Document:

[filed October 31, 2000]

                          CERTIFICATE OF DESIGNATIONS

                                       OF

                            SERIES A PREFERRED STOCK

                           (PAR VALUE $.01 PER SHARE)

                                       OF

                          BRIGHAM EXPLORATION COMPANY

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

                            PURSUANT TO SECTION 151
            OF THE GENERAL CORPORATION LAW OF THE STATE OF DELAWARE

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

     Brigham Exploration Company, a corporation organized and existing under the
laws of the State of Delaware (the "Corporation"), DOES HEREBY CERTIFY that,
pursuant to the authority conferred on the Board of Directors of the Corporation
by the Certificate of Incorporation, as amended, of the Corporation and in
accordance with Section 151 of the General Corporation Law of the State of
Delaware, the Board of Directors of the Corporation on October 31, 2000, duly
adopted the following preamble and resolution establishing and creating a series
of 1,500,000 shares of Preferred Stock, par value $.01 per share, of the
Corporation:

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

     SECTION 1. DESIGNATION AND NUMBER OF SHARES OF SERIES A PREFERRED STOCK.
There is hereby authorized and established a series of Preferred Stock that
shall be designated as "Series A Preferred Stock" (hereinafter referred to as
"Series A Preferred"), and the number of shares constituting such series shall
be 1,500,000. Such number of shares may be increased or decreased, but not to a
number less than the number of shares of Series A Preferred then issued and
outstanding, by resolution adopted by the full Board of Directors. The "Stated
Value" per share of the Series A 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:

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

     "Change of Control" means (i) any sale, lease, exchange or other transfer
(in one transaction or a series of related transactions) of all or substantially
all of the assets of the Corporation and its Subsidiaries; or (ii) the
acquisition by any Person or group of related Persons for purposes of Section 13
(d) of the Exchange Act, of the power, directly or indirectly, to vote or direct
the voting of securities having more than 50% of the ordinary voting power for
the election of directors of the Corporation or of any direct or indirect
holding company thereof; or (iii) during any period of two consecutive years,
individuals who at the beginning of such period constituted the Board of
Directors of the Corporation cease for any reason to constitute a majority of
the Board of Directors then in office; provided that any person becoming a
director subsequent to the beginning of such two-year period whose election, or
nomination for election by the stockholders of the Corporation, was approved by
a vote of at least a majority of the directors then comprising the Board of
Directors of the Corporation shall be, for purposes of this definition,
considered as though such person were a member of such Board at the beginning of
such two-year period.

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

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

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

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

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

     "Warrants" means the warrants to purchase Common Stock originally issued to
DLJ MB Funding III, Inc. and DLJ ESC II, LP on or about October 31, 2000,
pursuant to Warrant Certificates in the form attached hereto as EXHIBIT A.

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

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<PAGE>

     SECTION 3. DIVIDENDS AND DISTRIBUTIONS.

     (a) The holders of shares of the Series A 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 A 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 A 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 A
Preferred Stock. Such dividends shall accrue whether or not there shall be (at
the time such dividend becomes payable or at any other time) profits, surplus or
other funds of the Corporation legally available for the payment of dividends.
Except as provided below, the dividends shall be payable in cash.

     (b) Dividends shall be calculated on the basis of the time elapsed from and
including the date immediately following the most recent preceding Dividend
Payment Date (or, if none, the date of issuance) to and including the Dividend
Payment Date or the final distribution date relating to conversion or redemption
or to a dissolution, liquidation or winding up of the Corporation. Dividends
payable on the shares of Series A 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 A Preferred Stock in shares (including fractional shares) of Series A
Preferred Stock (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 A Preferred Stock. The
issuance of additional shares of Series A 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 A Preferred Stock that is equal to A divided by B where:

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

          "B" = the Stated Value.

     Certificates representing the shares of Series A Preferred Stock 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 A Preferred Stock
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 A Preferred Stock 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 A Preferred which are in arrears.

     (f) Dividends payable on each Dividend Payment Date shall be paid to record
holders of the shares of Series A 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 A 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 A Preferred have been paid.

     SECTION 4. LIQUIDATION PREFERENCE.

     (a) In the event of any liquidation, dissolution or winding up of the
Corporation (in connection with the bankruptcy or insolvency of the Corporation
or otherwise), whether voluntary or involuntary, before any payment or
distribution of the assets of the Corporation (whether capital or surplus) shall
be made to or set apart for the holders of shares of any Junior Securities, the
holders of the shares of Series A 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 A Preferred shall share ratably in such distribution in the proportion
that the number of each holder's Series A Preferred Shares bears to the total
number of shares of Series A 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 A 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 A 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 A 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.

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<PAGE>

     (b) After the payment of the full amount to the holders of Series A
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 A
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 A 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 A Preferred at any time after the
date of issuance of such shares.

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

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

          (iii) In the event the holders of the Warrants exercise any or all of
such warrants for consideration consisting of shares of Series A Preferred, then
(A) such exercise shall be deemed an optional redemption of such Series A
Preferred, (B) the notice required by Section 5(c) shall not be required, (C)
the exercise date shall be the Redemption Date, (C) the Optional Redemption
Price per share in such event shall be 100% of the Stated Value of such share as
of the Redemption Date, plus, without duplication, all accrued and unpaid
dividends on such share to and including such Redemption Date and (D) the
Optional Redemption Price shall be paid as set forth in Section 1 of the Warrant
Certificate.

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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 A 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 A 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 A Preferred held by such holder being redeemed by the Corporation. On or
after the Redemption Date, each holder of shares of Series A 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 A Preferred called for redemption shall cease to accumulate and
all rights of the holders of Series A 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 the tenth anniversary of the Original
Issue Date the Corporation shall redeem each outstanding Series A 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 A 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 A 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 A 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 A Preferred according to the respective number of shares of Series A
Preferred held by such holder.

     (c) Not less than ten nor more than sixty days prior to the Redemption Date
fixed for any redemption of any shares of Series A Preferred under Section 6(a),
a notice specifying the mandatory Redemption Date and place of such redemption
and the number of shares to be redeemed shall be given by first class mail,
postage prepaid, to the holders of record of the shares of Series A 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

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<PAGE>

notice the holder's certificate or certificates representing the number of
shares of Series A 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 A 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 A Preferred called for
redemption shall cease to accumulate and all rights of the shares of Series A
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.

     (d) 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 A 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 A
Preferred shares owned by each holder as compared to the total number of shares
of Series A 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 A 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 A Preferred, at the address appearing on the stock books of the
Corporation, a notice stating:

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

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

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

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

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

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

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

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

     (c) In the event that a Change of Control occurs and the holders of Series
A Preferred exercise their right to require the Corporation to purchase Series A
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 A 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 A Preferred certificate equal
to any unpurchased shares represented by a certificate surrendered. Unless the
Corporation defaults in the payment for the shares of Series A Preferred
tendered pursuant to the Change of Control Offer, dividends shall cease to
accrue with respect to the shares of Series A 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 A 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 A Preferred would

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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 A 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 A Preferred as provided
above. The Corporation will first comply with the covenant in the preceding
sentence before it will be required to redeem Series A Preferred pursuant to the
provisions described above.

     SECTION 8. EVENTS OF NONCOMPLIANCE.

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

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

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

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

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

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

     SECTION 9. REACQUIRED SHARES. Any shares of Series A 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 A 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

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represented at any meeting of stockholders of the Corporation. In any action
taken as a class, each holder of shares of Series A Preferred shall be entitled
to one vote for each share held.

     (b) So long as any shares of Series A Preferred remain outstanding, the
affirmative vote or consent of the holders of 75% of the shares of Series A
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 A Preferred Stock, 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 A 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 A 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 A 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 A 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 A 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 A Preferred and (ii) the Parity
Securities shall rank on a parity with the Series A Preferred.

     SECTION 13. RECORD HOLDERS. The Corporation may deem and treat the record
holder of any shares of Series A 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 A Preferred, to such holder at the address of such holder
of the Series A 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.

                                       10
<PAGE>

     SECTION 15. SUCCESSORS AND TRANSFEREES. The provisions applicable to shares
of Series A 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 A Preferred.

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

Dated: October 31, 2000
                                      BRIGHAM EXPLORATION COMPANY

                                      By:   /s/ David Brigham
                                           -------------------------------------
                                           Name: David T. Brigham
                                                 -------------------------------
                                           Title: Vice President
                                                  ------------------------------

                                       11SECURITIES AND NOTE ACQUISITION AGREEMENT
                    -----------------------------------------

                                    RECITALS:

         (a) Brigham Exploration Company ("BEC") and Chase Bank of Texas,
National Association, now The Chase Manhattan Bank, as Trustee (in such
capacity, herein called "Trustee"), have entered into that certain Indenture
dated as of August 20, 1998, as amended under that certain First Amendment to
Indenture dated as of March 26, 1999, and that Second Amendment to Indenture
dated as of February 17, 2000 (as so amended, and as otherwise heretofore
amended, herein called the "Indenture"); all capitalized terms used but not
defined herein shall have the meanings assigned to them in the Indenture or, if
not defined in the Indenture but defined in the form of Term ORRI Conveyance,
they shall have the meanings assigned to them in the form of Term ORRI
Conveyance.

         (b) Enron Capital & Trade Resources Corp. ("Enron Capital"),
predecessor in interest to ECT Merchant Investments Corp. ("ECT"), and Joint
Energy Development Investments II Limited Partnership ("JEDI II") (ECT and JEDI
II are herein collectively called "Noteholders") and BEC have entered into that
certain Securities Purchase Agreement dated as of August 20, 1998 (as heretofore
amended, the "SPA").

         (c) Pursuant to the terms of the SPA and the Indenture, BEC (i) issued
in favor of Enron Capital a Senior Subordinated Secured Note, in the original
principal amount of $12,500,000, which Senior Subordinated Secured Note was
replaced by a Senior Subordinated Secured Note issued to ECT (as same may have
been supplemented, amended or modified, and any other notes given in
substitution therefor or in renewal or extension thereof, herein called the "ECT
Note"), in the original principal amount of $12,500,000, and (ii) issued in
favor of JEDI II a Senior Subordinated Secured Note, in the original principal
amount of $37,500,000 (as same may have been supplemented, amended or modified,
and any other notes given in substitution therefor or in renewal or extension
thereof, herein called the "JEDI II Note") (the JEDI II Note and the ECT Note
are herein collectively called the "Notes").

         (d) Pursuant to the SPA, (i) BEC issued to Enron Capital 263,158 shares
of BEC's common stock, as evidenced by certificate number 0089, as replaced by
certificate number 0131, issued in favor of ECT, evidencing the change in
ownership of said 263,158 shares (the "ECT shares") from Enron Capital to ECT,
and (ii) BEC issued to JEDI II 789,474 shares of BEC's common stock, as
evidenced by certificate number 0131 (the "JEDI II Shares); the ECT Shares and
the JEDI II Shares are herein collectively called the "Shares".

         (e) Pursuant to the SPA and the Indenture, (i) BEC issued to ECT
250,000 warrants (the "ECT Warrants") to purchase common stock of BEC, as
evidenced by Warrant No. A-5 (the "ECT Warrant Certificate"), and (ii) BEC
issued to JEDI II 750,000 warrants to purchase common stock of BEC (the "JEDI II
Warrants"), as evidenced by Warrant No. A-6 (the JEDI II "Warrant
Certificates"); the ECT Warrants and the JEDI II Warrants are herein
collectively called the Warrants, the ECT Warrant Certificate and the JEDI II
Warrant Certificate are herein collectively called the "Warrant Certificates",

                                       1
<PAGE>

the shares of common stock and other securities, if any, receivable upon
exercise of the ECT Warrants are herein called the ECT Warrant Shares and the
shares of common stock and other securities, if any, receivable upon exercise of
the JEDI II Warrants are herein called the JEDI II Warrant Shares, and the ECT
Warrant Shares and the JEDI II Warrant Shares are herein collectively called the
"Warrant Shares".

         (f) Pursuant to the Indenture, Brigham Oil & Gas, L.P. ("BOG") has, at
the direction of BEC, executed in favor of Noteholders a series of instruments,
each entitled Conveyance of Adjustable Term Overriding Royalty Interest,
recorded as set forth in Schedule I hereto (such instruments, as well as any
other "Term ORRI Conveyance" executed pursuant to the Indenture, are herein
collectively called the "Conveyances").

         (g) BEC desires to (i) reacquire the Shares, (ii) except as expressly
provided otherwise herein below, acquire the Notes, and all other Obligations,
including without limitation the Accrued PIK Amount (the Notes, together with
such other Obligations being herein collectively called the "Enron
Indebtedness"), together with any and all rights and interests (the "Collateral
Interests") under any Mortgage or other Collateral Documents securing same,
including without limitation under any Collateral Document described in Schedule
1 to the "Full Release", hereafter defined, (iii) acquire, terminate and cancel
the Warrants and extinguish all rights of Noteholders under the Warrant
Certificates and in relation to the Warrant Shares, and (iv) extinguish all
rights and interests, whether vested or contingent, accrued or unaccrued, under
the Indenture, the SPA and any other Equity Documents or Loan Documents,
including without limitation under any Guaranty Agreement (all of items (i)
through and including (iv), above, are herein collectively called the "Acquired
Interests"), all upon and subject to the terms and conditions hereof.

                                   AGREEMENT:

1. PURCHASE PRICE. The aggregate purchase price (the "Purchase Price") to be
paid by BEC for the Acquired Interests is Twenty Million Dollars ($20,000,000).
The Purchase Price shall be paid, in immediately available funds, in the
relative percentage shares of 25% to ECT and 75% to JEDI II, upon performance by
Noteholders and Trustee of their respective obligations hereunder. As conditions
precedent to the Noteholder's obligations hereunder, BEC shall (i) pay all
outstanding fees and expenses of the Noteholder's counsel incurred in connection
with the Acquired Interests and (ii) deliver to the Noteholders, a consent and
release from the Senior Lenders, in form and substance identical to that
attached hereto as Schedule III.

2. ACQUISITION. Except as expressly provided otherwise in subsection (a) below,
Noteholders hereby severally and not jointly, generally assign, transfer,
release, surrender and deliver unto BEC all of their collective right, title and
interest in respect of the Acquired Interests, and Trustee hereby, at the
direction of Noteholders, hereby generally assigns, transfers, releases,
surrenders and delivers unto BEC all of its right, title and interest, of any
kind or character, in, to and under the Collateral Documents and the Collateral
Interests; in order to give further effect to the foregoing, the parties
covenant and agree as follows:

                                       2
<PAGE>

         (a)      THE TERM ORRI.
                  -------------

                  (1) At the direction of BEC, Noteholders shall, on even date
                  herewith, reassign, grant and convey to BOG, its successors
                  and assigns, under a form of reassignment substantially
                  identical to that attached hereto as Schedule I (the
                  "Reassignment"), the Term ORRI and any other rights titles and
                  interests created under a Conveyance or otherwise under or
                  pursuant to Section 7.12 of the Indenture (collectively, the
                  "Reassigned Interests"). The Reassignment shall be duly
                  executed by Noteholders, in a sufficient number of
                  counterparts as BEC shall reasonably request.

                  (2) Noteholders agree that all proceeds from or attributable
                  to the Reassigned Interests (regardless of when the severance
                  of the production to which such proceeds relates occurred),
                  other than only those proceeds that are attributable to
                  periods prior to the "Effective Date" of the Reassignment and
                  that are actually received by Noteholders on or before the
                  date hereof, shall be the property of and should be paid to
                  BOG.

                  (3) Brigham Exploration Company is an intended third party
                  beneficiary of the Reassignment.

         (b)      THE SHARES. On even date herewith, the originals of the stock
                  certificates representing the Shares, duly endorsed in blank,
                  or accompanied by stock powers duly executed in blank, and
                  otherwise in form acceptable to BEC for transfer on the books
                  of BEC, shall be delivered to BEC, and BEC shall receive from
                  Noteholders the written resignation of Jempy Neyman, a
                  representative of Noteholders as an observer on the Board of
                  Directors of BEC, such resignation to be effective as of
                  October 31, 2000.

         (c)      THE WARRANTS. On even date herewith, the original Warrant
                  Certificates, together with the associated Transfer Forms,
                  duly endorsed in blank, shall be surrendered to BEC.

         (d)      THE NOTES. On even date herewith, the Original Notes shall be
                  endorsed "pay to the order of Brigham Exploration Company,
                  without recourse or warranty" and delivered to BEC (or an
                  allonge will be attached to the same effect).

         (e)      RELEASE OF LIENS. On even date herewith, Trustee shall, at the
                  direction of Noteholders, execute a Full Release, in a form
                  substantially identical to that attached hereto as Schedule II
                  (the "Full Release"), in a sufficient number of counterparts
                  as BEC shall reasonably request.

                                    RELEASE:

(a)      DEFINED TERMS. As used in this section, the following terms shall have
         the following meanings:

                                       3
<PAGE>

         "RELEASED CLAIMS" SHALL MEAN ANY AND ALL CLAIMS (INCLUDING WITHOUT
LIMITATION ANY LIABILITIES, DAMAGES, DEMANDS AND CAUSES OF ACTION ARISING
THEREFROM), WHETHER (A) AT LAW OR IN EQUITY, (B) ON THE ALLEGED COMMISSION OF A
TORT, (C) ON THE ALLEGED BREACH (OR ANTICIPATORY BREACH OR REPUDIATION) OF ANY
CONTRACT, DUTY, OR WARRANTY (WHETHER ORAL OR WRITTEN, EXPRESS OR IMPLIED), (D)
ON THE ALLEGED VIOLATION OF ANY STATUTE, TARIFF, OR REGULATION (WHETHER
PROMULGATED BY THE UNITED STATES, ANY STATE THEREOF, ANY FOREIGN STATE OR
COUNTRY, OR ANY OTHER GOVERNMENTAL AGENCY OR ENTITY, WHEREVER LOCATED, OR (E) ON
ANY OTHER FACTUAL, LEGAL OR EQUITABLE THEORY, INCLUDING WITHOUT LIMITATION, ANY
CLAIM FOR DAMAGES OF ANY TYPE OR NATURE FOR INJUNCTIVE OR OTHER RELIEF, FOR
ATTORNEY'S FEES, INTEREST OR ANY OTHER LIABILITY WHATSOEVER ON ANY THEORY,
INCLUDING WITHOUT LIMITATION ANY LOSS COST OR DAMAGE IN CONNECTION WITH OR BASED
UPON "LENDER LIABILITY", UNFAIR DEALING, DURESS, COERCION, CONTROL OR UNDUE
INFLUENCE, EXTORTION OR COMMERCIAL BRIBERY, BREACH OF AN IMPLIED COVENANT OR
DUTY OF GOOD FAITH AND FAIR DEALING, MATERIAL MISREPRESENTATION OR OMISSION,
OVERREACHING, UNCONSCIONABILITY, CONFLICT OF INTEREST, BAD FAITH, MALPRACTICE,
DISPARATE BARGAINING POSITION, DETRIMENTAL RELIANCE, PROMISSORY ESTOPPEL,
ESTOPPEL BY DEED, WAIVER, LACHES, OR ANY OTHER EQUITABLE THEORY, EQUITABLE
SUBORDINATION, BREACH OF FIDUCIARY DUTY OR ANY OTHER DUTY, OR TORTIOUS
INDUCEMENT TO COMMIT SUCH BREACH, TORTIOUS INTERFERENCE WITH CONTRACT OR
PROSPECTIVE BUSINESS RELATIONS, NEGLIGENT PERFORMANCE OF CONTRACTUAL
OBLIGATIONS, OR OTHER THEORIES OF NEGLIGENCE, NEGLIGENT OR INTENTIONAL
INFLICTION OF EMOTIONAL DISTRESS, SLANDER, LIBEL, OTHER DEFAMATION, FRAUDULENT
TRANSFER, CONVERSION, TRESPASS TO (OR CLOUDING THE TITLE OF) PROPERTY, USURY,
VIOLATIONS OF THE RACKETEER INFLUENCED AND CORRUPT ORGANIZATIONS ACT, DECEPTIVE
TRADE PRACTICES, CONSPIRACY, OR ANY THEORY OF LIABILITY AS PARTNERS OR JOINT
VENTURERS, THAT ANY RELEASING PARTY MAY HAVE AS OF THE DATE HEREOF AGAINST ANY
RELEASED PARTY WITH RESPECT OR RELATED TO THE ACQUIRED INTERESTS, THE
TRANSACTIONS EVIDENCED THEREBY AND THE ACTIONS AND RELATIONSHIP ARISING OUT OF
OR RELATED THERETO, OTHER THAN CLAIMS ARISING OUT OF A BREACH OF ANY
REPRESENTATION, WARRANTY OR COVENANT MADE OR UNDERTAKEN BY ANY NOTEHOLDER OR
TRUSTEE UNDER THIS AGREEMENT, THE FULL RELEASE AND/OR THE REASSIGNMENT.

         "RELEASED PARTY" shall mean each of the Trustee, the Noteholders and
their representative predecessors, successors, assigns, directors, officers,
partners, employees, agents, attorneys, principals and Affiliates and all other
Persons liable or who might be claimed to be liable on their behalf
(collectively, the "Released Parties").

                                       4
<PAGE>

         "RELEASING PARTY" shall mean each of BEC, BOG and the Guarantors and
their respective predecessors, successors, assigns, directors, officers,
partners, employees, agents, attorneys, principals, Affiliates and all other
Persons who might have a claim against any Released Party (collectively, the
"Releasing Parties").

(b) RELEASE. EACH OF THE RELEASING PARTIES DESIRES AND INTENDS FULLY TO
COMPROMISE, RELEASE AND SETTLE ANY AND ALL OF THE RELEASED CLAIMS; AND EACH OF
THE RELEASING PARTIES HEREBY COVENANTS, WARRANTS AND REPRESENTS UNTO EACH OF THE
RELEASED PARTIES THAT SUCH RELEASING PARTY DOES HEREBY FOREVER RELEASE, ACQUIT,
WAIVE AND DISCHARGE EACH OF THE RELEASED PARTIES OF AND FROM THE RELEASED CLAIMS
AND EACH OF THE RELEASING PARTIES HEREBY DECLARES THE SAME FOREVER RELEASED,
ACQUITTED, WAIVED, SETTLED AND DISCHARGED. THIS RELEASE IS EFFECTIVE WITHOUT
REGARD TO WHETHER (I) SUCH RELEASED CLAIMS ARE KNOWN OR UNKNOWN, (II) DAMAGES
ARISING OUT OF SUCH RELEASED CLAIMS HAVE YET ACCRUED, (III) SUCH RELEASED CLAIMS
AROSE COLLATERALLY, DIRECTLY, DERIVATIVELY, OR OTHERWISE BETWEEN THE PARTIES
HERETO OR (IV) AN ORDINARY PERSON IN THE SAME OR SIMILAR CIRCUMSTANCES WOULD OR
WOULD NOT, THROUGH THE EXERCISE OF DUE CARE, HAVE DISCOVERED SUCH CLAIMS BY THE
DATE OF THIS AMENDMENT. IN CONNECTION WITH THE FOREGOING RELEASE:

                  (i) BEC, BOG and each of the Guarantors, represents and
                  warrants that it has the full power and authority to perform
                  the release granted in this section and that it has not in any
                  manner made any assignment of any Released Claim to any third
                  party.

                  (ii) The release granted in this section will be effective
                  upon execution of this Agreement by all of the parties hereto.

                  (iii) Each party executing this Agreement understands and
                  agrees that the release granted in this section is a full,
                  final and complete release of the Released Claims and that
                  such release may be pleaded as an absolute and final bar to
                  any or all suits which may hereafter be filed or prosecuted by
                  any one or more of the Releasing Parties or anyone claiming
                  by, through or under any one or more of the Releasing Parties
                  in respect of any of the matters released hereby, and that no
                  recovery on account of the Released Claims may hereafter be
                  had from any of the Released Parties; and that the
                  consideration given for such release is not an admission of
                  liability or fault on the part of any of the Released Parties
                  (it being the express intent of the parties hereto to obtain
                  peace of mind and avoid the expense and uncertainty of
                  potential litigation), and that none of the Releasing Parties
                  or those claiming by, through or under any of them will ever
                  claim that it is.

                                       5
<PAGE>

                             ADDITIONAL PROVISIONS:

1.       REPRESENTATIONS AND WARRANTIES:

         (a)    REPRESENTATIONS AND WARRANTIES OF NOTEHOLDERS. Each Noteholder
severally and not jointly represents and warrants that:

                  (i) it owns its respective Acquired Interests, free and clear
                  of any liens, encumbrances, security agreements, equities,
                  options, claims or charges created by, through or under such
                  Noteholder.

                  (ii) in connection with the sale of the Acquired Interests to
                  BEC, each Noteholder has (A) had available such information
                  concerning BEC and the Acquired Interests as it has deemed
                  necessary in order to make an informed investment decision
                  with respect such Noteholder's disposition of the Acquired
                  Interests; (B) completed its own independent investigation,
                  analysis and evaluation of BEC; (C) made all such reviews and
                  inspections of the business, assets, results of operations,
                  condition (financial or otherwise) and prospects of BEC as it
                  has deemed necessary or appropriate; and (D) has such
                  knowledge and experience in financial and business matters
                  that it is capable of, and has relied solely upon the
                  information described above in evaluating the risks relating
                  to its disposition of the Acquired Interests.

                  (iii) In connection with the transactions contemplated hereby,
                  such Noteholder has full legal right, power and authority to
                  execute and deliver this Agreement and that this Agreement is
                  a valid and binding agreement of such Noteholder, enforceable
                  in accordance with its terms, and other than consents already
                  obtained, no consents, notices, filings or approvals are
                  required to be made or received from any person in connection
                  with BEC's and the Noteholders' execution of this agreement
                  and the transactions contemplated hereby.

                           (iv) Except for the representations and warranties
                  contained in this Section 1, neither of the Noteholders makes
                  any representation or warranty regarding the Acquired
                  Interests (including the amount or enforceability thereof).

                           (v) There are no suits, actions, claims,
                  investigations, inquiries, proceedings or demands pending (or
                  to the best of such Noteholder's knowledge, threatened) which
                  affect Noteholder's title to any of the Acquired Interests, or
                  the execution and delivery of this Securities and Note
                  Acquisition Agreement (this "Agreement") or the consummation
                  of transactions contemplated hereby.

         (b) REPRESENTATIONS AND WARRANTIES OF BEC. In connection with the
transactions contemplated hereby, BEC hereby represents and warrants to
Noteholders that (i) BEC has full legal right, power and authority to execute
and deliver this Agreement and that this Agreement is a valid and binding
agreement of BEC, enforceable in accordance with its terms, (ii) there are no
suits, actions, claims, investigations, inquiries, proceedings or demands

                                       6
<PAGE>

pending (or to the best of BEC's knowledge, threatened) which affect any of the
Acquired Interests, or the execution and delivery of this Agreement or the
consummation of transactions contemplated hereby, and (iii) other than consents
already obtained, no consents, notices, filings or approvals are required to be
made or received from any person in connection with BEC's or the Guarantor's
execution of this agreement and the transactions contemplated hereby.

         (c) SURVIVAL OF COVENANTS, REPRESENTATIONS AND WARRANTIES. All
representations, warranties, covenants and agreements contained herein shall not
be discharged or dissolved upon, but shall survive, the Closing.

2. COUNTERPARTS: This Agreement is being executed in several counterparts, all
of which are identical; all such counterparts together shall constitute one and
the same instrument.

3. CHOICE OF LAW: THIS AGREEMENT SHALL, WITHOUT REGARD TO PRINCIPLES OF
CONFLICTS OF LAW, BE GOVERNED AND CONSTRUED UNDER AND IN ACCORDANCE WITH THE
LAWS OF THE STATE OF TEXAS.

4. FURTHER ASSURANCES: After the date hereof, Noteholders shall execute and
deliver, and shall otherwise cause to be executed and delivered, from time to
time, such further instruments, notices, division orders, transfer orders, lien
releases, financing statement releases and other documents, and do such other
and further acts and things, as may be reasonably necessary to more fully and
effectively assign or release to BOG the Acquired Interests provided that BEC
shall pay all reasonable costs and expenses incurred by the Noteholders in
connection therewith (including reasonable attorney's fees).

5. SUCCESSORS: This Agreement shall be binding upon and shall enure to the
benefit of Noteholders and BEC and their respective permitted successors and
assigns.

6. ENTIRETY AND MODIFICATION. This Agreement constitutes the entire agreement
between the parties hereto with respect to the subject matter hereof and
supercedes any and all prior agreements and understandings, whether oral or
written, between the parties hereto relating to such subject matter. No
modification, alteration, amendment or supplement to this Agreement shall be
valid or effective unless the same is in writing and signed by all parties
hereto.

         This Agreement is executed and delivered on this 31st day of October,
2000.

                                         ECT Merchant Investment Corp.
                                         By:    /s/ JESSE E. NEYMAN
                                                ----------------------------
                                         Name:  JESSE E. NEYMAN
                                                ----------------------------
                                         Title: VICE PRESIDENT
                                                ----------------------------

Brigham Oil & Gas, L.P.              Joint Energy Development Investments II
By:    Brigham, Inc.                     Limited Partnership
       Managing General Partner    By:   Enron Capital Management II
                                         Limited Partnership, General Partner
By:    /s/ KAREN E. LYNCH                By:    Enron Capital II Corp.,
       --------------------------               General Partner
Name:  KAREN E. LYNCH                    By:    /s/ JESSE E. NEYMAN
       --------------------------               ----------------------------
Title: VICE PRESIDENT                    Name:  JESSE E. NEYMAN
       --------------------------               ----------------------------
                                         Title: AGENT AND ATTORNEY-IN-FACT
                                                ----------------------------

                                        7
<PAGE>

Brigham, Inc.                            Brigham Exploration Company
By:    /s/ KAREN E. LYNCH                By:    /s/ KAREN E. LYNCH
       --------------------------               ----------------------------
Name:  KAREN E. LYNCH                    Name:  KAREN E. LYNCH
       --------------------------               ----------------------------
Title: VICE PRESIDENT                    Title: VICE PRESIDENT
       --------------------------               ----------------------------

Brigham Holdings I, LLC                  Brigham Holdings II, LLC
a Nevada Limited Liability Company       a Nevada Limited Liability Company
By:    /s/ BEN M. BRIGHAM                By:    /s/ BEN M. BRIGHAM
       --------------------------               ----------------------------
Name:  BEN M. BRIGHAM                    Name:  BEN M. BRIGHAM
       --------------------------               ----------------------------
Title: PRESIDENT                         Title: PRESIDENT
       --------------------------               ----------------------------

                                        8

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