Document:

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 NOVEMBER 1, 2000, BETWEEN BRIGHAM EXPLORATION COMPANY AND
THE INITIAL HOLDER OF SECURITIES NAMED THEREIN, A COPY OF WHICH IS ON FILE WITH
THE SECRETARY OF BRIGHAM EXPLORATION COMPANY AND WILL BE FURNISHED WITHOUT
CHARGE TO THE HOLDER HEREOF UPON WRITTEN REQUEST, AND THE HOLDER OF THIS
CERTIFICATE AGREES TO BE BOUND THEREBY.

                               WARRANT CERTIFICATE

NUMBER OF WARRANTS: 630,000                                      WARRANT NO.  2

       This Warrant certificate ("Warrant Certificate") certifies that, for
value received, DLJ ESC II, LP, a Delaware limited partnership, is the
registered holder of the number of warrants (the "Warrants") set forth above.
Each Warrant entitles the holder thereof, at any time or from time to time
during the Exercise Period, to purchase from the Company one fully paid and
nonassessable share of Common Stock at the Exercise Price, subject to adjustment
as provided herein. Initially capitalized terms used but not defined herein
shall have the meanings ascribed to them in the Securities Purchase Agreement.

               "COMMON STOCK" means the common stock, $.01 par value per share,
       of the Company and such other class of securities as shall then represent
       the common equity of the Company.

               "COMPANY" means Brigham Exploration Company, a Delaware
       corporation.

               "EXERCISE PERIOD" means the period of time between the Closing
       Date, as defined in the Securities Purchase Agreement and 5:00 p.m. (New
       York City time) on the Expiration Date.

               "EXERCISE PRICE," subject in all circumstances to adjustment in
       accordance with SECTION 2, means $3.00 per share.

               "EXPIRATION DATE" means the tenth anniversary of the Closing
       Date.

               "ISSUANCE DATE" means November 1, 2000.

               "PERSON" means any individual, corporation, company, partnership,
       joint

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       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 A 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 sales prices on the largest national
       securities exchange (based on the aggregate dollar value of securities
       listed) on which such shares are listed or traded, or if such shares are
       not listed or traded on any national securities exchange, then the
       average of the reported 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 November 1, 2000, between the Company, DLJ MB
       Funding III, Inc. and DLJ ESC II, LP.

               "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

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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 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

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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 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

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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

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<PAGE>

          minimum 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 upon the issuance of any such Common Stock,
          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,

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<PAGE>

          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 Equivalent shall be issued for cash
          consideration, the consideration received by the Company therefor, or,
          if such additional shares of Common Stock or Common Stock Equivalent
          are offered by the Company for subscription, the subscription price,
          or, if such additional shares of Common Stock or Common Stock
          Equivalent are sold to underwriters or dealers for public offering
          without a subscription offering, the initial public offering price, in
          any such case excluding any amounts paid or receivable for accrued
          interest or accrued dividends and without deduction of any
          compensation, discounts, commissions or expenses paid or incurred by
          the Company for and in the underwriting of , or otherwise in
          connection with, the issue thereof; (II) to the extent that such
          issuance shall be for a consideration other than cash, then, except as
          herein otherwise expressly provided, the fair value of such
          consideration at the time of such issuance as determined in good faith
          by the Board of Directors, as evidenced by a certified resolution of
          the Board of Directors delivered to the holder of this Warrant
          Certificate setting forth such determination. The consideration for
          any additional shares of Common Stock issuable pursuant to any Common
          Stock Equivalent shall be the consideration received by the Company
          for issuing such Common Stock Equivalent, plus the additional
          consideration payable to the Company upon the exercise, conversion or
          exchange of such Common Stock Equivalent. In case of the issuance at
          any time of any additional shares of Common Stock or Common Stock
          Equivalent in payment or satisfaction of any dividend upon any class
          of stock other than Common Stock, the Company shall be deemed to have
          received for such additional shares of Common Stock or Common Stock
          Equivalent (which shall not be deemed to be a dividend payable in, or
          other distribution of, Common Stock under 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

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          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 (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) NASDAQ MATTERS. Notwithstanding anything to the contrary
          herein, any adjustment 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.

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<PAGE>

       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 is greater than $5.00
per share (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 (the "Company Notice")
to the holder hereof of the satisfaction of the condition in clause (i), then
within fifteen (15) days after the effective date of the Company Notice, the
holder hereof shall exercise all of the Warrants. 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, 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

                                      -9-
<PAGE>

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 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

                                      -10-
<PAGE>

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

                                      -11-
<PAGE>

of Common Stock (and other securities) until such tax or other charge has been
paid or it has been established to the Company's satisfaction that no such tax
or charge is due.

               (e) As soon as practicable after the receipt from the holder of
this Warrant Certificate of notice of the 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, to such holder at:

                           277 Park Avenue
                           New York, New York 10172
                           Attention: Michael Isikow
                           Telefax: 212-892-2689

                                      -12-
<PAGE>

                  with a copy to:

                           Gardere Wynne Sewell, LLP
                           1000 Louisiana, Suite 3400
                           Houston, Texas 77002
                           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 11. 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 and 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 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

                                      -13-
<PAGE>

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.

                                      * * *

                                      -14-
<PAGE>

       IN WITNESS WHEREOF, the Company has caused this Warrant Certificate to be
executed as of November 1, 2000, by the undersigned, thereunto duly authorized.

                           BRIGHAM EXPLORATION COMPANY

                            By: /s/ Karen E. Lynch
                               -------------------------------------------------
                                    Karen E. Lynch
                                    Vice President

                           DLJ ESC II, LP

                            By:     DLJ LBO Plans Management Corporation, its
                                    general partner

                                    By: /s/ IVY B. DODES
                                       -----------------------------------------
                                            Ivy B. Dodes
                                            Principal

                                      -15-Exhibit 10.13

                          BRIGHAM EXPLORATION COMPANY
                          STOCKHOLDERS VOTING AGREEMENT

         This STOCKHOLDERS VOTING AGREEMENT, dated October 31, 2000 (this
"Agreement"), is made and entered into by and among Brigham Exploration Company,
a Delaware corporation (the "Company"), DLJ ESC II, L.P., a Delaware limited
partnership ("ES"), and DLJ MB Funding III, Inc., a Delaware corporation ("MB"),
and the following shareholders of the Company (the "Shareholders"): Ben M. and
Anne L. Brigham, individual residents of Travis County, Texas, Harold D. Carter,
a resident of Dallas County, Texas, General Atlantic Partners III, L.P., a
Delaware limited partnership, GAP-Brigham Partners, L.P., a Delaware limited
partnership, GAP Coinvestment Partners II, L.P., a Delaware limited partnership,
and Aspect Resources, LLC, a Colorado limited liability company.

                              W I T N E S S E T H:

         WHEREAS, the Company, DLJ and Webster, propose to enter into a
Securities Purchase Agreement concurrently with the execution hereof (the
"Purchase Agreement"), pursuant to which the Company will issue and sell to DLJ
and Webster an aggregate of up to one million shares of its Series A Preferred
Stock and warrants (the "Warrants") to acquire 6,666,667 shares (the "Warrant
Shares") of its common stock (the "Common Stock") at an exercise price of $3.00
per share (the "Exercise Price");

         WHEREAS, the Warrant Shares represent greater than 20% of the
outstanding Common Stock before issuance;

         WHEREAS, the Exercise Price was the closing sales price on the date a
binding term sheet was signed between the Company and DLJ, and, therefore, was
"market" price;

         WHEREAS, the rules of the Nasdaq Stock Market require shareholder
approval of issuances of warrants to purchase shares representing greater than
20% of a company's outstanding voting securities at a price below market.

         WHEREAS, the Warrants contain anti-dilution provisions that reduce the
Exercise Price, if the Company issues Common Stock or other securities
exchangeable for or convertible into Common Stock at a price below $3.00 or
below market price at the time of such issuance.

         WHEREAS, the Nasdaq Stock Market has required that the Company's
shareholders approve these anti-dilution provisions and any future adjustments
to the Exercise Price pursuant to such provisions; and

         WHEREAS, as a condition to the agreement of the parties to this
Agreement to enter into the Purchase Agreement, the Company and the Shareholders
have agreed to enter into this Agreement to provide for certain agreements
relating to approval of the Warrants and any future adjustments to the Exercise
Price pursuant to the terms thereof;

<PAGE>

         NOW, THEREFORE, in consideration of the foregoing and the mutual
agreements set forth herein, the parties to this Agreement hereby agree as
follows:

         1. AGREEMENT TO VOTE SHARES. Each Shareholder agrees that, at any
special or annual meeting of shareholders of the Company, such Shareholder shall
vote all shares of Common Stock registered in its, his or her name or
beneficially owned by it, him or her as of the date hereof and any and all other
capital stock of the Company legally or beneficially acquired by such
Shareholder after the date hereof to approve the Warrants and any future
adjustments to the exercise price of the Warrants pursuant to the terms thereof.
In the event that the Purchase Agreement is terminated for any reason, then this
Agreement shall automatically terminate and none of the parties hereto shall
have any liability hereunder. Each Shareholder represents to ES and MB that as
of the date hereof such Shareholder owns the number of outstanding shares of
Common Stock set forth opposite such Shareholder's name on attached SCHEDULE I.

         2. SUCCESSORS, ASSIGNS AND TRANSFEREES. The terms and provisions of
this Agreement shall not bind, inure to the benefit of or be enforceable by or
against the successors, assigns or transferees of each of the parties hereto. No
party hereto may assign its rights under this Agreement.

         3. ENTIRE AGREEMENT; AMENDMENTS. This Agreement, and such additional
instruments as may be concurrently executed and delivered pursuant to this
Agreement, constitutes the entire understanding of the parties with respect to
its subject matter. There are no restrictions, agreements, promises,
representations, warranties, covenants or undertakings other than those
expressly set forth herein or in the documents delivered concurrently herewith.
This Agreement may be amended only by a written instrument duly executed by all
the parties hereto.

         4. HEADINGS. The section headings contained in this Agreement are for
reference purposes only and shall not effect in any way the meaning or
interpretation of this Agreement.

         5. NOTICES, All notices, requests, claims, demands and other
communications hereunder shall be in writing and shall be given (and shall be
deemed to have been duly given if so given) by hand delivery, facsimile or by
mail (registered or certified, postage prepaid, return receipt requested) to the
respective parties as follows:

                  If to Brigham:
                           Brigham Exploration Company
                           6300 Bridge Point Parkway
                           Building Two, Suite 500
                           Austin, Texas 78730
                           Attention: Ben M. "Bud" Brigham
                           Fax No:  (512) 427-3400

                  If to DLJ ESC II, L.P.:
                           Donaldson Lufkin & Jenrette
                           277 Park Avenue
                           New York, New York 10172
                           Attention: Michael Isikow

                                       2
<PAGE>

                           Fax No: 212-892-2689
                           and
                           Mr. Steve Webster
                           1000 Louisiana, Suite 4900
                           Houston, Texas  77002
                           Fax No:  (713) 652-6050

                                    with a copy to:
                                            Gardere Wynne Sewell, LLP
                                            1000 Louisiana, Suite 3400
                                            Houston, Texas 77002
                                            Attention: N.L. Stevens III
                                            Telefax: 713-276-5807

                  If to DLJ MB Funding III, Inc.:
                           Donaldson Lufkin & Jenrette
                           277 Park Avenue
                           New York, New York 10172
                           Attention: Michael Isikow
                           Fax No: 212-892-2689
                           and
                           Mr. Steve Webster
                           1000 Louisiana, Suite 4900
                           Houston, Texas  77002
                           Fax No:  (713) 652-6050

                                    with a copy to:
                                            Gardere Wynne Sewell, LLP
                                            1000 Louisiana, Suite 3400
                                            Houston, Texas 77002
                                            Attention: N.L. Stevens III
                                            Telefax: 713-276-5807

                  If to Ben M. Brigham:
                           Ben M. Brigham
                           Brigham Exploration Company
                           6300 Bridge Point Parkway
                           Building Two, Suite 500
                           Austin, Texas 78730
                           Fax No:  (512) 427-3400

                  If to Anne L. Brigham:
                           Anne L. Brigham
                           Brigham Exploration Company
                           6300 Bridge Point Parkway
                           Building Two, Suite 500
                           Austin, Texas 78730

                                       3
<PAGE>

                           Fax No:  (512) 427-3400

                  If to Harold D. Carter:
                           Harold D. Carter
                           5949 Sherry Lane, Suite 620
                           Dallas, Texas 75225
                           Fax No.:  (214) 692-7820

                  If to General Atlantic Partners III, L.P.:
                           General Atlantic Partners III, L.P.
                           c/o General Atlantic Service Corporation
                           3 Pickwick Plaza
                           Greenwich, CT  06830
                           Attention:  Mr. Thomas J. Murphy
                           Fax No:  (203) 622-8818

                  If to GAP-Brigham Partners, L.P.:
                           GAP-Brigham Partners, L.P.
                           c/o General Atlantic Service Corporation
                           3 Pickwick Plaza
                           Greenwich, CT  06830
                           Attention:  Mr. Thomas J. Murphy
                           Fax No:  (203) 622-8818

                  If to GAP Coinvestment Partners II, L.P.:
                           GAP Coinvestment Partners II, L.P.
                           c/o General Atlantic Service Corporation
                           3 Pickwick Plaza
                           Greenwich, CT  06830
                           Attention:  Mr. Thomas J. Murphy
                           Fax No:  (203) 622-8818

                  If to Aspect Resources, LLC:
                           Aspect Resources, LLC
                           511 16th Street, Suite 300
                           Denver, CO  80202
                           Attention:  Mr. Alex Cranberg
                           Fax No:  (303) 573-7340

or to such other address as the person to whom notice is given may have
previously furnished to the others in writing in the manner set forth above.

         6. GOVERNING LAW. This Agreement shall be governed by and construed and
enforced in accordance with the laws of the State of Delaware, without reference
to the conflict of laws principles thereof.

                                       4
<PAGE>

         7. WAIVER. Any waiver by any party of a breach of any provision of this
Agreement shall not operate as or be construed to be a waiver of any other
breach of such provision or of any breach of any other provision of this
Agreement. The failure of a party to insist upon strict adherence to any term of
this Agreement on one or more occasions shall not be considered a waiver or
deprive that party of the right thereafter to insist upon strict adherence to
that term or any other term of this Agreement.

         8. CHALLENGES TO AGREEMENT. In the event that any part of this
Agreement or any transaction contemplated hereby is temporarily, preliminarily
or permanently enjoined or restrained by court of competent jurisdiction, the
parties hereto shall use their reasonable best efforts to cause any such
injunction or restraining order to be vacated or dissolved or otherwise declared
or determined to be of no further force or effect.

         9. SPECIFIC PERFORMANCE. Each of the Shareholders acknowledges and
agrees that irreparable harm would occur if any provision of this Agreement were
not performed in accordance with the terms thereof, or were otherwise breached,
and that such harm could not be remedied by an award of damages. Accordingly,
each of the Shareholders agrees that any non-breaching party shall be entitled
to an injunction to prevent breaches of this Agreement and to enforce
specifically the terms and provisions hereof.

         10. COUNTERPARTS. This Agreement may be executed in counterparts, each
of which shall be an original, but each of which together shall constitute one
and the same Agreement.

                                    * * * * *

                                       5
<PAGE>

         IN WITNESS WHEREOF, and intending to be legally bound hereby, each of
the undersigned parties has executed or caused this Agreement to be executed on
the date first above written.

                                     BRIGHAM EXPLORATION COMPANY

                                     By: /s/ DAVID T. BRIGHAM
                                        ---------------------------------------
                                          Name: DAVID T. BRIGHAM
                                                -------------------------------
                                          Title: VICE PRESIDENT
                                                -------------------------------

                                     DLJ ESC II, L.P.
                                     By DLJ LBO Plans Management Corporation
                                     Its General Partner

                                     By: /s/ IVY P. DODES
                                         --------------------------------------
                                          Name: IVY P. DODES
                                               --------------------------------
                                          Title: PRINCIPAL
                                                -------------------------------

                                     DLJ MB FUNDING III, INC.

                                     By: /s/ IVY P. DODES
                                         --------------------------------------
                                          Name: IVY P. DODES
                                               --------------------------------
                                          Title: PRINCIPAL
                                                -------------------------------

                                     /s/ BEN M. BRIGHAM
                                     ------------------------------------------
                                     Ben M. Brigham

                                     /s/ ANNE L. BRIGHAM
                                     ------------------------------------------
                                     Anne L. Brigham

                                     /s/ HAROLD D. CARTER
                                     ------------------------------------------
                                     Harold D. Carter

                                       6
<PAGE>

                                      GENERAL ATLANTIC PARTNERS III, L.P.
                                      By GAP III Investors, Inc.
                                      Its General Partner

                                      By: /s/ STEPHEN P. REYNOLDS
                                         --------------------------------------
                                           Name:  STEPHEN P. REYNOLDS
                                                 ------------------------------
                                           Title: PRESIDENT
                                                 ------------------------------

                                      GAP-BRIGHAM PARTNERS, L.P.

                                      By: /s/ STEPHEN P. REYNOLDS
                                         --------------------------------------
                                           Name:  STEPHEN P. REYNOLDS
                                                  ------------------------------
                                           Title: GENERAL PARTNER
                                                  ------------------------------

                                      GAP COINVESTMENT PARTNERS II, L.P.

                                      By: /s/ MATTHEW NIMITZ
                                         --------------------------------------
                                           Name: MATTHEW NIMITZ
                                                 -------------------------------
                                           Title: GENERAL PARTNER
                                                 -------------------------------

                                      ASPECT RESOURCES, LLC
                                      By Aspect Management Corporation
                                      Its Manager

                                      By: /s/ ALEX CRANBERG
                                         --------------------------------------
                                           Name: ALEX CRANBERG
                                                 ------------------------------
                                           Title:
                                                 ------------------------------

                                       7
<PAGE>

                                   Schedule I

                                               Number of Outstanding
Shareholder                                    Shares of Common Stock Owned
-----------                                    ----------------------------

Ben M. and Anne L. Brigham,                    3,719,792
collectively

Harold D. Carter                               314,893

General Atlantic Partners III, L.P.            2,679,418

GAP-Brigham Partners, L.P.                     127,725

GAP Coinvestment Partners II, L.P.             975,610

Aspect Resources, LLC                          487,805

                                       8

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