders.

   Shares represented by a proxy in the form enclosed, duly signed, dated and
returned to Brigham and not revoked, will be voted at the meeting in accordance
with the directions given, but in the absence of directions to the contrary,
such shares will be voted (i) for approval and ratification of the warrants to
purchase Brigham common stock that were issued to two affiliates of Credit
Suisse First Boston (USA), Inc. (formerly named Donaldson, Lufkin & Jenrette,
Inc.) in November 2000, and approval of any future adjustments to the exercise
price of such warrants pursuant to the terms of such warrants, (ii) for the
amendment to Brigham's Certificate of Incorporation to effect a one-for-________
reverse stock split of all issued shares of the Company's common stock, subject
to the discretion of the Board of Directors to delay filing the amendment or not
to file the amendment, and (iii) in accordance with the best judgment of the
persons voting on any other proposals that may come before the meeting. The
Board of Directors knows of no other matters, other than those stated in the
foregoing notice, to be presented for consideration at the meeting or any
adjournment(s) thereof. If, however, any other matters properly come before the
meeting or any adjournment(s) thereof, it is the intention of the persons named
in the enclosed proxy to vote such proxy in accordance with their judgment on
any such matters. The persons named in the enclosed proxy may also, if it is
deemed to be advisable, vote such proxy to adjourn the meeting from time to
time.

   Any stockholder executing and returning a proxy has the power to revoke it at
any time before it is voted by delivering to the Secretary of Brigham, 6300
Bridge Point Parkway, Building Two, Suite 500, Austin, Texas 78730, a written
revocation thereof or by duly executing a proxy bearing a later date. Any
stockholder attending the Special Meeting of Stockholders may revoke his proxy
by notifying the Secretary at such meeting and voting in person. Attendance at
the Special Meeting will not by itself revoke a proxy.

   The approximate date on which this proxy statement and the form of proxy are
intended to be released to stockholders is December ___, 2000.

   The cost of soliciting proxies will be borne by Brigham. Solicitation may be
made, without additional compensation, by directors, officers and regular
employees of Brigham in person or by mail, telephone or telegram. Brigham may
also request banking institutions, brokerage firms, custodians, trustees,
nominees and fiduciaries to forward solicitation material to the beneficial
owners of the Common Stock held of record by such persons, and Brigham
<PAGE>

will reimburse the forwarding expense. All costs of preparing, printing and
mailing the form of proxy and the material used in the solicitation thereof will
be borne by Brigham.

Shares Outstanding and Voting Rights

   The close of business on November 20, 2000 is the record date for
determination of stockholders entitled to notice of and to vote at the meeting
or any adjournment(s) thereof.  The only voting security of Brigham outstanding
which is entitled to vote at the meeting is the Common Stock, each share of
which entitles the holder thereof to one vote.  At the record date for the
meeting, there were outstanding and entitled to be voted 15,977,543 shares of
Common Stock.

   The affirmative vote of a majority of the votes cast at the Special Meeting
will be required for approval of Proposal One.  Thus, any abstentions, "broker
non-votes" (shares held by brokers or nominees as to which they have no
discretionary authority to vote on a particular matter and have received no
instructions from the beneficial owners or persons entitled to vote thereon) or
other limited proxies will have no effect on the proposal regarding the
Warrants. Holders of approximately 52% of the outstanding Common Stock as of
November 20, 2000 have agreed, in a Voting Agreement dated October 31, 2000, to
vote in favor of Proposal One.

   The affirmative vote of a majority of the shares of outstanding Common Stock
is necessary to approve Proposal Two. Thus, any abstentions, "broker non-votes"
or other limited proxies will have the effect of a vote against Proposal Two.


   Stockholders have no dissenters' rights or rights of appraisal under Delaware
law or Brigham's Certificate of Incorporation or bylaws in connection with
Proposal One or Proposal Two.

Security Ownership of Certain Beneficial Owners and Management

   The table below sets forth information concerning (i) the only persons known
by Brigham, based upon statements filed by such persons pursuant to Section
13(d) or 13(g) of the Securities Exchange Act of 1934, as amended (the "Exchange
Act"), to own beneficially in excess of 5% of the Common Stock as of November
29, 2000, and (ii) the shares of Common Stock beneficially owned, as of November
29, 2000 (except as noted for Mr. Glass), by each current director of Brigham,
each executive officer listed in the Summary Compensation Table included in
Brigham's proxy statement related to its 2000 annual meeting of stockholders,
and all current directors and executive officers of Brigham as a group.  Except
as indicated, each individual has sole voting power and sole investment power
over all shares listed opposite his name.

<TABLE>
<CAPTION>
                                                                                        Common Stock
                                                                                   Beneficially Owned (1)
                                                                                   ----------------------
                                                                                      Number     Percent
                        Name and Address of Beneficial Owner                        of Shares   of Class
       -----------------------------------------------------------------------     ----------   --------
       <S>                                                                         <C>          <C>
       Credit Suisse First Boston Corporation (2) (16).......................       6,666,667    29.44%
         11 Madison Avenue
         New York, New York 10010
       Shell Capital Inc. (3)................................................       5,480,769    25.54%
         910 Louisiana, Room 4555D
         Houston, Texas  77002-2463
       General Atlantic Partners, L.L.C. (4) (16)............................       4,107,956    25.20%
         3 Pickwick Plaza
         Greenwich, Connecticut  06830
       Ben M. and Anne L. Brigham (5) (16)...................................       3,719,892    23.28%
         6300 Bridge Point Parkway, Building Two, Suite 500
         Austin, Texas  78730
       Resource Investors Management Company (6).............................       1,754,464    10.98%
         600 Travis Street, Suite 6875
         Houston, Texas  77002
       Veritas DGC Land, Inc.................................................       1,211,580     7.58%
         3701 Kirby Drive, Suite 112
         Houston, Texas  77098-3982
</TABLE>

                                       2
<PAGE>

<TABLE>
<CAPTION>
                                                                                        Common Stock
                                                                                   Beneficially Owned (1)
                                                                                   ----------------------
                                                                                      Number     Percent
                        Name and Address of Beneficial Owner                        of Shares   of Class
       -----------------------------------------------------------------------     ----------   --------
       <S>                                                                         <C>          <C>
       David T. Brigham (7)..................................................         146,296         *
       Curtis F. Harrell (8).................................................          30,298         *
       A. Lance Langford (9).................................................          90,265         *
       Karen E. Lynch (10)...................................................          46,625         *
       Harold D. Carter (11) (16)............................................         315,193      1.97%
       Alexis M. Cranberg (12)...............................................             300         *
       Stephen P. Reynolds (13)..............................................             300         *
       Steven A. Webster (2).................................................              --        --
       Jon L. Glass (14).....................................................          66,964         *
       All current directors and executive officers as a group (12 persons)
        (15) (16)............................................................       4,407,169     27.35%
</TABLE>

______________________________
* Represents less than 1%.

(1)  Beneficial ownership is determined in accordance with the rules of the SEC
     and generally includes voting or disposition power with respect to
     securities.

(2)  On November 3, 2000, Credit Suisse First Boston (USA), Inc. (formerly named
     Donaldson, Lufkin & Jenrette, Inc.) ("CSFB-USA") became an indirect,
     wholly-owned subsidiary of Credit Suisse First Boston Corporation (the
     "Bank"). The Bank, on behalf of itself and its subsidiaries, to the extent
     that they constitute a part of the Credit Suisse Boston Business unit (the
     "CSFB business unit"), beneficially owns 6,036,667 shares of Common Stock
     issuable upon the exercise of currently exercisable warrants held by DLJ MB
     Funding III, Inc. ("DLJ MB Funding") and 630,000 shares of Common Stock
     issuable upon exercise of currently exercisable warrants held by DLJ ESC
     II, L.P. ("DLJ ESC"). DLJ MB is an indirect, wholly-owned subsidiary of
     CSFB-USA. The managing general partner of DLJ ESC is also an indirect,
     wholly-owned subsidiary of CSFB-USA. DLJ MB Funding and DLJ ESC are
     collectively referred to as the "CSFB Affiliates" in this proxy statement.
     The ultimate parent company of the Bank is Credit Suisse Group ("CSG"). Due
     to the separate management and independent operation of its business units,
     CSG disclaims beneficial ownership of the reported Common Stock that is
     beneficially owned by its direct and indirect subsidiaries, including the
     CSFB business unit. The CSFB business unit disclaims beneficial ownership
     of shares of Common Stock beneficially owned by CSG and any of CSG's and
     the Bank's other business units. Steven A. Webster is a Managing Director
     of Global Energy Partners, Ltd., a merchant banking affiliate of the CSFB
     Affiliates.

(3)  Consists of shares of Common Stock issuable upon the exercise of currently
     exercisable warrants to purchase 5,480,769 shares of Common Stock,
     calculated based on Brigham's $75 million of outstanding borrowings under
     its senior credit facility as of November 29, 2000.

(4)  Includes 2,679,418 shares held by General Atlantic Partners III, L.P. ("GAP
     III"); and 127,725 shares held by GAP-Brigham Partners, L.P. ("GAP-
     Brigham") and 975,610 shares held by GAP Coinvestment Partners II, L.P.
     ("GAP Coinvestment") and shares of stock issuable upon the exercise of
     325,203 currently exercisable warrants held by GAP Coinvestment. Stephen P.
     Reynolds is the general partner and a limited partner in GAP-Brigham,
     President of GAP III Investors, Inc., the general partner of GAP III, and a
     limited partner of GAP Coinvestment.

(5)  Includes 1,830,514 shares owned by Ben M. Brigham and 1,821,010 shares and
     100 shares of Common Stock issuable upon exercise of certain vested stock
     options owned by Anne L. Brigham, who are husband and wife; 27,022 shares
     owned by Ben M. Brigham and Anne L. Brigham as Trustees under Brigham
     Parental Trust I; 28,246 shares owned by Ben M. Brigham and Anne L. Brigham
     as Trustees under Brigham Parental Trust II; and 13,000 shares held by
     David T. Brigham, as custodian for each of Mr. and Mrs. Brigham's four
     children under the Texas Uniform Transfers to Minors Act.

(6)  Includes 612,308 shares held by RIMCO Partners, L.P. II, 307,031 shares
     held by RIMCO Partners, L.P. III and 835,125 shares held by RIMCO Partners,
     L.P. IV (collectively, the "RIMCO Partnerships"). Resource Investors
     Management Company ("RIMCO") is the general partner of each of the RIMCO
     Partnerships. The general partner of RIMCO is RIMCO Associates, Inc.

                                       3
<PAGE>

(7)  Includes 44,643 shares of vested restricted stock; 62,653 shares of
     unvested restricted stock; 13,000 shares held as a custodian under the
     Texas Uniform Transfers to Minors Act for the children of Ben M. Brigham
     and Anne L. Brigham; 2,000 shares gifted by Ben M. Brigham and Anne L.
     Brigham; and 24,000 shares of Common Stock issuable upon exercise of
     certain vested stock options.

(8)  Includes 249 shares held indirectly by R. Chaney Partners III L.P.; 49
     shares held indirectly by R. Chaney Partners IV L.P.; and 30,000 shares of
     Common Stock issuable upon exercise of certain vested stock options.

(9)  Includes 59,491 shares of unvested restricted stock; and 26,000 shares of
     Common Stock issuable upon exercise of certain vested stock options.

(10) Includes 20,000 shares of unvested restricted stock; and 26,000 shares of
     Common Stock issuable upon exercise of certain vested stock options.

(11) Includes 300 shares of Common Stock issuable upon exercise of certain
     vested stock options.

(12) Includes 300 shares of Common Stock issuable upon exercise of certain
     vested stock options.  Alexis Cranberg is the President of Aspect Resources
     LLC ("Aspect").  As such, Mr. Cranberg may be deemed to share voting and
     investment power with respect to 487,805 shares of Common Stock held by
     Aspect and 162,602 shares of Common Stock issuable upon the exercise of
     currently exercisable warrants held by Aspect.  Mr. Cranberg disclaims
     beneficial ownership of shares owned by Aspect except to the extent of his
     pecuniary interest therein.

(13) Includes 300 shares of Common Stock issuable upon exercise of certain
     vested stock options.  Stephen P. Reynolds is the general partner and a
     limited partner in GAP-Brigham, President of GAP III Investors, Inc., the
     general partner of GAP III, and a limited partner of GAP Coinvestment.  As
     such, Mr. Reynolds may be deemed to share voting and investment power with
     respect to the 2,679,418 shares held by GAP III, 127,725 shares held by
     GAP-Brigham and 975,610 shares held by GAP Coinvestment and 325,203 shares
     of Common Stock issuable upon the exercise of currently exercisable
     warrants held by GAP Coinvestment.  Mr. Reynolds disclaims beneficial
     ownership of shares owned by GAP III, GAP-Brigham, and GAP Coinvestment
     except to the extent of his pecuniary interest therein.

(14) Includes 66,964 shares of vested restricted stock.  Mr. Glass served as
     Brigham's Vice President of Exploration and a Director until September 30,
     1999.  Beneficial ownership shown for Mr. Glass is as of February 4, 2000,
     the most recent date for which Brigham has such information.

(15) Includes 136,900 shares of Common Stock issuable upon exercise of certain
     vested stock options.

(16) The following Brigham shareholders, owning an aggregate of 8,305,243 shares
     of Common Stock, have agreed with the CSFB Affiliates, pursuant to a Voting
     Agreement dated October 31, 2000, to vote at the Special Meeting to approve
     the Warrants and any future adjustments to the exercise price of the
     Warrants pursuant to the terms thereof: Ben M. and Anne L. Brigham, Harold
     D. Carter, General Atlantic Partners III, L.P., GAP-Brigham Partners, L.P.,
     GAP Coinvestment Partners II, L.P. and Aspect Resources, LLC. The table
     above does not reflect any deemed shared voting power of such 8,305,243
     shares.

                                       4
<PAGE>

                                 PROPOSAL ONE

                   APPROVAL AND RATIFICATION OF THE WARRANTS

General

     To ensure compliance with a stockholder approval rule of the Nasdaq Stock
Market, Brigham is seeking stockholder approval and ratification of the warrants
to purchase Common Stock (the "Warrants") that were issued to two affiliates
(the "CSFB Affiliates") of Credit Suisse First Boston (USA), Inc. (formerly
named Donaldson, Lufkin & Jenrette, Inc.) in November 2000, and approval of any
future adjustments to the exercise price of the Warrants pursuant to the terms
of the Warrants.  Brigham agreed with the CSFB Affiliates to convene a special
meeting of stockholders for this purpose.  The following Brigham shareholders,
owning an aggregate of 8,305,243 shares of Common Stock, have agreed, pursuant
to a Voting Agreement dated October 31, 2000, to vote for in favor of such
matters:  Ben M. and Anne L. Brigham, Harold D. Carter, General Atlantic
Partners III, L.P., GAP-Brigham Partners, L.P., GAP Coinvestment Partners II,
L.P. and Aspect Resources, LLC.

     The issuance of the Warrants was part of a series of financing agreements
that Brigham announced on November 2, 2000.  The agreements provided funding (i)
to repurchase all subordinated debt and equity securities in Brigham held by
affiliates of Enron North America (the "Enron Affiliates") at a substantial
discount, and (ii) to continue Brigham's planned drilling program into 2001.
Brigham raised an aggregate of $40 million in these financing transactions
through the issuance of (i) $20 million in new subordinated notes and warrants
to purchase Brigham common stock to Shell Capital Inc., and (ii) $20 million in
new mandatorily redeemable preferred stock designated as Series A Preferred (the
"Series A Preferred Stock") and the Warrants to the CSFB Affiliates.  With a
portion of the proceeds from these two financing transactions, Brigham purchased
all of the Enron Affiliates' interests in Brigham, which included (i) $51.2
million of outstanding senior subordinated notes due 2003 (which bore interest
at annual rates of 12% to 14%) and associated accrued interest obligations, (ii)
warrants to purchase one million shares of common stock at $2.43 per share, and
(iii) 1,052,632 shares of common stock (collectively, the "Enron Securities"),
for total cash consideration of $20 million. The remaining approximate $17.5
million in net capital availability raised from these financing transactions
after the repurchase of the Enron Securities and the payment of estimated fees
and expenses will be used by Brigham to fund its planned drilling program into
2001.  Brigham's stock price had traded at or below $3.00 per share for over 120
consecutive trading days prior to negotiation of the financing agreements with
Shell Capital and the CSFB Affiliates.

Description of the Warrants

  General

     The Warrants entitle the holders thereof to purchase an aggregate of
6,666,667 shares of Common Stock (the "Warrant Shares") at an exercise price of
$3.00 per share.  The exercise price of the Warrants is payable either in cash
or in shares of the Series A Preferred Stock, valued at liquidation value plus
accrued dividends.  The Warrants will expire on November 1, 2010 (the "Warrant
Expiration Date").  The warrantholders are entitled to exercise all or a portion
of their Warrants at any time after issuance of the Warrants and on or prior to
the Warrant Expiration Date, at which time all unexercised Warrants will expire.
The Warrants must be exercised, if Brigham so requires, in the event that the
Common Stock trades at or above $5.00 per share for 60 consecutive trading days.
If Brigham requires exercise of the Warrants, proceeds from the exercise of the
Warrants will be used to fund the redemption of a similar value of then-
outstanding Series A Preferred Stock.  Subject to restrictions relating to the
Securities Act of 1933, the Warrants are transferable.

  Mergers, Consolidations of Brigham; Anti-Dilution Adjustments

     In case of any reclassification or change of outstanding 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

                                       5
<PAGE>

subdivision or combination to which a separate provision applies), or in case of
any consolidation or merger of Brigham with or into any entity or other person
(other than a merger with another entity or other person in which Brigham is the
surviving corporation and which does not result in any reclassification or
change in the securities issuable upon exercise of the Warrants), provision must
be made for warrantholders to receive, upon the exercise of Warrants and in lieu
of Warrant Shares, such securities or assets as would be issued or paid in
respect of shares of Common Stock upon such reclassification, change,
consolidation or merger.

     If Brigham declares a dividend on its Common Stock payable in stock or
other securities of Brigham to the holders of its Common Stock, the
warrantholders will be entitled to receive upon any exercise of a Warrant, in
addition to Warrant Shares, 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
was established, the payment date for such dividend) of the number of Warrant
Shares purchasable on exercise of such Warrant immediately prior to such record
date or payment date, as the case may be.

     The number of Warrant Shares issuable upon exercise of a Warrant will also
be adjusted in the event of a combination or subdivision of the Common Stock.

  Exercise Price Adjustments; Resulting Warrant Share Adjustments

     Common Stock Issuances.  If Brigham issues any additional shares of Common
     ----------------------
Stock, otherwise than as described above under "Mergers, Consolidations of
Brigham; Anti-Dilution Adjustments," 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 by the Board of Directors or
compensation committee of Brigham (the "Market Price"), then upon each such
issuance the exercise price of the Warrants will be adjusted.  The new exercise
price will be determined by multiplying the current exercise price by the
following fraction:

          (A)  the sum of (i) 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 (ii) the consideration, if any,
     received by Brigham upon the issuance of such additional shares of Common
     Stock, divided by

          (B)  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 such adjustments of the exercise price will be made upon the issuance of any
additional shares of Common Stock that:

     .    are issued pursuant to any grant or award made prior to the Warrant
          issuance date under any thrift plan, stock purchase plan, stock bonus
          plan, stock option plan, employee stock ownership plan, incentive or
          profit sharing arrangement or other benefit or compensation plan for
          the benefit of Brigham's officers, directors and/or employees
          ("Employee Benefit Plans") that has been approved by Brigham's Board
          of Directors or its compensation committee and that otherwise would
          cause an adjustment;

     .    are issued pursuant to any grant or award made on or after the
          Warrant issuance date under any Employee Benefit Plan if the "Market
          Price" of any such issuance is not less than the lesser of the Market
          Price as determined above and the "Fair Market Value", as defined
          under the applicable Employee Benefit Plan, on the date of Board or
          compensation committee authorization;

     .    are issued pursuant to any Common Stock Equivalent (as defined under
          the following heading) (i) if upon the issuance of any such Common
          Stock Equivalent, any such adjustments shall previously have been made
          pursuant to provisions described in the following paragraph, (ii) if
          no adjustment was

                                       6
<PAGE>

          required pursuant to the provisions described in the following
          paragraph, or (iii) if such Common Stock Equivalent was issued prior
          to the date the Warrant was issued;

     .    are issued pursuant to a public offering by Brigham; or

     .    results in an adjustment pursuant to provisions described below under
          "-- Special Adjustments."

     Common Stock Equivalent Issuances.  If Brigham issues 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"), then the exercise price upon each such issuance will
be adjusted if the consideration received and receivable by Brigham 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.  If an adjustment
is to be made, it will be made as set forth under the preceding heading on the
basis that:

          (i)  the maximum number of additional shares of Common Stock issuable
     pursuant to all such Common Stock Equivalents will be deemed to have been
     issued as of the date of issuance of such Common Stock Equivalent; and

          (ii) the aggregate consideration for such maximum number of additional
     shares of Common Stock will be deemed to be the minimum consideration
     received and receivable by Brigham for the issuance of such additional
     shares of Common Stock pursuant to such Common Stock Equivalent.

No such adjustment of the exercise price will be made 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 previously has
been made in the exercise price then in effect upon the issuance of such
warrants or other rights pursuant to the provisions described under this
heading. In addition, no adjustment shall be made under the provisions described
under this heading (a) if an adjustment is to be made under the provisions
described under the following heading or (b) as a result of adjustment in the
exercise or conversion price of Common Stock Equivalents, if those adjustments
occur by the terms of such Common Stock Equivalents. Appropriate readjustments
to the purchase price will be made upon the expiration of the right to convert,
exchange or exercise any Common Stock Equivalent if any such Common Stock
Equivalent has not been converted, exercised or exchanged.

     Special Adjustments.  Until November 1, 2002, special exercise adjustment
     -------------------
provisions will apply. If during that time Brigham issues any additional shares
of Common Stock at a price per share less than the current Warrant exercise
price, then the Warrant exercise price will be adjusted to equal the per share
purchase price of the newly-issued Common Stock. These adjustment provisions do
not apply to Common Stock issued pursuant to any Employee Benefit Plan or
pursuant to any Common Stock Equivalent outstanding as of the Warrant issuance
date, nor to any issuance of Common Stock for which an adjustment was previously
made under the provisions described in the next paragraph.

     If before November 1, 2002, Brigham issues any Common Stock Equivalents and
the exercise price of such Common Stock Equivalents is less than the Warrant
exercise price then in effect, then the Warrant exercise price will be adjusted
to equal the exercise price of the new Common Stock Equivalents.  The exercise
price of the new Common Stock Equivalents will be determined by dividing

          (A)  the total amount, if any, received or receivable by Brigham as
     consideration for the issuance of such Common Stock Equivalents, plus the
     minimum aggregate amount of additional consideration payable to Brigham
     upon the exercise, conversion or exchange of such Common Stock Equivalents,
     plus, in the case of any such Common Stock Equivalents which relate to
     Convertible Securities, the minimum aggregate amount of additional
     consideration, if any, payable to Brigham upon the conversion or exchange
     of such Convertible Securities, by

                                       7
<PAGE>

          (B)  the total maximum number of shares of Common Stock issuable upon
     the exercise, conversion or exchange of all such Common Stock Equivalents.

     Resulting Adjustments to Number of Warrant Share Adjustments.
     ------------------------------------------------------------

     Upon each adjustment of the Warrant exercise price as a result of the
calculations described in this "Exercise Price Adjustments; Resulting Warrant
Share Adjustments" section, the number of Warrant Shares issuable upon exercise
of a Warrant will be adjusted to the following number:

          (A)  the product of (i) the number of shares covered by the Warrants
     immediately prior to such adjustment of the number of shares and (ii) the
     Warrant exercise price in effect immediately prior to such adjustment of
     the exercise price; divided by

          (B)  the Warrant exercise price in effect immediately after such
     adjustment of the exercise price.

  Reports

     Brigham will cause to be delivered, by first-class mail, postage prepaid,
to the warrantholders a copy of any reports delivered by Brigham to the holders
of Common Stock.  Warrantholders also will (i) receive prior notice of any
proposed board action, receive reasonable notice of and have the right to attend
at its sole discretion any meeting of Brigham's Board of Directors, (ii)
receive, promptly after they are produced, all management reports and management
accounts relating to Brigham and (iii) upon reasonable notice, have access to
the books and records of Brigham, including statutory books, minute books, and
customer lists.

Effect of the Warrants on Existing Stockholders

     Following the issuance of the Warrants, the existing holders of the Common
Stock, other than the Enron Affiliates, continued to own the shares of Common
Stock owned by them prior to the financing transactions.   As a result of the
collective financing and repurchase transactions with the CSFB Affiliates, Shell
Capital and the Enron Affiliates, the number of shares of Brigham common stock
outstanding decreased from approximately 17.0 million shares to 16.0 million
shares on November 1, 2000, while its number of fully-diluted shares outstanding
(including all stock options and warrants to purchase common stock) increased
from approximately 26.7 million shares to 32.5 million shares on November 1,
2000.   As of November 1, 2000, if the CSFB Affiliates had exercised the
Warrants, they would collectively own approximately 30% of the outstanding
Brigham Common Stock.   Following any such exercise, the CSFB Affiliates would
have the ability to influence the outcome of any stockholder vote.  Therefore,
after any exercise of the Warrants,  the CSFB Affiliates may be in a position to
influence the timing and the terms upon which any acquisition or other business
combination involving Brigham may occur.

                                       8
<PAGE>

Nasdaq Approval Requirement

     Under the rules of the Nasdaq Stock Market, Inc., companies that are listed
on the Nasdaq National Market must obtain stockholder approval prior to issuing
shares of common stock, or securities convertible into common stock, equal to
20% or more of the common stock outstanding prior to the issuance for less than
the greater of book or market value of the stock.   As described under
"Description of the Warrants -- Exercise Price Adjustments" above, the exercise
price of the Warrants could be adjusted downward in the future as a result of
the economic antidilution provisions included in the Warrants.  To ensure that
any such downward adjustment to the exercise price of the Warrants pursuant to
their terms does not cause a violation of the "less than market value" Nasdaq
rule in the future, Brigham and the CSFB Affiliates agreed to include a
provision in the Warrants making adjustment to the exercise price that would
require stockholder approval pursuant to the Nasdaq rules  subject to Brigham's
obtaining such requisite approval.   The CSFB Affiliates required Brigham to
agree that, prior to obtaining stockholder approval of the Warrants, it will not
take any action that  would cause an adjustment, pursuant to the terms of the
Warrants, to the Warrants' exercise price but for this provision in the
Warrants.

     Brigham is seeking stockholder approval of the Warrants and the exercise
price adjustments pursuant to the Warrants' terms in order to satisfy the "less
than market value" Nasdaq stockholder approval requirement that would be
triggered by a downward adjustment of the Warrants' exercise price.  If
stockholder approval is not obtained, because of its contractual prohibition on
taking action that might cause an exercise price adjustment, Brigham would be
limited in its ability to issue stock and other securities in negotiated
transactions or for compensatory purposes to the extent that such issuances
would trigger the Warrant's exercise price adjustments.

Interest of Certain Persons

     Pursuant to the terms of the securities purchase agreement related to the
Warrants and the Series A Preferred Stock, the holders of the Series A Preferred
Stock have the right to designate one member to Brigham's board of directors. As
a result, Steven A. Webster joined the board of directors of Brigham
contemporaneously with the issuance of the Series A Preferred Stock, increasing
the number of Brigham directors from six to seven members.   Mr. Webster is a
Managing Director of Global Energy Partners, Ltd., a merchant banking affiliate
of Credit Suisse First Boston (USA), Inc. (formerly named Donaldson, Lufkin &
Jenrette, Inc.).   The CSFB Affiliates are affiliates of Credit Suisse First
Boston (USA), Inc.

     The Board of Directors recommends that stockholders vote FOR the proposal
to approve and ratify the Warrants, and approval of any future adjustments to
the exercise price of the Warrants pursuant to the terms of the Warrants.

                                 PROPOSAL TWO

        APPROVAL OF AMENDMENT TO BRIGHAM'S CERTIFICATE OF INCORPORATION
TO IMPLEMENT A ONE-FOR-________ REVERSE STOCK SPLIT, SUBJECT TO THE DISCRETION
OF THE BOARD OF DIRECTORS TO DELAY FILING THE AMENDMENT (FOR A PERIOD OF UP TO
NINE MONTHS FROM THE DATE OF THE SPECIAL MEETING) OR NOT TO FILE THE AMENDMENT

General

     Brigham's Board of Directors has adopted resolutions to approve, and to
submit to stockholders for approval, a one-for-________ reverse stock split of
Brigham's issued shares of Common Stock, $.01 par value, on the basis of one new
share of Common Stock for each ________ shares of presently issued Common Stock.
This action would be effected by an amendment to Brigham's Certificate of
Incorporation, as amended (the "Certificate of Incorporation").

                                       9
<PAGE>

     If the proposed amendment to the Certificate of Incorporation effecting the
reverse stock split of shares of Common Stock is approved and the Board of
Directors decides to implement the reverse stock split, a Certificate of
Amendment amending the Certificate of Incorporation would be filed with the
Secretary of State of the State of Delaware.  The amendment and the proposed
reverse stock split would become effective as of the date of such filing or such
later date as is specified in the filing  (the "Effective Date").  The Board of
Directors is seeking stockholder approval for the one-for-________ reverse stock
split at this  time in order to provide it flexibility in the event that the
Board determines that it is in the best interest of the  stockholders to
implement the reverse stock split due to market or other conditions.
Notwithstanding stockholder approval of the reverse stock split, the Board of
Brigham may elect not to file, or elect to delay the filing of, the reverse
stock split amendment, if the Board determines that filing such amendment would
not be advisable.  The actual timing of such filing (and whether such filing is
made) will be determined by the Board based upon their evaluation as to when
such action will be most advantageous to Brigham and its stockholders.  In
addition, the Board may make any and all changes to the reverse stock split
amendment that it deems necessary to give effect to the intent and purpose of
the one-for-________ reverse stock split.  In the event the Board decides to
implement the reverse stock split, it will notify the stockholders by a public
announcement in advance of the Effective Date.

Principal Effects of the Proposed Reverse Stock Split

     If the reverse stock split is approved by the stockholders and implemented
by the Board, at the Effective Date each ________ (___) shares of Common Stock
issued will automatically be reclassified and converted into one (1) share of
Common Stock.  The authorized number of shares will remain the same.  Any
fractional interest resulting from such reclassification will be paid for upon
exchange of the outstanding certificates based upon the average of the high and
low price for the Common Stock on the date immediately preceding the Effective
Date as reported in The Wall Street Journal's listing for such day.  Other than
adjusting the total number of shares issued, adoption of the one-for-________
reverse stock split will result in no other material changes to ownership of the
Common Stock.  The voting rights and other privileges that each share of Common
Stock enjoy before the proposed one-for-________ reverse stock split will be the
same following the one-for-________ reverse stock split.  Each  stockholder will
hold the same percentage of Common Stock outstanding immediately following the
one-for-________ reverse stock split each stockholder did immediately prior to
the one-for-________ reverse stock split, except that the reverse stock split
may result in an immaterial adjustment due to the purchase of any fractional
shares of Common Stock that result from the reverse stock split.  See "Exchange
of Stock Certificate; No Fractional Shares."

     The number of shares of Common Stock that may be purchased upon the
exercise of outstanding options, warrants and conversion rights convertible into
Common Stock or exercisable or exchangeable for shares of Common Stock
(collectively,  "Convertible  Securities") and the per share exercise or
conversion prices thereof will be adjusted appropriately as of the Effective
Date so that the aggregate number of shares of Common Stock issuable in respect
of Convertible Securities immediately following the Effective Date will be one-
____ (without taking into account the effect of rounding up) of the number
issuable in respect thereof immediately prior to the Effective Date and the
total exercise or conversion prices for all of such shares issuable in respect
of Convertible Securities will be ______.  For example, a holder of a stock
option to purchase 1,000 shares of Common Stock at an exercise price of $1.00
per share prior to the Effective Date will be the holder of a stock option to
purchase ___ shares of Common Stock at an exercise price of $____ per share at
the Effective Date.  The number of shares of Common Stock reserved for issuance
under an option or incentive plan would also be reduced after the Effective Date
to one-half of the number reserved for issuance under an option plan prior to
the Effective Date.

     In addition to Common Stock, the Certificate of Incorporation authorizes
the issuance of 10,000,000 shares of preferred stock, $.01 par value.  At
November 29, 2000, there were issued and outstanding 1,000,000 shares of Series
A Preferred Stock.  The authorized and outstanding number of shares of preferred
stock, and the par value thereof, will not change as a result of this Proposal
Two.

     The one-for-________ reverse stock split may result in some stockholders
owning "odd lots" of less than 100 shares of Common Stock received as a result
of the one-for-________ reverse stock split.  Brokerage commissions and

                                       10
<PAGE>

other costs of transactions in odd lots may be higher, particularly on a per-
share basis, than the cost of transactions in even multiples of 100 shares.

     The par value of the Common Stock will remain at $0.01 per share following
the one-for-________ reverse stock split, and the number of shares of the Common
Stock outstanding will be reduced.  As a consequence, the aggregate par value of
the outstanding Common Stock will be reduced, while the aggregate capital in
excess of par value attributable to the outstanding Common Stock for statutory
and accounting purposes will be correspondingly increased. The one-for-________
reverse stock split will not affect the Company's total stockholders' equity.
If the one-for-________ reverse stock split is implemented, all share and per
share information would be retroactively adjusted following the Effective Date
to reflect the one-for-________ share reverse stock split for all periods
presented in future filings by Brigham with the Securities and Exchange
Commission.

Reasons For The Potential Reverse Stock Split

     The Board of Directors believes that the relatively low per share market
price of the Common Stock impairs the acceptability of the Common Stock to
certain institutional investors and other members of the investing public.
Theoretically, the number of shares outstanding should not, by itself, affect
the marketability of the Common Stock, the type of investor who acquires it, or
Brigham's reputation in the financial community.  In practice this is not
necessarily the case since many institutional investors look upon low-priced
stock as unduly speculative in nature and, as a matter of policy, avoid
investment in such stocks.

     Further, the Board of Directors believes that the current per-share level
of the Common Stock has reduced the effective marketability of the shares
because of the reluctance of many leading brokerage firms to recommend low-
priced stock to their clients. In addition, a variety of brokerage house
policies and practices tend to discourage individual brokers within those firms
from dealing in low-priced stocks. Some of those policies and practices pertain
to the payment of brokers' commissions and to time-consuming procedures that
function to make the handling of low-priced stock unattractive to brokers from
an economic standpoint. Additionally, the structure of trading commissions also
tends to have an adverse impact upon holders of low-priced stock because the
brokerage commission on a sale of low-priced stock generally represents a higher
percentage of the sales price than the commission on a relatively higher priced
stock.

     The proposed reverse stock split is intended to result in a higher per
share market price for Brigham's Common Stock.   However, many factors beyond
Brigham's control will affect the ultimate market trading price, and Brigham
cannot assure you that the market price of the Common Stock after the proposed
reverse stock split will approximate ________ times the market price before the
proposed reverse stock split, or that such price will either exceed or remain in
excess of the current market price.   Further, the effect of the proposed
reverse stock split and the resulting decrease in the number of shares of Common
Stock on the market could adversely affect the trading value of such Common
Stock if there is not a corresponding increase in the per share price level for
such stock following the one-for-________ reverse stock split.  Trading
liquidity could therefore be affected  adversely by the reduced number of shares
of common stock outstanding  after the proposed reverse stock split.

     If the one-for-________ reverse stock split is adopted and implemented, the
authorized number of shares will remain the same.  The Board believes that the
availability of additional shares may be beneficial to Brigham in the future.
The availability of additional authorized shares will allow the Board to issue
shares for corporate purposes, if appropriate opportunities should arise,
without further action by stockholders or the time delay involved in obtaining
stockholder approval (unless approval is required by law or regulation or the
rules of The Nasdaq Stock Market).  Such purposes could include share issuances
for future acquisitions of other businesses or meeting requirements for working
capital or capital expenditures through the issuance of shares.  To the extent
that any additional shares (or securities convertible into Common Stock) may be
issued on other than a pro rata basis to current stockholders, the present
ownership position of current stockholders may be diluted.  The Common Stock has
no preemptive rights.  In addition, if another party should seek to acquire or
take over control of Brigham, and the Board does not believe such transaction

                                       11
<PAGE>

is in the best interest of Brigham and its stockholders, some or all of the
authorized shares could be issued to another party to try to block such
transaction.

Exchange Of Stock Certificates; No Fractional Shares

     If the one-for-________ reverse stock split is adopted and implemented, the
combination and reclassification of shares of Common Stock pursuant to the one-
for-________ reverse stock split will occur automatically on the Effective Date
without any action on the part of stockholders of Brigham and without regard to
the date certificates representing shares of Common Stock prior to the one-for-
________ reverse stock split are physically surrendered for new certificates.
Every ________ (___) shares of issued Common Stock would be converted and
reclassified into one (1) share of post-one-for-________ reverse stock split
Common Stock.  Any fractional interest resulting from such reclassification will
be paid for upon exchange of the outstanding certificates based upon the average
of the high and low price for the Common Stock on the date immediately preceding
the Effective Date as reported in The Wall Street Journal's listing for such
day.

     If the one-for-________ reverse stock split is adopted and implemented, as
soon as practicable after the Effective Date, transmittal forms will be mailed
to each holder of record of certificates for shares of Common Stock to be used
in forwarding such certificates for surrender and exchange for certificates
representing the number of shares of Common Stock such stockholder is entitled
to receive as a consequence of the one-for-________ reverse stock split. The
transmittal forms will be accompanied by instructions specifying other details
of the exchange.  Upon receipt of such transmittal form, each stockholder should
surrender the certificates representing shares of Common Stock prior to the one-
for- reverse stock split in accordance with the applicable instructions.  Each
holder who surrenders certificates  will receive new  certificates representing
the whole number of shares of Common Stock that such stockholder holds as a
result of the one-for-________ reverse stock split.  No scrip or fractional
share certificates of post-one-for-________  reverse stock split  Common Stock
certificate will be issued in connection with the proposed reverse stock split.
Stockholders who would otherwise receive fractional shares will receive,
instead, the cash value for such fractional shares determined by multiplying the
fractional shares by the average of the high and low bid price for Brigham's
Common Stock on the Effective Date.  Stockholders will not be required to pay
any transfer fee or other fee in connection with the exchange of certificates.
As previously stated, the Board of Directors has not determined whether it would
be in Brigham's best interest to implement a reverse stock split.  Therefore,
stockholders should not send their stock certificates until they receive a
transmittal form.

     As of the Effective Date, each certificate representing shares of Common
Stock outstanding prior to the Effective Date will be deemed canceled and, for
all corporate purposes, will be deemed only to evidence ownership of the number
of shares of Common Stock into which the shares of Common Stock evidenced by
such certificate have been converted by the one-for-________ reverse stock
split.

Certain Federal Income Tax Consequences

     Brigham believes that the federal income tax consequences  of the one-for
________ reverse stock split will be as follows:

     i.   No income, gain or loss will be recognized by stockholders on the
          surrender of their existing shares of common stock in exchange for the
          issuance of the new number of shares of common stock, except to the
          extent cash is received in lieu of fractional shares.

     ii.  The tax basis of the common stock issued in the reverse stock split
          will equal the tax basis of the common stock exchanged therefore (less
          basis attributable to fractional shares surrendered for cash).

     iii. The holding period of the common stock issued in the reverse stock
          split will include the holding period of the original common stock if
          such shares were held as capital assets.

                                       12
<PAGE>

     iv.  The  conversion  of the old common  stock into the common stock issued
          in the reverse stock split will produce no taxable income or gain or
          loss to Brigham.

     The foregoing  summary  represents Brigham's  opinion only and is based on
the  existing  provisions  of the Internal  Revenue  Code of 1986,  as amended,
and existing administrative  interpretations  thereof, any of which may be
revised retroactively.  Brigham's opinion is not binding upon the Internal
Revenue Service or the courts,  and there can be no assurance that the Internal
Revenue Service or the courts would accept the positions  expressed above.

     The state and local tax consequences of the reverse stock split may vary
significantly as to each stockholder, depending upon the state in which such
stockholder resides. Stockholders are urged to consult their own tax advisors
with respect to the federal, state, and local tax consequences of the reverse
stock split.

Registration and Trading

     Assuming the one-for-________ share reverse stock split is approved and
implemented, the post one-for-________ reverse stock split shares of Common
Stock will continue to be registered under the Securities Exchange Act of 1934,
as amended (the "Exchange Act"), and Brigham will continue to file periodic and
current reports with the Securities and Exchange Commission (the "Commission")
pursuant to the Exchange Act. In addition, Brigham's post-one-for-________
reverse stock split shares of Common Stock will continue to be traded on The
Nasdaq National Market. Brigham intends to file all required notifications with
The Nasdaq National Market to provide for continued trading (on a post-
consolidated basis) in coordination with the Effective Date. Certificates
representing the post-one-for-________ reverse stock split shares of Common
Stock will, however, contain a new CUSIP number. Further, Brigham intends to
file all reports with regulatory authorities and issue a press release in the
event the Board decides to implement the one-for-________ reverse stock split.

     The Board of Directors unanimously recommends voting FOR the approval of
the amendment to Brigham's Certificate of Incorporation to implement a one-for-
________ reverse stock split subject to the discretion of the Board of Directors
to delay filing the amendment (for a period of up to nine months from the date
of the Special Meeting) or not to file the amendment.


                    STOCKHOLDER PROPOSALS AND OTHER MATTERS

Stockholder Proposals

     It is contemplated that the Annual Meeting of Stockholders of Brigham in
2001 will take place during the second week of May 2001.  Stockholder proposals
for inclusion in Brigham's proxy materials for the Annual  Meeting of
Stockholders in 2001 must be received at Brigham's principal executive office in
Austin, Texas, addressed to the Secretary of Brigham, not later than December
20, 2000.

     With respect to stockholder proposals which are not intended to be included
in Brigham's proxy materials, the bylaws of Brigham provide that notice of any
such stockholder proposal nominating persons for election to the Board of
Directors of Brigham must be received at Brigham's principal executive office
not later than 90 days prior to the annual meeting; and all other stockholder
proposals must be received not less than 60 nor more than 120 days prior to the
meeting.

                                       13
<PAGE>

Other Matters

     The Board of Directors of Brigham does not intend to present any other
matters at the meeting and knows of no other matters which will be presented.
However, if any other matters come before the meeting, it is the intention of
the persons named in the enclosed proxy to vote in accordance with their
judgment on such matters.



                                   By Order of the Board of Directors


                                   David T. Brigham
                                   Secretary
December  __, 2000
Austin, Texas

                                       14
<PAGE>

                                                                PRELIMINARY COPY


                          BRIGHAM EXPLORATION COMPANY
                   PROXY FOR SPECIAL MEETING OF STOCKHOLDERS
                                JANUARY 9, 2001

     The undersigned hereby appoints Ben M. Brigham and David T. Brigham, or any
of them, each with full power of substitution, to represent the undersigned at
the Special Meeting of Stockholders of Brigham Exploration Company to be held at
1:00 p.m., local time, on January 9, 2001 at the Company's offices at 6300
Bridge Point Parkway, Building Two, Suite 500, Austin, Texas, and at any
adjournments or postponements thereof, and to vote the number of shares the
undersigned would be entitled to vote if personally present at the meeting.

                The Board of Directors recommends that you vote

                      FOR Proposal 1 and FOR Proposal 2.

     THIS PROXY IS SOLICITED ON BEHALF OF THE BOARD OF DIRECTORS OF BRIGHAM
EXPLORATION COMPANY.  THIS PROXY WILL BE VOTED AS DIRECTED.  IN THE ABSENCE OF
DIRECTION, THIS PROXY WILL BE VOTED FOR PROPOSAL 1 AND FOR PROPOSAL 2.  In their
discretion, the proxy holders are authorized to vote upon such other business as
may properly come before the meeting or any adjournment thereof to the extent
authorized by Rule 14a-4(c) promulgated by the Securities and Exchange
Commission and by applicable state laws.

      (Continued, and to be marked, dated and signed, on the other side)

                                       1
<PAGE>

1.  Approval and ratification of the warrants issued by the Company in November
    2000 to affiliates of Credit Suisse First Boston (USA), Inc. (formerly named
    Donaldson, Lufkin & Jenrette, Inc.), and approval of any future adjustments
    to the exercise price of such warrants pursuant to the terms of such
    warrants.

    [ ]  FOR       [ ]  AGAINST        [ ]  ABSTAIN

2.  Approval of an amendment to the Company's Certificate of Incorporation to
    effect a one-for-________ reverse stock split of all issued shares of the
    Company's common stock, subject to the discretion of the Board of Directors
    to delay filing the amendment (for a period of up to nine months from the
    date of the meeting) or not to file the amendment.

    [ ]  FOR       [ ]  AGAINST        [ ]  ABSTAIN

3.  The transaction of such other Business as may properly come before the
    meeting or any adjournments or postponements of the meeting.

     Whether or not you plan to attend the meeting in person, you are urged to
complete, date, sign and promptly mail this proxy in the enclosed return
envelope so that your shares may be represented at the meeting.


     The undersigned hereby revokes any proxy or proxies heretofore given to
represent or vote such common stock and hereby ratifies and confirms all actions
that the proxies named herein, their substitutes, or any of them, may lawfully
take in accordance with the terms hereof.


Dated:___________, 200__      __________________________________________________
                              Signature(s)*

                              __________________________________________________
                              Signature if held jointly

*NOTE:  Please sign exactly as your name(s) appear(s) on your stock certificate.
        If shares of stock stand of record in the names of two or more persons
        or in the name of husband and wife, whether as joint tenants or
        otherwise, both or all of such persons should sign the proxy. If shares
        of stock are held of record by a corporation, the proxy should be
        executed by the president or vice president and the secretary or
        assistant secretary. Executors, administrators or other fiduciaries who
        execute the above proxy for a stockholder should give their full title.
        Please date the proxy.

                                       2


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