Exhibit 4.4

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

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

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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:



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

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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 asExhibit 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

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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:



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

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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.



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(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

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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:



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(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:



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(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.

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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.



Dated:
December 20, 2002

| | BRIGHAM EXPLORATION COMPANY
| | ---------------------------
| | By:                        
| |                            
| |                            

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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.



"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

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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.



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 inSection 10of this Warrant Certificate with the Election To
Exercise, attached hereto asExhibit 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 inSection 10and 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

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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 thisSection 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

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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 thisSection 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:



No
adjustments of the Exercise Price shall be made under thisSection 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 toSection 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 toSection 2(f).



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(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;providedthat
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.



(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

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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 thisSection 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

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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.

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(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):



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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 inSection 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).

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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:                             
| |  |                                 

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EXHIBIT AELECTION 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.

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EXHIBIT BASSIGNMENT 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:                                                                                                                                                                                                                                                                                                                                                                         |  | 

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