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                                                                 Exhibit 10(s)

FOLKSAMERICA HOLDING COMPANY, INC.
WHITE MOUNTAINS PERFORMANCE SHARE PLAN

1.   PURPOSE

     The purpose of the Folksamerica Holding Company Plan (the "Company" and the
     "Plan" respectively) is to advance the interests of White Mountains
     Insurance Group, Ltd. ("White Mountains") and its stockholders by providing
     long-term incentives to certain key executives of the Company and of its
     subsidiaries who perform services for White Mountains and its affiliates
     and subsidiaries from time to time.

2.   ADMINISTRATION

     The Plan shall be administered by the Board of Directors (the "Board") of
     the Company or a "Committee" of disinterested Directors of the Board in
     consultation with White Mountains executives.

     The Board in consultation with White Mountains shall have exclusive
     authority to select the employees of the Company to be granted Awards, to
     determine the type, size and terms of the Awards and to prescribe the form
     of the instruments embodying Awards. The Board shall be authorized to
     interpret the Plan and the Awards granted under the Plan, to establish,
     amend and rescind any rules and regulations relating to the Plan and to
     make any other determinations which it believes necessary or advisable for
     the administration of the Plan. The Board may correct any defect or supply
     any omission or reconcile any inconsistency in the Plan or in any Award in
     the manner and to the extent the Board deems desirable to carry it into
     effect. Any decision of the Board in the administration of the Plan, as
     described herein, shall be final and conclusive. The Board may act only by
     a majority of its members in office, except that the members thereof may
     authorize any one or more of their number or any officer of the Company to
     execute and deliver documents on behalf of the Board. No member of the
     Company shall be liable for anything done or omitted to be done by him or
     by any other member of the Board in connection with the Plan, except for
     his own willful misconduct or as expressly provided by statute.

3.   PERFORMANCE SHARES

     The Award of Performance Shares to a participant will entitle him to
     receive, without payment to the Company, all or part of a specified amount
     (the "Actual Value") as determined by the Board. Payment in respect of an
     Award shall be made as provided in subparagraph 3(e). Each Award of
     Performance Shares shall be subject to the following terms and conditions:

     (a) The Board shall determine the number of Performance Shares to be
         granted to each participant. The "Maximum Value" of each Performance
         Share shall be the market value per Share on the date the award is paid
         or becomes payable to participants. Performance Shares may be issued in
         different classes or series having different terms and conditions.

     (b) The award period (the "Award Period") in respect of any Award of
         Performance Shares shall be such periods as the Board shall determine
         commencing as of the beginning of the fiscal year of the Company in
         which such Award is made. At the time each Award is made, the Board
         shall establish performance objectives to be attained within the
         performance periods as the means of determining Actual Value. Subject
         to adjustment by the Board from Award Period to Award Period, such
         Award shall be based upon the economic performance target of White
         Mountains over a rolling three year performance period which Award
         shall be based upon the growth in economic value of White Mountains and
         to the extent deemed appropriate by the Board in their sole judgment,
         the economic return of Folksamerica. The Actual Value of

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         a Performance Share shall be equal to its Maximum Value only if the
         performance objectives are attained in full. In determining Actual
         Value, the Board shall multiply the total number of Shares available
         for payout at that time with respect to the participant by the Actual
         Value of each individual Share.

     (c) Performance Shares shall be cancelled if the participant's continuous
         employment with the Company or any of its subsidiaries shall terminate
         for any reason prior to the end of the Award Period, except solely by
         reason of a period of Related Employment as defined in paragraph 5, and
         except as otherwise specified in this subparagraph 3(c) or in
         subparagraph 3(d). Notwithstanding the foregoing and without regard to
         subparagraph 3(b), if a participant shall,

         (i)      while in such employment, die or become disabled as described
                  in paragraph 4 prior to the end of the Award Period, the
                  Performance Shares shall be cancelled at the end of the next
                  ending performance period and he, or his legal representative,
                  as the case may be, shall receive payment in respect of such
                  Shares which he would have received had he been in continuous
                  employment with the Company through the end of that period and
                  had the individual performance objectives, if any, that were
                  imposed been achieved; provided, however, that no such
                  continuation shall be deemed to have occurred for purposes of
                  applying subparagraph 3(d) in the event of an Adverse Change
                  in the Plan in respect of the participant following a Change
                  in Control; or

         (ii)     retire under an approved retirement program of the Company or
                  a subsidiary (or such other plan as may be approved by the
                  Board, in its sole discretion, for this purpose) prior to the
                  end of the Award Period, and

                  (A)      at the time of his retirement, the participant is 65
                           years old or older, the Performance Shares shall be
                           cancelled at the end of the next ending performance
                           period, and he shall receive the Maximum Value in
                           respect to such Shares, at the date of cancellation,

                  (B)      at the time of his retirement the participant is less
                           than 65 years old and his retirement occurs prior to
                           the end of the first performance period, and before
                           24 months have elapsed since the first day of the
                           Award Period, the participant shall receive payment
                           with respect to the Actual Value of one-ninth of the
                           Performance Shares awarded to him under the Award,
                           and

                  (C)      at the time of his retirement the participant is less
                           than 65 years old and his retirement occurs prior to
                           the end of the first performance period and after at
                           least 24 months have elapsed since the first day of
                           the Award Period, the participant shall receive
                           payment with respect to the Actual Value of
                           two-ninths of the Performance Shares awarded to him
                           under the Award.

     (d) If within 24 months after a Change in Control of the Company as defined
         in subparagraph 6(a) and prior to the end of an Award Period:

         (i)      there is a Termination Without Cause, as defined in paragraph
                  7, of the employment of a participant;

         (ii)     there is a Constructive Termination, as defined in paragraph
                  8, of the employment of a participant; or

         (iii)    there occurs an Adverse Change in the Plan, as defined in
                  paragraph 9, in respect of a participant, then:

                  (A)      the participant shall receive the Maximum Value of:

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                           (1)      that number of Performance Shares which is
                                    in the same proportion to the total number
                                    of Performance Shares awarded to the
                                    participant under such Award as

                                    (x)     the number of full months which have
                                            elapsed since the first day of the
                                            Award Period to the end of the first
                                            month in which occurs one of the
                                            events described in clauses (i),
                                            (ii) or (iii) of subparagraph 3(d)
                                            is to

                                    (y)     the total number of months in the
                                            Award Period, less

                           (2)      the number of Performance Shares awarded to
                                    the participant under the Award in respect
                                    of which payment has already been made to
                                    the participant, and

                  (B)      if the number of Performance Shares determined
                           pursuant to subclause (1) of clause (A) is less than
                           the number of Performance Shares subject to the
                           particular Award, the participant shall receive the
                           Actual Value of the remaining Performance Shares. The
                           Actual Value of the remaining Performance Shares
                           shall be determined as follows:

                           (x)      if the Board shall have determined, prior to
                                    the Change in Control and based on the most
                                    recent performance status reports, that the
                                    performance objectives for the particular
                                    Award were being met at the date of the
                                    determination, the Actual Value of the
                                    remaining Performance Shares subject to the
                                    particular Award shall be equal to their
                                    Maximum Value, and

                           (y)      if the determination of the Board was that
                                    the performance objectives for the
                                    particular Award were not being met at the
                                    date of the determination, the Actual Value
                                    of the remaining Performance Shares subject
                                    to the particular Award shall be such amount
                                    as shall have been determined by the Board
                                    as provided above in this subparagraph 3(d),
                                    but in no event shall Actual Value be less
                                    than fifty percent (50%) of Maximum Value.
                                    Payment of any amount in respect of
                                    Performance Shares as described above in
                                    this subparagraph 4(d) shall be made as
                                    promptly as possible after the occurrence of
                                    one of the events described in clauses
                                    3(d)(i) through 3(d)(iii). Notwithstanding
                                    anything herein to the contrary, if,
                                    following a Change in Control of the Company
                                    as defined in subparagraph 6(a), a
                                    participant's employment remains continuous
                                    through the end of a performance period,
                                    then the participant shall be paid with
                                    respect to those Performance Shares for
                                    which he would have been paid had there not
                                    been a Change in Control and the Actual
                                    Value of those Shares shall be determined in
                                    accordance with subparagraph 3(e).

     (e) Payment of any amount in respect of the Performance Shares shall be
         made by the Company as promptly as practicable or shall be deferred to
         such other time or times as the Board shall determine, and may be made
         in cash, in White Mountains Shares, or partly in cash and partly in
         White Mountains Shares as determined by the Board. Such deferred
         payments may be made by undertaking to pay cash in the future, together
         with such additional amounts as may accrue thereon until the date or
         dates of payment, as determined by the Board in its discretion.

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4.   DISABILITY

     For the purposes of this Plan, a participant shall be deemed to be disabled
     if the Board shall determine that the physical or mental condition of the
     participant is such as would entitle him to payment of monthly disability
     benefits under any disability plan of the Company or a subsidiary in which
     he is a participant .

5.   RELATED EMPLOYMENT

     For the purposes of this Plan, Related Employment shall mean the employment
     of an individual by an employer which is neither the Company nor a
     subsidiary provided: (i) such employment is undertaken by the individual
     and continued at the request of the Company or a subsidiary; (ii)
     immediately prior to undertaking such employment, the individual was an
     officer or employee of the Company or a subsidiary, or was engaged in
     Related Employment as herein defined; and (iii) such employment is
     recognized by the Board, in its sole discretion, as Related Employment for
     the purposes of this paragraph 6. The death or disability of an individual
     during a period of Related Employment as herein defined shall be treated,
     for purposes of this Plan, as if the death or onset of disability had
     occurred while the individual was an officer or employee of the Company.

6.   CHANGE IN CONTROL

     (a) For purposes of this Plan, a "Change in Control of White Mountains or
         the Company" within the meaning of this subparagraph 7(a) shall occur
         if:

         (i)      Any person or group (within the meaning of Section 13(d) and
                  14(d)(2) of the Exchange Act), other than John J. Byrne,
                  Berkshire Hathaway, Inc. or one of its wholly owned
                  subsidiaries, becomes the beneficial owner (within the meaning
                  of Rule 13d-3 under the Exchange Act) of thirty-five percent
                  (35%) or more of the White Mountains' then outstanding Shares
                  or fifty percent (50%) or more of the then outstanding shares
                  of the Company;

         (ii)     the Continuing Directors, as defined in subparagraph 6(b),
                  cease for any reason to constitute a majority of the Board of
                  White Mountains; or

         (iii)    the business of the Company for which the participant's
                  services are principally performed is disposed of by White
                  Mountains pursuant to a sale or other disposition of all or
                  substantially all of the business or business related assets
                  of the Company (including stock of a subsidiary of the
                  Company).

     (b) For the purposes of this Plan, "Continuing Director" shall mean a
         member of the White Mountains Board (A) who is not an employee of the
         Company or its subsidiaries or of a holder of, or an employee or an
         affiliate of an entity or group that holds, thirty-five percent (35%)
         or more of the Company's Shares and (B) who either was a member of the
         Board on September 4, 1985, or who subsequently became a director of
         the Company and whose election, or nomination for election, by the
         Company's shareholders was approved by a vote of a majority of the
         Continuing Directors then on the Board (which term, for purposes of
         this definition, shall mean the whole Board and not any Board thereof).
         Any action, approval of which shall require the approval of a majority
         of the Continuing Directors, may be authorized by one Continuing
         Director, if he is the only Continuing Director on the Board, but no
         such action may be taken if there are not Continuing Directors on the
         Board.

7.   TERMINATION WITHOUT CAUSE

     For purposes of this Plan, "Termination Without Cause" shall mean a
     termination of the participant's employment with the Company or a
     subsidiary by the Company or the subsidiary other than (i) for disability
     as described in paragraph 4 or (ii) for Cause. "Cause" shall mean (a) an
     act or omission by the participant that constitutes a felony or any crime
     involving moral turpitude; or (b) willful gross negligence or willful gross

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     misconduct by the participant in connection with his employment by the
     Company or by a subsidiary which causes, or is likely to cause, material
     loss or damage to the Company. Notwithstanding anything herein to the
     contrary, if the participant's employment with the Company or one of its
     subsidiaries shall terminate due to a Change in Control of the Company as
     described in Subsection 6(a)(iii), where the purchaser, as described in
     such subsection, formally assumes the Company's obligations under this Plan
     or places the participant in a similar or like plan with no diminution of
     the value of the awards, such termination shall not be deemed to be a
     "Termination Without Cause."

8.   CONSTRUCTIVE TERMINATION

     "Constructive Termination" shall mean a termination of employment with the
     Company or a subsidiary at the initiative of the participant that the
     participant declares by prior written notice delivered to the Secretary of
     the Company to be a Constructive Termination by the Company or a subsidiary
     and which follows (a) a material decrease in his salary or (b) a material
     diminution in the authority, duties or responsibilities of his position
     with the result that the participant makes a determination in good faith
     that he cannot continue to carry out his job in substantially the same
     manner as it was intended to be carried out immediately before such
     diminution. Notwithstanding anything herein to the contrary, Constructive
     Termination shall not occur within the meaning of this paragraph 9 until
     and unless 30 days have elapsed from the date the Company receives such
     written notice without the Company curing or causing to be cured the
     circumstance or circumstances described in this paragraph 9 on the basis of
     which the declaration of Constructive Termination is given.

9.   ADVERSE CHANGE IN THE PLAN

     An "Adverse Change in the Plan" shall mean

     (a) termination of the Plan pursuant to subparagraph 14(a);

     (b) amendment of the Plan pursuant to paragraph 13 that materially
         diminishes the value of Awards that may be granted under the Plan,
         either to individual participants or in the aggregate, unless there is
         substituted concurrently authority to grant long-term incentive awards
         of comparable value to individual participants in the Plan or in the
         aggregate, as the case may be; or

     (c) in respect of any holder of an Award a material diminution in his
         rights held under such Award (except as may occur under the terms of
         the Award as originally granted) unless there is substituted
         concurrently a long-term incentive award with a value at least
         comparable to the loss in value attributable to such diminution in
         rights.

10.  DILUTION AND OTHER ADJUSTMENTS

     In the event of any change in the Outstanding Shares of White Mountains by
     reason of any stock split, stock dividend, recapitalization, merger,
     consolidation, reorganization, combination or exchange of Shares or other
     similar event, and if the Board shall determine, in its sole discretion,
     that such change equitably requires an adjustment in the number or kind of
     Shares that may be issued under the Plan, in the number or kind of Shares
     subject to, or the Stock Option price per share under, any outstanding
     Stock Option, in the number or kind of Shares which have been awarded as
     Restricted Stock or in the repurchase option price per share relating
     thereto, in the number of Maximum Value or Actual Value of Performance
     Shares which have been awarded to any participant, or in any measure of
     performance, then such adjustment shall be made by the Board and shall be
     conclusive and binding for all purposes of the Plan.

11.  DESIGNATION OF BENEFICIARY BY PARTICIPANT

     A participant may name a beneficiary to receive any payment to which he may
     be entitled in respect of

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     Performance Shares under the Plan in the event of his death, on a form to
     be provided by the Board. A participant may change his beneficiary from
     time to time in the same manner. If no designated beneficiary is living on
     the date on which any amount becomes payable to a participant's executors
     or administrators, the term "beneficiary" as used in the Plan shall include
     such person or persons.

12.  MISCELLANEOUS PROVISIONS

     (a) No employee or other person shall have any claim or right to be granted
         an Award under the Plan. Neither the Plan nor any action taken
         hereunder shall be construed as giving an employee any right to be
         retained in the employ of the Company or any subsidiary.

     (b) A participant's rights and interest under the Plan may not be assigned
         or transferred in whole or in part either directly or by operation of
         law or otherwise (except in the event of a participant's death),
         including but not limited to, execution, levy, garnishment, attachment,
         pledge, bankruptcy or in any other manner and no such right or interest
         of any participant in the Plan shall be subject to any obligation or
         liability or such participant.

     (c) No Shares shall be issued hereunder unless counsel for the Company
         shall be satisfied that such issuance will be in compliance with
         applicable Federal and state securities laws and Bermuda law.

     (d) The Company and its subsidiaries shall have the right to deduct from
         any payment made under the Plan any federal, state or local income or
         other taxes required by law to be withheld with respect to such
         payment. Notwithstanding anything in this Plan to the contrary, if the
         Company is unable to take a tax deduction for any period for which the
         Award is otherwise paid by reason of Section 162(m) of the Code, then
         in such event, such Award shall be deferred to the participants account
         as part of the Company Deferred Compensation Plan. It shall be a
         condition to the obligation of the Company to pay a Performance Share
         that the participant pay any and all withholding taxes upon demand of
         the Company, in such amounts as may be required by the Company for the
         purpose of satisfying any liability to withhold Federal, state or local
         income or other taxes of the participant. If the amount requested is
         not paid, the Company may refuse to make payment.

     (e) The expenses of the Plan shall be borne by the Company. However, if an
         Award is made to an employee of a subsidiary:

         (i)      if such Award results in payment of cash to the participant,
                  such subsidiary shall pay to the Company an amount equal to
                  such cash payment; and

         (ii)     if the Award results in the issuance to the participant of
                  Shares, such subsidiary shall pay to the Company an amount
                  equal to fair market value thereof, as determined by the
                  Board, on the date such Shares are issued (or, in the case of
                  issuance of Restricted Stock or of Shares subject to transfer
                  and forfeiture conditions, equal to the fair market value
                  thereof on the date on which such Shares are no longer subject
                  to applicable restriction), minus the amount, if any received
                  by the Company in exchange for such Shares.

     (f) The Plan shall be unfunded. The Company shall not be required to
         establish any special or separate fund or to make any other segregation
         of assets to assure the payment of any Award under the Plan.

     (g) By accepting any Award or other benefit under the Plan, each
         participant and each person claiming under or through him shall be
         conclusively deemed to have indicated his acceptance and ratification
         of, and consent to, any action taken under the Plan by the Company, the
         Board or the Board.

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13.  AMENDMENT

     The Plan may be amended at any time and from time to time by the Board, but
     no amendment which increases the aggregate number of Shares which may be
     issued pursuant to the Plan or the class of employees eligible to
     participate shall be effective unless and until the same is approved by the
     shareholders of the Company. No amendment of the Plan shall adversely
     affect any right of any participant with respect to any Award previously
     granted without such participant's written consent.

14.  TERMINATION

     This Plan shall terminate upon the earlier of the following dates or events
to occur:

     (a) the adoption of a resolution of the Board terminating the Plan; or

     (b) ten years from the date the Plan is initially or subsequently approved
         and adopted by the shareholders of the Company.

     No termination of the Plan shall alter or impair any of the rights or
     obligations of any person, without his consent, under any Award previously
     granted under the Plan.

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Exhibit 4.4    
  

 
 

CERTIFICATE OF DESIGNATIONS
  
    of
  
    SERIES B PREFERRED STOCK
  (Par Value $.01 Per Share)
  
    of
  
    BRIGHAM EXPLORATION COMPANY    
  

 
 

Pursuant to Section 151
  of the General Corporation Law of the State of Delaware    
  

        Brigham
Exploration Company, a corporation organized and existing under the laws of the State of Delaware (the "Corporation"), DOES HEREBY CERTIFY that, pursuant to the authority
conferred on the Board of Directors of the Corporation by the Certificate of Incorporation, as amended, of the Corporation and in accordance with Section 151 of the General Corporation Law of
the State of Delaware, the Board of Directors of the Corporation on December 20, 2002, duly adopted the following preamble and resolution establishing and creating a series of 1,000,000 shares
of Preferred Stock, par value $.01 per share, of the Corporation: 

        RESOLVED, that pursuant to the authority vested in the Board of Directors of the Corporation (the "Board of Directors") in accordance with
the provisions of its Certificate of Incorporation, as amended, a series of Preferred Stock, par value $.01 per share, of the Corporation is hereby created, and that the designation and number of
shares thereof and the preferences, limitations and relative rights thereof are as follows: 

        Section 1.    Designation and Number of Shares of Series B Preferred
Stock. There is hereby authorized and established a series of Preferred Stock that shall be designated as "Series B Preferred Stock" (hereinafter referred to as
"Series B Preferred"), and the number of shares constituting such series shall be 1,000,000. Such number of shares may be increased or decreased, but not to a number less than the number of
shares of Series B Preferred then issued and outstanding, by resolution adopted by the full Board of Directors. The "Stated Value" per share of the Series B Preferred shall be equal to
Twenty Dollars ($20.00). 

        Section 2.    Definitions. In addition to the definitions set forth
elsewhere herein, the following terms shall have the meanings indicated: 

        "Business
Day" means any day other than a Saturday, Sunday or a day on which banking institutions in New York, New York are authorized or obligated by law or executive order to close. 

        "Change
of Control" means (i) any sale, lease, exchange or other transfer (in one transaction or a series of related transactions) of all or substantially all of the assets of the
Corporation and its Subsidiaries; or (ii) the acquisition by any Person or group of related Persons for purposes of Section 13 (d) of the Exchange Act, of the power, directly or
indirectly, to vote or direct the voting of securities having more than 50% of the ordinary voting power for the election of directors of the Corporation or of any direct or indirect holding company
thereof; or (iii) during any period of two consecutive years, individuals who at the beginning of such period constituted the Board of Directors of 

the Corporation cease for any reason to constitute a majority of the Board of Directors then in office; provided that any person becoming a director subsequent to the beginning of such
two-year period whose election, or nomination for election by the stockholders of the Corporation, was approved by a vote of at least a majority of the directors then comprising the Board
of Directors of the Corporation shall be, for purposes of this definition, considered as though such person were a member of such Board at the beginning of such two-year period. 

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

        "Exchange
Act" means the Securities Exchange Act of 1934, as amended. 

        "Junior
Securities" means the Common Stock or any other series of stock issued by the Corporation ranking junior as to the Series B Preferred upon liquidation, dissolution or
winding up of the Corporation. 

        "Original
Issue Date" means the date on which shares of the Series B Preferred are first issued. 

        "Parity
Security" means the Corporation's Series A Preferred Stock and any other class or series of stock issued by the Corporation ranking on a parity with the Series B
Preferred upon liquidation, dissolution or winding up of the Corporation. 

        "Person"
means any individual, corporation, association, partnership, joint venture, limited liability company, trust, estate, or other entity or organization, other than the
Corporation, any subsidiary of the Corporation, any employee benefit plan of the Corporation or any subsidiary of the Corporation, or any entity holding shares of Common Stock for or pursuant to the
terms of any such plan. 

        "Redemption
Date" means the date fixed for any redemption of the Series B Preferred as provided in Section 6 or 7. 

        "Senior
Securities" means any class or series of stock issued by the Corporation ranking senior to the Series B Preferred upon liquidation, dissolution or winding up of the
Corporation. 

        "Warrants"
means the warrants to purchase Common Stock originally issued to DLJ Merchant Banking Partners III, LP; Millennium Partners II, L.P.; MBP III Plan Investors, L.P.; DLJ
Merchant Banking III, Inc., as Advisory General Partner on behalf of DLJ Offshore Partners III, C.V.; DLJ Merchant Banking III, Inc., as Advisory General Partner on behalf of DLJ
Offshore Partners III-1, C.V. and as attorney-in-fact for DLJ Merchant Banking III, L.P., as Associate General Partner of DLJ Offshore Partners III-1,
C.V.; DLJ Merchant Banking III, Inc., as Advisory General Partner on behalf of DLJ Offshore Partners III-2, C.V. and as attorney-in-fact for DLJ Merchant
Banking III, L.P., as Associate General Partner of DLJ Offshore Partners III-2, C.V.; and DLJ MB Partners III GmbH & Co. KG on the Original Issue Date, pursuant to Warrant
Certificates in the form attached hereto as Exhibit A. 

        "Warrant
Certificates" means the Warrant Certificates representing the Warrants. 

        Section 3.    Dividends and Distributions.

        (a)      The
holders of shares of the Series B Preferred shall be entitled to receive, when, as and if declared by the Board of Directors out of funds
legally available therefor, dividends at the times and at the rates provided in this Section 3. Subject to the provisions of Section 3(c) below, dividends shall accrue on each
outstanding share of the Series B Preferred at the rate of six percent (6%) per annum of the Stated Value (the "Dividend Rate") of such share. Such dividends on shares of Series B
Preferred shall be cumulative from the date such shares are issued, whether or not in any period there shall be funds of the Corporation legally available for the payment of such dividends and whether
or not such dividends are declared, and shall be payable quarterly, when, as and if declared by the Board of Directors, on March 31, June 30, September 30 and December 31
in each year (each a "Dividend Payment Date"), except that if such Dividend Payment Date is not a Business Day, then such dividend shall be payable on the first Business Day immediately thereafter to
the holders of the Series B Preferred. Such dividends shall accrue whether or not there shall be (at the time such dividend becomes payable or at any other time) profits, surplus or other funds
of the Corporation legally 

available for the payment of dividends. Except as provided below, the dividends shall be payable in cash. 

        (b)      Dividends
shall be calculated on the basis of the time elapsed from and including the date immediately following the most recent preceding Dividend Payment
Date (or, if none, the date of issuance) to and including the Dividend Payment Date or the final distribution date relating to conversion or redemption or to a dissolution, liquidation or winding up
of the Corporation. Dividends payable on the shares of Series B Preferred for any period that is not a full quarter shall be calculated at the Dividend Rate on the basis of a
360-day year of twelve 30-day months. 

        (c)      Notwithstanding
anything to the contrary in Section 3(a), on any Dividend Payment Date occurring on or before the fifth anniversary of the Original
Issue Date, if the Corporation does not pay all or part of the cash dividend payable on such Dividend Payment Date (or, if applicable, the first Business Day immediately thereafter), then the
Corporation shall pay such unpaid portion of the dividend payable on such Dividend Payment Date to the holders of Series B Preferred in shares (including fractional shares) of Series B
Preferred (a "Payment in Kind"). Each Payment in Kind shall be payable as of such Dividend Payment Date, except that if such Dividend Payment Date is not a Business Day, then such Payment in Kind
shall be on the first Business Day immediately thereafter to the holders of the Series B Preferred. The issuance of additional shares of Series B Preferred pursuant to subparagraphs
(c) and (d) of this Section 3 shall constitute full payment of any dividend paid through Payment in Kind, and such dividends shall not accumulate. 

        (d)      Each
Payment in Kind shall be equal to that number of additional shares of Series B Preferred that is equal to A divided by B where: 

        "A" =
133.33% of the aggregate dollar amount of the unpaid cash dividends payable on any such Dividend Payment Date; and 

        "B" =
the Stated Value. 

        Certificates
representing the shares of Series B Preferred issuable on payment of any Payment in Kind shall be delivered to each holder entitled to receive such Payment in Kind
(in appropriate denominations) on or before the twentieth (20th) day following the Dividend Payment Date for which such Payment in Kind is elected to be paid hereunder. Shares of Series B
Preferred issued on payment of any Payment in Kind shall be duly authorized, validly issued and nonassessable and, upon issuance, shall have rights (including without limitation, dividend, voting and
redemption rights) and a Stated Value identical to the outstanding shares of Series B Preferred in respect of which they are issued. 

        (e)      Except
as provided in Section 8, no interest, or sum of money in lieu of interest, shall be payable in respect of any dividend payment or payments
on the Series B Preferred which are in arrears. 

        (f)        Dividends
payable on each Dividend Payment Date shall be paid to record holders of the shares of Series B Preferred as they appear on the books of
the Corporation at the close of business on the tenth Business Day immediately preceding the respective Dividend Payment Date or on such other record date as may be fixed by the Board of Directors of
the Corporation in advance of a Dividend Payment Date, provided that no such record date shall be less than ten nor more than 60 calendar days preceding such Dividend Payment Date. 

        (g)      So
long as any shares of Series B Preferred are outstanding, the Corporation shall not issue any Senior Securities. 

        (h)      No
dividends (other than those payable solely in the common stock of the Corporation) shall be paid on any common stock unless and until all accrued and
unpaid dividends on the Series B Preferred have been paid. 

        Section 4.    Liquidation Preference.

        (a)      In
the event of any liquidation, dissolution or winding up of the Corporation (in connection with the bankruptcy or insolvency of the Corporation or
otherwise), whether voluntary or involuntary, before any payment or distribution of the assets of the Corporation (whether capital or surplus) shall 

be made to or set apart for the holders of shares of any Junior Securities, the holders of the shares of Series B Preferred shall be entitled to receive an amount per share equal to
(i) the Stated Value per share held by them plus (ii) an amount equal to the aggregate dollar amount of all accrued and unpaid dividends through the final distribution date. To the
extent the available assets are insufficient to fully satisfy such amounts, then the holders of the Series B Preferred shall share ratably in such distribution in the proportion that the number
of each holder's Series B Preferred Shares bears to the total number
of shares of Series B Preferred outstanding. No further payment on account of any such liquidation, dissolution or winding up of the Corporation shall be paid to the holders of the shares of
Series B Preferred or the holders of any Parity Securities unless there shall be paid at the same time to the holders of the shares of Series B Preferred and the holders of any Parity
Securities proportionate amounts determined ratably in proportion to the full amounts to which the holders of all outstanding shares of Series B Preferred and the holders of all such
outstanding Parity Securities are respectively entitled with respect to such distribution. For purposes of this Section, neither a consolidation or merger of the Corporation with one or more
partnerships, corporations or other entities nor a sale, lease, exchange or transfer of all or any substantial part of the Corporation's assets for cash, securities or other property shall be deemed
to be a liquidation, dissolution or winding-up of the Corporation, whether voluntary or involuntary. 

        (b)      After
the payment of the full amount to the holders of Series B Preferred pursuant to the preceding subparagraph (a), and subject to the rights of
holders of Junior Securities other than the Common Stock, the holders of Common Stock shall share ratably in the distribution of the remaining available assets of the Corporation, in the proportion
that each holder's shares of Common Stock bears to the total number of shares of Common Stock of the Corporation outstanding. 

        (c)      Written
notice of any liquidation, dissolution or winding up of the Corporation, stating the payment date or dates when and the place or places where the
amounts distributable in such circumstances shall be payable, shall be given by first class mail, postage prepaid, not less than 15 days prior to any payment date stated therein, to the holders
of record of the shares of Series B Preferred at their respective addresses as the same shall appear in the records of the Corporation. 

        Section 5.    Optional Redemption by the Corporation. The outstanding
shares of Series B Preferred are subject to redemption in accordance with the following provisions: 

        (a)      Subject
to the terms hereof, the Corporation may at its option, so long as it has sufficient funds legally available therefor, elect to redeem, in whole or
in part, the outstanding shares of Series B Preferred at any time after the five-year anniversary of the date of issuance of such shares. 

        (b)      (i)
The redemption price per share for Series B Preferred redeemed on any optional redemption date shall, subject to the provisions below in this
Section 5(b), be an amount equal to 101% of the Stated Value of such share plus, without duplication, all accrued and unpaid dividends on such share to and including such Redemption Date (the
"Optional Redemption Price"). The Optional Redemption Price shall be paid in cash from any source of funds legally available therefor. 

        (ii)  In
the event the holders of the Warrants exercise any or all of such Warrants for cash consideration (otherwise than pursuant to the mandatory exercise provisions in
Section 5 of each Warrant Certificate), then the Optional Redemption Price for a number of shares of Series B Preferred equal to (A) the aggregate exercise price received by the
Corporation pursuant to such exercise divided by (B) the Stated Value as of the exercise date, shall thereafter be deemed to be 100% of the Stated Value of such share
plus, without duplication, all accrued and unpaid dividends on such share to and including such Redemption Date. If less than all of the outstanding Series B Preferred are to be redeemed
pursuant to this Section 5(b) at the price specified in the preceding sentence, then the Corporation shall redeem a pro rata portion from each holder of Series B Preferred according to
the respective number of shares of Series B Preferred held by such holder. 

        (iii)  In
the event the holders of the Warrants exercise any or all of such warrants for consideration consisting of shares of Series B Preferred, then (A) such
exercise shall be deemed an optional redemption of such Series B Preferred, (B) the notice required by Section 5(c) shall not 

be required, (C) the exercise date shall be the Redemption Date, (C) the Optional Redemption Price per share in such event shall be 100% of the Stated Value of such share as of the
Redemption Date, plus, without duplication, all accrued and unpaid dividends on such share to and including such Redemption Date and (D) the Optional Redemption Price shall be paid as set forth
in Section 1 of the Warrant Certificate. 

        (c)      Not
less than 30 nor more than 60 days prior to the date fixed for any redemption of any shares of Series B Preferred, a notice specifying
the Redemption Date and place of such redemption and the number of shares to be redeemed shall be given by first class mail, postage prepaid, to the holders of record of the shares of Series B
Preferred to be redeemed at their respective addresses as the same shall appear on the books of the Corporation (but no failure to mail such notice or any defect therein shall affect the validity of
the proceedings for redemption except as to the holder to whom the Corporation has failed to mail such notice or except as to the holder whose notice was defective), calling upon each such holder of
record to surrender to the Corporation on the Redemption Date at the place designated in such notice such holder's certificate or certificates representing the then outstanding shares of
Series B Preferred held by such holder being redeemed by the Corporation. On or after the Redemption Date, each holder of shares of Series B Preferred called for redemption shall
surrender such holder's certificate or certificates for such shares to the Corporation at the place designated in the redemption notice and shall thereupon be entitled to receive payment of the
Optional Redemption Price. Unless there shall have occurred an Event of Noncompliance (as defined hereinafter) that is continuing, from and after the Redemption Date, dividends on the Series B
Preferred called for redemption shall cease to accumulate and all rights of the holders of Series B Preferred designated for redemption (except the right to receive the Optional Redemption
Price without interest upon surrender of their certificate or certificates) shall cease with respect to such shares, and such shares shall not thereafter be transferred on the books of the Corporation
or be deemed to be outstanding for any purpose whatsoever. In the event that less than all of the shares represented by any such certificate are redeemed, a new certificate shall be issued
representing such unredeemed shares. 

        Section 6.    Mandatory Redemption.

        (a)      As
soon as possible following November 1, 2012, the Corporation shall redeem each outstanding Series B Preferred share for cash for an amount
per share equal to the Stated Value of such share plus, without duplication, all accrued and unpaid dividends on such share to and including such Redemption Date (the "Redemption Price"). 

        (b)      In
the event that (i) the Corporation gives a "Company Notice" (as defined in the Warrant Certificates) and (ii) the Warrants are thereafter
exercised pursuant to the mandatory exercise provisions in Section 5 of each Warrant Certificate for cash consideration, then the Corporation shall redeem, for cash for an amount per share
equal to the Redemption Price, a number of shares of Series B Preferred equal to (A) the aggregate exercise price received by the Corporation pursuant to such mandatory exercise divided
by (B) the Redemption Price as of the Redemption Date, rounded down to the nearest whole share of Series B Preferred. Such redemption shall occur not more than ninety days after the date
on which such Warrants are exercised. If less than all of the outstanding Series B Preferred are to be redeemed pursuant to this Section 6(b), then the Corporation shall redeem a pro
rata portion from each holder of Series B Preferred according to the respective number of shares of Series B Preferred held by such holder. 

        (c)      In
the event that (i) the Corporation gives a "Company Notice" (as defined in the Warrant Certificates) and (ii) all of the outstanding
Warrants are thereafter exercised pursuant to the mandatory exercise provisions in Section 5 of each Warrant Certificate for consideration consisting exclusively of Series B Preferred,
then the Corporation shall redeem, for cash for an amount per share equal to the Redemption Price, all of the remaining shares of Series B Preferred. Such redemption shall occur simultaneously
with the exercise of the Warrants by the holders. 

        (d)      Not
less than ten nor more than sixty days prior to the Redemption Date fixed for any redemption of any shares of Series B Preferred under
Section 6(a), a notice specifying the mandatory 

Redemption Date and place of such redemption and the number of shares to be redeemed shall be given by first class mail, postage prepaid, to the holders of record of the shares of Series B
Preferred at their respective addresses as the same shall appear on the books of the Corporation, calling upon each such holder of record to surrender to the Corporation on the mandatory Redemption
Date at the place designated in such notice the holder's certificate or certificates representing the number of shares of Series B Preferred owned by such holder and being redeemed on such
mandatory Redemption Date. On or after the mandatory Redemption Date, each holder of shares of Series B Preferred shall surrender his certificate or certificates for such shares to the
Corporation at the place and amount designated in the redemption notice and shall thereupon be entitled to receive payment of the aggregate Redemption Price for such shares. Unless there shall have
occurred an Event of Noncompliance that is continuing, from and after the mandatory Redemption Date, dividends on the Series B Preferred called for redemption shall cease to accumulate and all
rights of the shares of Series B Preferred being redeemed (except the right to receive the Redemption Price without interest upon surrender of the related certificate or certificates) shall
cease, and such shares shall not thereafter be transferred on the books of the Corporation or be deemed to be outstanding for any purpose whatsoever. In the event that less than all of the shares
represented by any such certificate are redeemed, a new certificate shall be issued representing such unredeemed shares. 

        (e)      In
connection with a redemption under this Section 6, if the Corporation has insufficient funds (whether by legal or contractual prohibition or
otherwise) to initially redeem all shares required to be redeemed thereunder, then the Corporation shall from time to time whenever possible use the maximum amount of funds available (until all shares
of Series B Preferred are redeemed), and in each
partial redemption the number of shares redeemed and the redemption price therefor shall be allocated according to the relative number of Series B Preferred shares owned by each holder as
compared to the total number of shares of Series B Preferred outstanding at such time. 

        Section 7.    Change of Control.

        (a)      Within
20 days of the occurrence of a Change of Control, the Corporation shall make an offer to purchase (the "Change of Control Offer") the
outstanding Series B Preferred shares at an amount per share equal to (x) 101% of the Stated Value of such shares plus, without duplication, (y) all accrued and unpaid dividends
on such shares to and including the Change of Control Payment Date (such applicable purchase price being hereinafter referred to as the "Change of Control Purchase Price") in accordance with the
procedures set forth in this Section 7. 

        (b)      Within
20 days of the occurrence of a Change of Control, the Corporation also shall send by first-class mail, postage prepaid, to each holder of
Series B Preferred, at the address appearing on the stock books of the Corporation, a notice stating: 

          (i)  that
the Change of Control Offer is being made pursuant to this Section 7 and that all Series B Preferred tendered will be accepted for payment, and
otherwise subject to the terms and conditions set forth herein; 

        (ii)  the
Change of Control Purchase Price and the purchase date (which shall be a Business Day no earlier than 20 Business Days from the date such notice is mailed (the
"Change of Control Payment Date")); 

        (iii)  that
any Series B Preferred not tendered will continue to accumulate dividends; 

        (iv)  that,
unless the Corporation defaults in the payment of the Change of Control Purchase Price, any Series B Preferred accepted for payment pursuant to the Change
of Control Offer shall cease to accumulate dividends after the Change of Control Payment Date; 

        (v)  that
holders accepting the offer to have their Series B Preferred purchased pursuant to a Change of Control Offer will be required to surrender their certificates
representing Series B Preferred to the Corporation at the address specified in the notice prior to the close of business on the Business Day preceding the Change of Control Payment Date; 

        (vi)  that
holders will be entitled to withdraw their acceptance if the Corporation receives, not later than the close of business on the third Business Day preceding the
Change of Control Payment Date, a telegram, telex, facsimile transmission or letter setting forth the name of the holder, the number of shares of Series B Preferred delivered for purchase, and
a statement that such holder is withdrawing his election to have such Series B Preferred purchased; 

      (vii)  that
holders whose Series B Preferred is being purchased only in part will be issued new certificates representing the number of shares of Series B
Preferred equal to the unpurchased portion of the certificates surrendered; and 

      (viii)  any
other procedures that a holder must follow to accept a Change of Control Offer or effect withdrawal of such acceptance. 

        (c)      In
the event that a Change of Control occurs and the holders of Series B Preferred exercise their right to require the Corporation to purchase
Series B Preferred, if such purchase constitutes a "tender offer" for purposes of Rule 14e-1 under the Exchange Act at that time, the Corporation will comply with the
requirements of Rule 14e-1 as then in effect with respect to such repurchase and, in the event of a conflict between the requirements of the Exchange Act and this Certificate of
Designation, the provisions of the Exchange Act shall govern. 

        (d)      On
the Change of Control Payment Date, the Corporation shall (A) accept for payment the shares of Series B Preferred validly tendered
pursuant to the Change of Control Offer, (B) promptly mail to the holders of shares so accepted the Change of Control Purchase Price therefor and (C) cancel and retire each surrendered
Certificate and execute a new Series B Preferred certificate equal to any unpurchased shares represented by a certificate surrendered. Unless the Corporation defaults in the payment for the
shares of Series B Preferred tendered pursuant to the Change of Control Offer, dividends shall cease to accrue with respect to the shares of Series B Preferred tendered and all rights of
holders of such tendered shares shall terminate, except for the right to receive payment therefor, on the Change of Control Payment Date. 

        (e)      The
Corporation will not be required to make a Change of Control Offer upon a Change of Control if a third party makes such Change of Control Offer
contemporaneously with or upon a Change of Control in the manner, at the times and otherwise in compliance with the requirements of this Section 7 and purchases all Series B Preferred
validly tendered and not withdrawn under such Change of Control Offer. 

        (f)        Prior
to the mailing of the notice referred to in Section 7(b), but in any event within 20 days following the date on which a Change of
Control occurs, the Corporation covenants that, if the purchase of the Series B Preferred would violate or constitute a default or be prohibited under any instrument governing indebtedness
outstanding at the time, then the Corporation will, to the extent needed to
permit such purchase of Series B Preferred, either (i) repay in full all such indebtedness or (ii) obtain the requisite consents under such instruments to permit the redemption of
the Series B Preferred as provided above. The Corporation will first comply with the covenant in the preceding sentence before it will be required to redeem Series B Preferred pursuant
to the provisions described above. 

        Section 8.    Events of Noncompliance.

        (a)      Notwithstanding
any provision to the contrary contained herein, an "Event of Noncompliance" shall have occurred if the Corporation: 

          (i)  fails
to pay on or before twenty days after any Dividend Payment Date the full amount of dividends then accrued on the Preferred Stock, whether or not such payments are
legally permissible; or 

        (ii)  the
Corporation fails to pay the deemed Optional Redemption Price that is payable pursuant to Section 5(b)(iii) or the Redemption Price payable pursuant
to Section 6 on the date that the certificates for the shares of Series B Preferred are properly presented to the Corporation for redemption, whether or not such payment is legally
permissible; or 

        (iii)  the
Corporation fails to pay the Optional Redemption Price payable pursuant to Sections 5(b)(i) and (ii) on the date that the certificates for the shares
of Series B Preferred are properly presented to the Corporation for redemption, whether or not such payment is legally permissible. 

        (b)      Immediately
upon an Event of Noncompliance pursuant to Section 8(a)(i), the Dividend Rate then in effect shall be increased to an amount equal to
the Dividend Rate then in effect plus 2.0%, until such time as the dividends accrued but not paid on the applicable Dividend Payment Date are paid in full. 

        (c)      Immediately
upon an Event of Noncompliance pursuant to Section 8(a)(ii), the Dividend Rate then in effect shall be increased to an amount equal to
the Dividend Rate then in effect plus 1.0% and, until such time as the Option Redemption Price, or the Redemption Price, as applicable, is paid in full, such Dividend Rate then in effect shall be
further increased by 100 basis points on every 90th day after the date any prior adjustment is made pursuant to this Section 8(c). 

        Section 9.    Reacquired Shares. Any shares of Series B Preferred
repurchased, redeemed, converted or otherwise acquired by the Corporation shall be retired and canceled promptly after the acquisition
thereof. All such shares shall upon their cancellation become authorized but unissued shares of Preferred Stock, without designation as to series. 

        Section 10.    Voting Rights.

        (a)      Except
as otherwise required by law and as specified in this Section, the holders of shares of Series B Preferred shall not have any right or power
to vote on or consent with respect to any matter or in any proceeding or to be represented at any meeting of stockholders of the Corporation. In any action taken as a class, each holder of shares of
Series B Preferred shall be entitled to one vote for each share held. 

        (b)      So
long as any shares of Series B Preferred remain outstanding, the affirmative vote or consent of the holders of 75% of the shares of
Series B Preferred outstanding at the time, voting as a class, given in person or by proxy, either in writing or at a meeting, shall be necessary to permit, effect or validate (i) the
issuance of any shares of Series B Preferred, other than as a Payment in Kind of dividends payable thereon (ii) the authorization, creation or issuance, or any increase in the authorized
or issued amount, of any class or series of Parity Security, other than any Payment or Kind or any increase in the number of authorized shares of Series B Preferred in connection therewith, or
(iii) the amendment, alteration or repeal of any of the provisions of the Certificate of Incorporation, as amended, of the Corporation which would adversely affect any right, preference,
privilege or voting power of shares of Series B Preferred or of the holders thereof. The increase in the amount of authorized Preferred Stock of the Corporation or the creation and issuance, or
increase in amount of authorized shares of other series of Parity Security or Junior Security shall not be deemed to affect materially and adversely such rights, preferences, privileges or voting
power. 

        Section 11.    Certain Taxes. So long as any shares of Series B
Preferred are outstanding the Corporation shall pay all taxes and other governmental charges (other than any income, franchise or similar taxes) that may be imposed with respect to the issue or
delivery of shares of Common Stock upon conversion of Series B Preferred as provided herein. The Corporation shall not be required, however, to pay any tax or other charge imposed in connection
with any transfer involved in the issue of any certificate for shares of Common Stock in any name other than that of the registered holder of the shares of the Series B Preferred surrendered in
connection with the conversion thereof, and in such case the Corporation shall not be required to issue or deliver any stock certificate until such tax or other charge has been paid, or it has been
established to the Corporation's satisfaction that no tax or other charge is due. 

        Section 12.    Ranking. For purposes of the distribution of assets upon
liquidation, dissolution or winding up of the Corporation, (i) the Junior Securities shall rank junior to the Series B Preferred and (ii) the Parity Securities shall rank on a
parity with the Series B Preferred. 

        Section 13.    Record Holders. The Corporation may deem and treat the
record holder of any shares of Series B Preferred as the true and lawful owner thereof for all purposes, and the Corporation shall not be affected by any notice to the contrary. 

        Section 14.    Notice. Except as may otherwise be provided by law or
provided for herein, all notices referred to herein shall be in writing, and all notices hereunder shall be deemed to have been given upon receipt, in the case of a notice of conversion given to the
Corporation, or, in all other cases, upon the earlier of receipt of such notice or three Business Days after the mailing of such notices sent by Registered Mail (unless first-class mail shall be
specifically permitted for such notice under the terms hereof) with postage prepaid, addressed: If to the Corporation, to its principal executive offices or to any agent of the Corporation designated
as permitted hereby; or if to a holder of the Series B Preferred, to such holder at the address of such holder of the Series B Preferred as listed in the stock record books of the
Corporation, or to such other address as the Corporation or holder, as the case may be, shall have designated by notice similarly given. 

        Section 15.    Successors and Transferees. The provisions applicable to
shares of Series B Preferred shall bind and inure to the benefit of and be enforceable by the Corporation, the respective successors to the Corporation, and by any record holder of shares of
Series B Preferred. 

        RESOLVED FURTHER, that the appropriate officers of the Corporation be, and they are hereby, authorized and directed from time to time to
execute such certificates, instruments or other documents and do all such things as may be necessary or advisable in their discretion in order to carry out the terms hereof, including the filing with
the Secretary of State for the State of Delaware of a copy of the foregoing resolution executed by an officer of the Corporation. 

Dated:
December 20, 2002 

	

 	
BRIGHAM EXPLORATION COMPANY
	

 	

By:	

 
	 	 	/s/  EUGENE B. SHEPHERD, JR.      
	 	 	
 Name: Eugene B. Shepherd, Jr.

Title: CFO

  

 
 

EXHIBIT A    
  

        THE SECURITIES REPRESENTED BY THIS CERTIFICATE HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED, OR ANY APPLICABLE
STATE SECURITIES LAWS, AND MAY NOT BE SOLD OR TRANSFERRED IN THE ABSENCE OF SUCH REGISTRATION OR AN EXEMPTION THEREFROM. SUCH SECURITIES ARE SUBJECT TO THE RESTRICTIONS AND PRIVILEGES SPECIFIED IN
THIS WARRANT CERTIFICATE AND IN A SECURITIES PURCHASE AGREEMENT, DATED AS OF DECEMBER    , 2002, BETWEEN BRIGHAM EXPLORATION COMPANY AND THE INITIAL HOLDER OF SECURITIES NAMED THEREIN, A
COPY OF WHICH IS ON FILE WITH THE SECRETARY OF BRIGHAM EXPLORATION COMPANY AND WILL BE FURNISHED WITHOUT CHARGE TO THE HOLDER HEREOF UPON WRITTEN REQUEST, AND THE HOLDER OF THIS CERTIFICATE AGREES TO
BE BOUND THEREBY.

 
 

WARRANT CERTIFICATE    
  

	Number of Warrants: ______________	 	Warrant No. ______________

        This
Warrant certificate ("Warrant Certificate") certifies that, for value received,                        is the registered holder of
the number of warrants (the "Warrants") set forth above.
Each Warrant entitles the holder thereof, at any time 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. 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
Deferral Period" means the period of time beginning on the Issuance Date and ending six months after the Issuance Date. 

        "Exercise
Period" means the period of time beginning six months after the Issuance Date and ending at 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 $4.35 per share. 

        "Expiration
Date" means the tenth anniversary of the Issuance Date. 

        "Issuance
Date" means                        , 2002. 

        "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. 

        "Preferred
Stock" means shares of the Series B Preferred Stock, par value $0.01 per share, of the Company. 

        "Preferred
Value" per share of Preferred Stock means the Stated Value of such Share, plus, without duplication, all accrued and unpaid dividends on such share to and including the
applicable date of Warrant exercise. 

        "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 

A-1

 

exchange (based on the aggregate dollar value of securities listed) on which such shares are listed or traded, or if such shares are not listed or traded on any national securities exchange, then the
average of the reported high and low sales prices for such shares in the over-the-counter market, as reported on the National Association of Securities Dealers Automated
Quotations System, or, if such prices shall not be reported thereon, the average of the closing bid and asked prices so reported, or, if such prices shall not be reported, then the average of the
closing bid and asked prices reported by the National Quotations Bureau Incorporated. The "Average" Price per share for any period shall be determined by dividing the sum of the Prices determined for
the individual trading days in such period by the number of trading days in such period. 

        "Securities
Purchase Agreement" means the Securities Purchase Agreement, dated as of December    , 2002, between the Company and the Credit Suisse First Boston entities listed
in Schedule A thereto. 

        "Stated
Value" means the stated value per share of Preferred Stock, which is $20.00 per share. 

        Section 1. Exercise of Warrants.    (a) The Warrants may be exercised in whole or in part, at any
time or from time to time, during the Exercise Period, by (i) presentation and surrender to the Company at its address set forth in Section 10  of this Warrant Certificate with the Election To
Exercise, attached hereto as Exhibit A, duly completed and executed, and
(ii) payment of the Exercise Price, for the number of Warrants being exercised by either: (1) bank draft or cashiers check, or (2) provided that the Company receives at least
5 days prior notice and subject to Section 1(d), delivery to the Company of certificate(s) representing a number of shares of Preferred Stock having an aggregate Preferred Value equal to
the aggregate Exercise Price for the number of Warrants being exercised. If the aggregate Preferred Value of the Preferred Stock delivered in payment of the aggregate Exercise Price exceeds (because
of fractional shares) the aggregate Exercise Price for the number of Warrants being exercised; then (subject to Section 1(d)) the Company will promptly pay to the holder of the Warrants in cash
such excess amount; provided that such excess amount shall in no event be more than the Preferred Value of one share of Preferred Stock. If the holder of this Warrant Certificate at any time exercises
less than all the Warrants, the Company shall issue to such a holder a warrant certificate identical in form to this Warrant Certificate, but evidencing a number of Warrants equal to the number of
Warrants originally represented 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 10 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. 

        (c)  Upon
surrender of this Warrant Certificate in conformity with the foregoing provisions, the Company shall transfer to the holder of this Warrant Certificate appropriate
evidence of ownership of the shares of Common Stock or other securities or property (including any money) to which the holder is entitled, registered or otherwise placed in, or payable to the order
of, the name or names of the holder or such transferee as may be directed in writing by the holder, and shall deliver such evidence of ownership and any other securities or property (including any
money) to the Person or Persons entitled to receive the same, together with an amount in cash in lieu of any fraction of a share. 

        (d)  In
connection with payment of the Exercise Price with shares of Preferred Stock, the Company may require that at the time of such exercise it receive representations and
warranties from the applicable holder of the Warrants regarding such holder's title to the Preferred Stock and the lack of encumbrances thereon. If the Company is unable to consummate an exercise of
Warrants through payment of the Exercise Price with shares of Preferred Stock because of any limitations contained or 

A-2

 

construed in the Delaware General Corporation Law, the Company shall use its best efforts to take all such action as may be necessary to place the Company in a position to do so. In the event the
Company, after the taking of any action by it as contemplated above, is unable to consummate such exercise, the Company shall accept such number of shares of Preferred Stock in payment as it shall
then be authorized to do so under the Delaware General Corporation Law. 

        (e)  The
Company shall not be required to issue a fractional share of Common Stock upon the exercise of Warrants. As to any fraction of a share which the Warrant holder would
otherwise be entitled to purchase upon such exercise, the Company may pay a cash adjustment in respect of such fraction in an amount equal to the same fraction of the Price per share of Common Stock
on the date of exercise. 

        Section 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 Section 2(b) applies), or in case of any consolidation or merger of the Company with or into any entity or other person (other than a merger with
another entity or other person in which the Company is the surviving corporation and which does not result in any reclassification or change in the securities issuable upon exercise of this Warrant
Certificate), the holder of the Warrants shall have, and the Company, or such successor corporation or other entity, shall covenant in the constituent documents effecting any of the foregoing
transactions that such holder does have the right to obtain, upon the exercise of the Warrants, in lieu of each share of Common Stock, other securities, money or other property theretofore issuable
upon exercise of a Warrant, the kind and amount of shares of stock, other securities, money or other property receivable upon such reclassification, change, consolidation or merger by a holder of the
shares of Common Stock, other securities, money or other property issuable upon exercise of a Warrant if the Warrants had been
exercised immediately prior to such reclassification, change, consolidation or merger. The constituent documents effecting 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 Section 2(a). The provisions of this  Section 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 

A-3

 

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.    Subject to  Section 2(f), if the Company at any time after the Issuance Date shall
issue any additional shares of Common Stock (otherwise than as provided in
subsections (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 or its compensation committee (as applicable), 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 Section 2(d) upon the issuance of any additional shares of Common
Stock that (v) are issued pursuant to any grant or award made prior to the 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 the Company's officers, directors and/or employees ("Employee Benefit Plans") that has
been approved by the Board of Directors of the Company or its compensation committee and that otherwise would cause an adjustment under this  Section 2(d); (w) are issued pursuant to any grant
or award made on or after the 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); (x) are issued pursuant to any Common Stock Equivalent (as hereinafter defined) (i) if upon the issuance of any such Common Stock
Equivalent, any such adjustments shall previously have been made pursuant to Section 2(e), (ii) if no adjustment was required pursuant to  Section 2(e)
, or (iii) if such Common Stock Equivalent was issued prior to this Warrant Certificate; (y) are issued pursuant to a
public offering by the Company; or (z) results in an adjustment pursuant to Section 2(f). 

        (e)  Common Stock Equivalents.

        (i)    Subject
to Section 2(f), 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"), then the Exercise Price upon each such issuance shall be adjusted as provided
in Section 2(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 date of 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 

A-4

 

consideration received and receivable by the Company for the issuance of such additional shares of Common Stock pursuant to such Common Stock Equivalent. 

        (ii)  Notwithstanding
the foregoing, no adjustment shall be made pursuant to this Section 2(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 Section 2(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 Section 2(e). No adjustment shall be made under this Section 2(e)  if an adjustment is to be made under
Section 2(f). No adjustment shall be made 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. 

        (f)    Special Adjustments of Exercise Price. Notwithstanding anything to the contrary in  Section 2(d) or Section 2(e),
 this Section 2(f)  shall govern adjustments to the Exercise Price for the transactions described in this Section 2(f). 

        (i)    If
the Company at any time after the Issuance Date and prior to the second anniversary of the Issuance Date shall issue any additional shares of Common Stock (otherwise
than as provided in subsections (a) through (c) of Section 2; pursuant to any Employee Benefit Plan; pursuant to any Common Stock
Equivalent outstanding as of the Issuance Date; or pursuant to a public offering) or upon the issuance of any such Common Stock for which any adjustments shall previously have been made pursuant to
Section 2(e) or Section 2(f)(ii); and the New Stock Issue Price (defined below) of such additional shares is less than the Exercise Price then in effect, then the Exercise Price upon
each such issuance shall be adjusted to the New Stock Issue Price of such additional shares. The "New Stock Issuance Price" shall be determined by dividing the total amount of consideration received
by the Company for such issue or sale by the number of shares of Common Stock issued or sold. 

        (ii)  If
the Company at any time after the Issuance Date and prior to the second anniversary of the Issuance Date, issues any Common Stock Equivalent (which by definition
excludes Employee Benefit Plan securities) (otherwise than as provided in subsections (a) through (c) of Section 2; or pursuant to any Common Stock Equivalent outstanding as of
the Issuance Date) and the New CSE Exercise Price (defined below) of such Common Stock Equivalents is less than the Exercise Price then in effect, then the Exercise Price upon each such issuance shall
be adjusted to the New CSE Exercise Price of such Common Stock Equivalents. The "New CSE Exercise Price" shall be determined by dividing (x) the total amount, if any, received or receivable by
the Company as consideration for the issuance of such Common Stock Equivalents, plus the minimum aggregate amount of additional consideration payable to the Company 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 the Company upon the conversion or exchange of such Convertible Securities, by (y) the total maximum number of shares of Common Stock issuable upon the exercise, conversion or
exchange of all such Common Stock Equivalents. 

        (g)  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 

A-5

 

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 Company's 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 Section 2(c) above) consideration equal to the amount of such dividend so paid or satisfied. In the event
additional shares of Common Stock or Common Stock Equivalents are issued together with other shares or securities or other assets of the Company or its subsidiaries for consideration which covers
both, the consideration for such shares of Common Stock and Common Stock Equivalents shall be computed based on the respective portions of such consideration so received, computed as provided in this  Section 2(g)
i., as determined and allocated in good faith by the Board of Directors of the Company. 

        (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 Section 2(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 this Section 2(f)(i)) 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)  Upon
each adjustment of the Exercise Price as a result of the calculations made in Section 2(d), (e) and (f) hereof, this Warrant shall thereafter
evidence the right to purchase, at the adjusted Exercise Price, that number of shares of Common Stock obtained by 

A-6

 

(i) multiplying the number of shares covered by this Warrant immediately prior to such adjustment of the number of shares by the Exercise Price in effect immediately prior to such adjustment
of the Exercise Price and (ii) dividing the product so obtained by the Exercise Price in effect immediately after such adjustment of the Exercise Price. 

        (v)  For
the purpose of this Section 2, the term "shares of Common Stock" shall mean shares of (i) the class of
stock designated as the Common Stock at the date hereof or (ii) any other class of stock resulting from successive changes or reclassifications of such shares consisting solely of changes in
par value, or from par value to no par value, or from no par value to par value. If at any time, because of an adjustment pursuant to  Section 2(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. 

        (h)  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. 

        (i)    Shareholder Approval. Notwithstanding anything to the contrary herein, any provision hereof providing for adjustments to
the Exercise Price that would require shareholder approval pursuant to the Nasdaq Market Rules shall be subject to the Company's obtaining such requisite approval. 

        Section 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. 

        Section 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. 

 Section 5. Mandatory Exercise. 

        (a)  If
(i) the Price of the Common Stock averages at least 150% of the Exercise Price (as adjusted to reflect any stock split, combination, reclassification,
recapitalization, exchange, stock dividend or other distribution payable in Common Stock with respect to shares of Common Stock) for sixty (60) consecutive trading days in the principal market
in which the Common Stock is traded and (ii) the Company gives written notice pursuant to Section 10 hereof (the "Company Notice") to the holder hereof of the satisfaction of the
condition in clause (i) within thirty (30) days after the 

A-7

 

expiration of the relevant 60-day-trading period, then (x) within ten (10) days after the Company Notice, the holder shall notify the Company whether the holder
will pay all of the Exercise Price by delivery of Preferred Stock in accordance with Section 1(a)(ii)(2), and (y) within fifteen (15) days after the Company Notice, the holder
hereof shall exercise all of the Warrants. If the Company gives the Company Notice on a timely basis within the Exercise Deferral Period, and the exercise of the Warrants pursuant to the foregoing
would otherwise occur during the Exercise Deferral Period, then the exercise of the Warrants shall be deferred until no later than the third Business Day (as defined in the Securities Purchase
Agreement) following the expiration of the Exercise Deferral Period (the "Deferred Exercise Date"). If required by this Section 5, the holder
hereof agrees to exercise the Warrants, and to purchase shares of Common Stock pursuant to the terms of this Warrant Certificate. If the holder has not fulfilled its obligations to exercise the
Warrants pursuant to this Section 5 within fifteen (15) days after the holder's receipt of the Company Notice or by the Deferred Exercise Date, as applicable, then (without limiting the
Company's available remedies) (A) the obligations of holder under this Section 5 shall continue but the purchase rights otherwise represented by this Warrant Certificate shall terminate,
(B) the Company may thereafter refuse, in its sole discretion, to allow holder to exercise the Warrants (including pursuant to this Section 5), (C) all obligations of the Company
under Sections 3, 6, 7 and 8 shall terminate, (D) no further adjustments to the Exercise Price shall be made unless the Company in its sole discretion consents in writing. Each Warrant holder's
obligations under this Section 5(a) shall be subject to the expiration or termination of all waiting periods (and any extensions thereof) applicable to exercise of such holder's Warrants under
the HSR Act (as defined below); provided that such holder shall have certified in writing to the Company that a filing under the HSR Act is required and provided further that such holder shall use its
best efforts to cause the expiration or termination of such waiting period to occur as promptly as practicable. 

        (b)  Holder
represents and warrants to the Company that holder has full corporate power and authority to execute, deliver, and perform this Warrant Certificate and to
consummate the transactions contemplated hereby. The execution, delivery, and performance by holder of this Warrant Certificate have been duly authorized by all necessary corporate action of holder.
This Warrant Certificate has
been duly executed and delivered by holder and constitutes a valid and legally binding obligation of holder, enforceable against holder in accordance with its terms, except that such enforceability
may be limited by (i) applicable bankruptcy, insolvency, reorganization, moratorium, and similar laws affecting creditors' rights generally and (ii) general equitable principles
(regardless of whether such enforceability is considered in a proceeding in equity or at law). 

        (c)  The
right to require exercise of the Warrants is hereby declared by the parties hereto to be a unique right, the loss of which is not readily susceptible to monetary
quantification. Consequently, the parties hereto agree that an action for specific performance of the exercise and purchase obligations created by this Section 5 is an available remedy for the
breach of the provisions of this Section 5. If the Company is forced to institute legal proceedings to enforce its rights in accordance with the provisions of this Section 5, it shall be
entitled to recover its reasonable attorneys' fees and court costs incurred in enforcing such rights. 

        (d)  Holder
is executing this Warrant Certificate in order to make and agree to the covenants, representations and warranties of holder contained in this Section 5,
which shall be binding upon the holder's successors and assigns. 

        Section 6. 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 result of a subdivision 

A-8

 

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, other than dividends on the Shares, as
defined in the Securities Purchase Agreement; 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. 

        Section 7. Reports to Warrant Holders.    The Company will cause to be delivered, by first-class
mail, postage prepaid, to holder at such holder's address appearing hereon, or such other address as the holder shall specify, a copy of any reports delivered by the Company to the holders of Common
Stock. 

        Section 8. Covenants of the Company.    The Company covenants and agrees that: 

        (a)  Until
the Expiration Date, the Company shall at all times reserve and keep available, out of the aggregate of its authorized but unissued Common Stock (and other
securities), for the purpose 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 the Securities Purchase Agreement, any stockholders agreement and except for restrictions arising under state or federal securities laws. 

        (d)  All
original issue taxes payable in respect of the issuance of shares of Common Stock to the registered holder hereof upon the exercise of the Warrants shall be borne by
the Company; provided, that the Company shall not be required to pay any tax or charge imposed in connection with any transfer involved in the issuance of any certificates representing shares of
Common Stock (and other securities) in any name other than that of the registered holder hereof, and in such case the Company shall not be required to issue or deliver any certificate representing
shares of Common Stock (and other securities) until such tax or other charge has been paid or it has been established to the Company's satisfaction that no such tax or charge is due. 

A-9

 

        (e)  As
soon as practicable after the receipt from the holder of this Warrant Certificate of notice of the intent to 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") (and
after the receipt, if applicable, of the notice referred to in Rule 803.5 of the HSR Act), but in any event no later than the 15th business day after receipt of such notice(s), the Company will
(i) if required by the HSR Act, prepare and file with Antitrust Division of the Department of Justice (the "DOJ") and the Federal Trade Commission (the "FTC") the Notification and Report Form
(accompanied by all documentary attachments contemplated thereby) required by the HSR Act, (ii) upon request of the holder, request early termination of the waiting period imposed by the HSR
Act, and (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. Notwithstanding the foregoing, if the holder is required to file with the DOJ and FTC the Notification and Report Form solely as a result of its holding and/or purchasing shares of
Common Stock issued pursuant to this Warrant (with no regard to any other securities held by such holder or its affiliates) and the holder certifies such fact to the Company in writing, the Company
agrees to promptly reimburse the holder for all fees and expenses for the preparation and filing of such form, including all legal expenses and filing fees. 

        (f)    The
Company will not change the par value of the Common Stock from par value $0.01 per share to any higher par value which exceeds the Exercise Price then in effect, and
will reduce the par value of the Common Stock upon any event described in Section 2 that would, but for this provision, reduce the Exercise Price below the par value of the Common Stock. 

        Section 9. 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. 

        Section 10. Notices.    All notices, requests, demands, and other communications required or
permitted to be given or made hereunder by any party hereto shall be in writing and shall be deemed to have been duly given or made if (i) delivered personally, (ii) sent by prepaid
overnight courier service, or (iii) sent by telecopy or facsimile transmission, answer back requested, to the parties at the following addresses (or at such other addresses as shall be
specified by the parties by like notice): 

if
to the holder: 

Global
Energy Partners

1100 Louisiana Street

Houston, Texas 77002

Fax: 713-890-1429

Attn: Steven A. Webster 

and

CSFB
Private Equity

11 Madison Avenue

New York, New York 10010

Fax: 917-326-8076

Attn: Ivy Dodes 

with
a copy to: 

Gardere
Wynne Sewell LLP

1000 Louisiana, Suite 3400

Houston, Texas 77002

A-10

 

Attention: N.L. Stevens III

Telefax: 713-276-5807 

and
if to the Company: 

Brigham
Exploration Company

6300 Bridge Point Parkway

Building 2, Suite 500

Austin, Texas 78730

Attention: Chief Financial Officer

Telecopier: (512) 472-3400 

Such
notices, requests, demands, and other communications shall be effective (i) if delivered personally or sent by courier service, upon actual receipt by the intended recipient, or
(ii) if sent by telecopy or facsimile transmission, when the answer back is received. 

        Section 1. Governing Law.    This Warrant Certificate shall be governed by and construed in
accordance with the laws of the State of New York without regard to principles of conflict of laws. 

        Section 12. 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. 

        Section 13. Transfer.    Subject to Section 14 hereof and to the Securities Purchase
Agreement, transfer of Warrants, in whole or in part, shall be registered on the books of the Company to be maintained for such purposes, upon surrender of the Warrant Certificate representing such
Warrants at the principal office of the Company referred to in Section 10, together with a written assignment substantially in the form of
Exhibit B to this Warrant Certificate and a written agreement, in form reasonably satisfactory to the Company, setting forth the new Warrant holder's agreement to be bound by all of the terms
of this Warrant Certificate (including without limitation Section 14) and by Section 5.5 of the Securities Purchase Agreement, each duly executed by the holder, and funds sufficient to
pay any transfer taxes payable by such holder upon the making of such transfer. Upon such surrender and, if required, such payment, the Company shall execute and deliver a new Warrant Certificate or
Warrant Certificates in the name of the assignee or assignees and in the denomination specified in such instrument of assignment, and shall issue to the assignor a new Warrant Certificate or Warrant
Certificates evidencing the portion of the old Warrant Certificate not so assigned, and the old Warrant Certificate shall promptly be canceled. 

        Section 14. Restrictions on Transferability.    The Warrant Certificate represents Warrants
referred to in the Securities Purchase Agreement. Said Securities Purchase Agreement is hereby incorporated by reference in and made a part of this instrument and is hereby referred to for a
description of certain limitations of rights, obligations, duties and immunities thereunder of the Company and the holders, and in the event of any conflict between the terms of this Warrant
Certificate and the provisions of the Securities Purchase Agreement, the provisions of the Securities Purchase Agreement shall control. 

        Section 15. Severability.    If any provision of this Warrant Certificate is held to be
unenforceable, then this Warrant Certificate shall be considered divisible and such provision shall be deemed inoperative to the extent it is deemed unenforceable, and in all other respects this
Warrant Certificate shall remain in full force and effect to the maximum extent permitted by Applicable Law (as defined in the Securities Purchase Agreement). 

A-11

 

        IN
WITNESS WHEREOF, the Company has caused this Warrant Certificate to be executed as of December    , 2002, by the undersigned, thereunto duly authorized. 

	 	 	BRIGHAM EXPLORATION COMPANY
	

 	
 	

By:
	 	 	

	

 	
 	
[INSERT APPROPRIATE CSFB ENTITY]
	

 	
 	

By:
	 	 	

A-12

 
 
 

EXHIBIT A
  
  
  ELECTION TO EXERCISE    
  

        [To be executed on exercise of the Warrant evidenced by this Warrant Certificate pursuant to Section 1(a)] 

        TO:    Brigham
Exploration Company 

        The
undersigned, the holder of the Warrants evidenced by the attached Warrant Certificate, hereby irrevocably elects to
exercise                        of such Warrants, and herewith makes
payment of                        representing the aggregate Exercise Price thereof, and requests that the certificate
representing the securities issuable hereunder be issued in the name of                        
and delivered to                        , whose address
is                        . 

        The
Exercise Price is being paid by bank draft or cashier's check. 

	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.

A-13

 
 
 

EXHIBIT B
  
  
  ASSIGNMENT FORM    
  

        FOR VALUE RECEIVED the undersigned registered owner of the attached Warrant Certificate hereby sells, assigns and transfers unto the assignee named below all of
the rights of the undersigned under this Warrant Certificate, with respect to the number of shares of Common Stock set forth below: 

Name
and Address of Assignee:    ______________ 

No.
of Shares of

Common Stock    _______ 

and
does hereby irrevocably constitute and appoint                        attorney-in-fact to register such transfer on the books of
Brigham Exploration Company maintained for that
purpose, with full power of substitution in the premises. 

	Dated:	 	

	

Name:	
 	

	

Signature:	
 	

	

Witness:	
 	

	

The assignee named above hereby agrees to purchase and take the attached Warrant Certificate pursuant to and in accordance with the terms and conditions of the Warrant Certificate and Section 5.5 of the Securities Purchase Agreement, dated as of
December    , 2002, between Brigham Exploration Company and the initial holder named therein and agrees to be bound thereby.
	

Dated:	
 	

	

Name:	
 	

	

Signature:	
 	

A-14

QuickLinks

Exhibit 4.4

CERTIFICATE OF DESIGNATIONS of SERIES B PREFERRED STOCK (Par Value $.01 Per Share) of BRIGHAM EXPLORATION COMPANY

Pursuant to Section 151 of the General Corporation Law of the State of Delaware

EXHIBIT A

WARRANT CERTIFICATE

EXHIBIT A ELECTION TO EXERCISE

EXHIBIT B ASSIGNMENT FORM

Source: [{"source": "alea-institute/alea-institute/kl3m-data-edgar-agreements/train-00050-of-00352.parquet"}, [{"source": "alea-institute/alea-institute/kl3m-data-edgar-agreements/train-00050-of-00352.parquet"}]]