REGISTRATION RIGHTS AGREEMENT


         THIS REGISTRATION RIGHTS AGREEMENT (this "AGREEMENT") is entered into
as of November 1, 2000, by and among Brigham Exploration Company, a Delaware
corporation (the "COMPANY"), and the parties listed on SCHEDULE A hereto (the
"INVESTORS").

                                    RECITALS

                  WHEREAS, each Investor is a party to a certain Warrant
Certificate (the "WARRANT CERTIFICATE") dated as of November 1, 2000, by and
between the Company and such Investor;

                  WHEREAS, the Warrant Certificates were executed and delivered
in connection with the consummation of transactions contemplated by that certain
Securities Purchase Agreement dated as of November 1, 2000 by and among the
Company and the Investors;

                  WHEREAS, pursuant to the Warrant Certificates, the Holder (as
defined below) has been issued a warrant (the "WARRANT") to purchase shares of
the Company's common stock, par value $.01 per share (the "COMPANY'S COMMON
STOCK");

                  WHEREAS, to induce the Investors to enter into the Warrant
Certificates and the Securities Purchase Agreement, the Company has agreed to
grant the registration and other rights contained in this Agreement;

                                    AGREEMENT

         1.       DEFINITIONS

         For purposes of this Agreement, the following terms have the following
meanings:

         (1) "FORM S-3" means such form under the Act as in effect on the date
hereof or any registration form under the Act subsequently adopted by the
Securities and Exchange Commission (the"SEC") that similarly permits inclusion
or incorporation of substantial information by reference to other documents
filed by the Company with the SEC;

         (2) "HOLDER" means any person owning or having the right to acquire
Registrable Securities who is a party to this Agreement as of the date hereof or
who may be added as a party pursuant to the terms of this Agreement, and any
assignee thereof;

         (3) "REGISTER," "REGISTERED" and "REGISTRATION" refer to a registration
effected by preparing and filing a registration statement or similar document in
compliance with the Securities Act of 1933, as amended (the "ACT"), and the
declaration or order of effectiveness of such registration statement or
document;


                                       1


         (4) "REGISTRABLE SECURITIES" means (i) the Common Stock of the Company
issuable or issued upon exercise of the Warrants and (ii) any Common Stock of
the Company issued as (or issuable upon the conversion or exercise of any
warrant, right or other security which is issued as) a dividend or other
distribution with respect to, or in exchange for or in replacement of, such
Warrants or Common Stock, excluding in all cases, however, any Registrable
Securities sold by a person in a transaction in which its rights under this
Agreement are not assigned ; and

         (5) "REGISTRABLE SECURITIES THEN OUTSTANDING" means the number of
shares of Common Stock outstanding which are, and the number of shares of Common
Stock issuable pursuant to then exercisable or convertible securities which are,
Registrable Securities.

         (6) "SEC" means the Securities and Exchange Commission.

         2. REQUEST FOR REGISTRATION

         (1) If the Company shall receive a written request from the Holders of
at least 25% of the Registrable Securities then outstanding (the "INITIATING
HOLDERS") that the Company file a registration statement under the Act covering
the registration of at least 25% of the Registrable Securities, then the Company
shall, within 10 days after the receipt of such request, give written notice of
such request to all Holders and shall, subject to the limitations set forth
below, use its reasonable best efforts to effect as soon as practicable the
registration under the Act of all Registrable Securities that the Holders
request to be registered in a written request to be given within 30 days of
receipt of such notice by the Company.

         (2) The Company is obligated to effect only two registrations pursuant
to this Section 2.

         (3) Notwithstanding the foregoing, if the Company shall furnish to the
Initiating Holders requesting a registration pursuant to this Section 2 within
30 days of receiving such request a certificate signed by the President of the
Company stating that in the good faith Judgment of the Board of Directors of the
Company it would be seriously detrimental to the Company and its stockholders
for such in registration statement to be filed and it is therefore essential to
defer the filing of such registration statement, the Company shall have the
right to defer such filing for up to 2 periods of not more than 45 days each
after receipt of the request of the Initiating Holders; provided, however, that
the Company may not use this right more than once (for a total of up to 90 days)
in any 12-month period; provided, however, that the Company shall promptly
notify the Initiating Holders requesting a registration pursuant to this Section
2 of any decision by the Company to abandon or indefinitely delay such public
offering.

         3. COMPANY REGISTRATION

         If the Company proposes to register (including for this purpose a
registration effected by the Company for stockholders (ARequesting Holders@)
other than the Holders) any of its stock or other securities under the Act in
connection with the public offering of such securities solely for


                                       2


cash (other than a registration relating solely to the sale of securities to
participants in a Company stock plan, or a registration on any form that does
not include substantially the same information as would be required to be
included in a registration statement covering the sale of Registrable
Securities), the Company shall, at each such time, promptly give each Holder
written notice of such registration. Upon the written request of each such
Holder given within 20 days after receipt of such notice by the Company, the
Company shall, subject to the provisions of Section 8, use its reasonable best
efforts to cause to be registered under the Act all of the Registrable
Securities that each such Holder has requested to be registered. In the event
that the Company decides for any reason not to complete the registration of
shares of Common Stock other than Registrable Securities, the Company shall have
no obligation under this Section 3 to continue with the registration of
Registrable Securities. Any request pursuant to this Section 3 to register
Registrable Securities as part of an underwritten public offering of Common
Stock shall specify that such Registrable Securities are to be included in the
underwriting on the same terms and conditions as the shares of Common Stock
otherwise being sold through underwriters under such registration.

         4. FORM S-3 REGISTRATION

         (1) If the Company shall receive a written request from the Holders of
25% of the Registrable Securities then outstanding that the Company effect a
registration on Form S-3, the reasonably anticipated aggregate offering price to
the public of which would equal or exceed $2,000,000,then the Company shall,
within 10 days after the receipt of such request, give written notice of such
request to all Holders and shall, subject to the limitations set forth below,
use its reasonable best efforts to effect as soon as practicable the
registration under the Act of all Registrable Securities that the Holders
request to be registered in a written request to be given within 30 days of
receipt of such notice by the Company.

         (2) Notwithstanding the foregoing, the Company shall not be obligated
to effect any such registration pursuant to this Section 4 if (i) Form S-3 is
not available for such offering by the Holders; (ii) the Company shall furnish
to the Holders a certificate signed by the President of the Company stating
that, in the good faith judgment of the Board of Directors of the Company, it
would be seriously detrimental to the Company and its stockholders for such Form
S-3 registration to be effected at such time, in which event the Company shall
have the right to defer the filing of the Form S-3 registration statement for a
period of not more than 90 days after receipt of the request of the Holders
under this Section 4; provided, however, that the Company shall not use this
right more than once in any 12-month period; or (iii) if the Company has, within
the 12-month period preceding the date of such request, already effected one
such registrations on Form S-3 for the Holders pursuant to this Section 4.

         5. OBLIGATIONS OF THE COMPANY

         Whenever required under this Agreement to effect the registration of
any Registrable Securities, the Company shall, as expeditiously as reasonably
possible:

         (1) Prepare and file with the SEC a registration statement with respect
to such Registrable Securities and use its commercially reasonable efforts to
cause such registration statement to become effective, and, upon the request of
the Holders of 25% of the


                                       3


Registrable Securities registered thereunder, keep such registration statement
effective for up to one year.

         (2) Prepare and file with the SEC such amendments and supplements to
such registration statement and the prospectus used in connection with such
registration statement as may be necessary to comply with the provisions of the
Act with respect to the disposition of all securities covered by such
registration statement.

         (3) Furnish to the Holders such copies of a prospectus, including a
preliminary prospectus, in conformity with the requirements of the Act and such
other documents as they may reasonably request to facilitate the disposition of
all securities covered by such registration statement

         (4) Use commercially reasonable efforts to register and qualify the
securities covered by such registration statement under such other securities or
blue sky laws of such jurisdictions as shall be reasonably requested by the
Holders, provided that the Company shall not be required to qualify to do
business or to file a general consent to service of process in any such states
or jurisdictions.

         (5) In the event of any underwritten public offering, enter into and
perform its obligations under an underwriting agreement, in usual and customary
form, with the managing underwriter(s) of such offering. Each Holder
participating in such registration shall also enter into and perform its
obligations under such an agreement.

         (6) Notify each Holder of Registrable Securities covered by such
registration statement, during the time when a prospectus is required to be
delivered under the Act, of the happening of any event as a result of which the
prospectus included in such registration statement, as then in effect, includes
an untrue statement of a material fact or omits to state a material fact
required to be stated therein or necessary to make the statements therein not
misleading in the light of the circumstances then existing.

         (7) At the request of any Holder selling Registrable Securities in such
registration, furnish on the date that such Registrable Securities are delivered
to the underwriters for sale in connection with such registration (i) an
opinion, dated such date, of legal counsel representing the Company for the
purposes of such registration, in form and substance as is customarily given by
Company counsel to underwriters in an underwritten public offering, addressed to
the underwriters and (ii) a letter, dated such date, from the independent
certified public accountants of the Company, in form and substance as is
customarily given by independent certified public accountants to underwriters in
an underwritten public offering, addressed to the underwriters.

         (8) List the Registrable Securities being registered on any national
securities exchange on which a class of the Company's equity securities is
listed or qualify the Registrable Securities being registered for inclusion on
Nasdaq if the Company does not have a class of equity securities listed on a
national securities exchange.


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         6. FURNISH INFORMATION

         It shall be a condition precedent to the obligations of the Company to
take any action pursuant to this Agreement that the selling Holders shall
furnish to the Company such information regarding themselves, the Registrable
Securities held by them and the intended method of disposition of such
securities as shall be reasonably required to effect the registration of their
Registrable Securities and shall execute such documents in connection with such
registration as the Company may reasonably request.

         7. EXPENSES OF REGISTRATION

         In connection with any registration pursuant to this Agreement, the
Company shall be responsible for the payment of all reasonable expenses of the
registration, with the exception of (i) underwriting discounts and commissions,
which shall be paid by the Company, the Holders and any other selling holders of
the Company's securities in proportion to the aggregate value of the securities
offered for sale by each of them, and (ii) the fees and expenses of more than
one law firm acting as counsel to the selling Holders selected by a majority in
interest of the selling Holders, which additional counsel, if any, shall be paid
by the Holder or Holders that engage such counsel. The expenses to be paid by
the Company shall include, without limitation, all registration, filing and
qualification fees, printing and accounting fees, the fees and disbursements of
counsel for the Company and the fees and disbursements of one counsel for the
selling Holders; provided, however, that the Company shall not be required to
pay for any expenses of any registration proceeding begun pursuant to Section 2
or 4 if the registration request is subsequently withdrawn (other than a
withdrawal due to a material adverse change in the Company's business or
financial condition), unless, in the event of a registration initiated pursuant
to the provisions of Section 2, the Holders of 25% of the Registrable Securities
agree to forfeit the right to one demand registration.

         8. UNDERWRITING REQUIREMENTS

         (1) The Holders requesting registration under Section 2 must distribute
the Registrable Securities covered by their request by means of a public
offering underwritten by a reputable national or regional underwriter. The right
of any Holder to include its Registrable Securities in such registration under
Section 2 shall be conditioned upon such Holder's participation in such
underwriting and the inclusion of such Holder's Registrable Securities in the
underwriting to the extent provided herein. All Holders proposing to distribute
their Registrable Securities through such underwriting shall (together with the
Company as provided in Section 5(e)) enter into an underwriting agreement in
customary form with the underwriter or underwriters selected for such
underwriting by a majority in interest of the Initiating Holders.
Notwithstanding any other provision of Section 2, if the underwriter advises the
Initiating Holders in writing that marketing factors require a limitation of the
number of shares to be underwritten, then the Initiating Holders shall so advise
all Holders of Registrable Securities which would otherwise have been
underwritten pursuant to Section 2, and the number of shares of Registrable
Securities that may be included in the registration shall be apportioned first
pro rata among the selling Holders, including the Initiating Holders, according
to the total amount of Registrable Securities requested to be sold in such
registration by such Holders, then to the Company and then pro rata among any
other selling stockholders according to the total amount of securities otherwise
entitled to be included therein


                                       5


owned by each such selling stockholder, or in such other proportions as shall
mutually be agreed to by such selling stockholders.

         (2) The Company shall not be required under Section 3 to include any of
the Holders' securities in an underwritten offering of the Company's securities
unless such Holders accept the terms of the underwriting as agreed upon between
the Company and the underwriters selected by it. If the underwriters advise the
Company that marketing factors require a limitation on the number of shares,
including Registrable Securities, to be included in such offering, then the
Company shall so advise all Holders of Registrable Securities that would
otherwise have been underwritten pursuant to Section 3, and the number of
shares, including Registrable Securities, that may be included in the
registration shall be apportioned first to the Company or Requesting Holders, as
the case may be, then pro rata among the selling Holders according to the total
amount of Registrable Securities requested to be sold in such registration by
such Holders, then pro rata among any other selling stockholders according to
the total amount of securities otherwise entitled to be included therein owned
by each such other selling stockholder, or in such other proportions as shall
mutually be agreed to by such selling stockholders; provided that in no event
shall the amount of securities of the selling Holders included in the
registration be reduced below 20% of the total amount of securities included in
such registration.

         9. DELAY OF REGISTRATION

         No Holder shall have any right to obtain or seek an injunction
restraining or otherwise delaying any registration of the Company as the result
of any controversy that might arise with respect to the interpretation or
implementation of this Agreement.

         10. INDEMNIFICATION

         In the event any Registrable Securities are included in a registration
statement under this Agreement:

         (1) To the extent permitted by law, the Company will indemnify and hold
harmless each Holder, any underwriter (as defined in the Act) for such Holder
and each person, if any, who controls such Holder or underwriter within the
meaning of the Act or the Securities Exchange Act of 1934, as amended (the "1934
ACT"), against any actual expenses (including legal fees and costs), losses,
claims, damages (including settlement amounts) or liabilities joint or several)
(collectively, "LOSSES") to which they may become subject under the Act, the
1934 Act or other federal or state law, insofar as such Losses arise out of or
are based upon any of the following statements, omissions or violations
(collectively, a "VIOLATION"): (i) any untrue statement or alleged untrue
statement of a material fact contained in such registration statement, including
any preliminary prospectus or final prospectus contained therein, or any
amendments or supplements thereto, untrue in light of the circumstances under
which they were made, (ii) the omission or alleged omission to state therein a
material fact required to be stated therein, or necessary to make the statements
therein, in light of the circumstances under which they were made, not
misleading, or (iii) any violation or alleged violation by the Company of the
Act, the 1934 Act, any state securities law or any rule or regulation
promulgated under the Act, the 1934 Act or any state securities law. The Company
will reimburse (as incurred) each such Holder, underwriter or controlling person
for


                                       6


any Losses reasonably incurred by them in connection with investigating or
defending any Violations; provided, however, that the indemnity agreement
contained in this Section 10(a) shall not apply to amounts paid in settlement of
any claims for Violations if such settlement is made without the consent of the
Company, which consent shall not be unreasonably withheld, nor shall the Company
be liable in any such case for any Losses that arise out of or are based upon a
Violation that occurs in reliance upon and in conformity with written
information furnished expressly for use in connection with such registration by,
or on behalf of, any such Holder, underwriter or controlling person.

         (2) To the extent permitted by law, each selling Holder will indemnify
and hold harmless the Company and its officers, directors, agents and employees,
each underwriter and each other Holder selling securities in such in
registration statement, and any person who controls any of the foregoing within
the meaning of the Act or the 1934 Act, against any Losses to which the Company
or such officer, director, agent, employee, or underwriter or other selling
Holder or controlling person may become subject under the Act, the 1934 Act or
other federal or state law, insofar as such Losses arise out of or are based
upon any Violation that occurs in reliance upon and in conformity with written
information furnished by, or on behalf of, such Holder expressly for use in
connection with such registration; and each such Holder will reimburse any
Losses reasonably incurred by the Company or its officers, directors, agents,
employees, or underwriters or other selling Holders or controlling persons in
connection with investigating or defending any Violations; provided, however,
that (i) the indemnity agreement contained in this Section 10(b) shall not apply
to amounts paid in settlement of any claims for Violations if such settlement is
made without the consent of the Holder, which consent shall not be unreasonably
withheld and (ii) the obligations of such Holders shall be limited to an amount
equal to the gross proceeds before expenses and commissions to each such Holder
of Registrable Securities sold as contemplated herein.

         (3) Promptly after receipt of notice of the commencement of any action
(including any governmental action), an indemnified party will, if a claim is to
be made against any indemnifying party under this Section 10, deliver to the
indemnifying party a written notice of the commencement, and the indemnifying
party shall have the right to participate in, and, to the extent the
indemnifying party so desires, jointly with any other indemnifying party
similarly notified to assume the defense thereof with counsel mutually
satisfactory to the parties; provided, however, that an indemnified party shall
have the right to retain its own counsel, with the fees and expenses to be paid
by the indemnifying Party, if, in the opinion of counsel for the indemnifying
party, representation of such indemnified party by the counsel retained by the
indemnifying party would be inappropriate due to actual or potential differing
interests between such indemnified party and any other party represented by such
counsel in the proceeding. The failure to deliver written notice to the
indemnifying party within a reasonable period of time after notice of the
commencement of any such action shall relieve such indemnifying party of any
liability to the indemnified party under this Section 10 to the extent such
failure is prejudicial to its ability to defend such action, but the omission to
deliver written notice to the indemnifying party will not relieve it of any
liability that it may have to any indemnified party otherwise than under this
Section 10.

         (4) If the indemnification provided for in this Section 10 is held by a
court of competent jurisdiction to be unavailable to an indemnified party with
respect to any


                                        7


Losses, then the indemnifying party, in lieu of indemnifying such indemnified
party, shall contribute to the amount paid or payable by such indemnified party
as a result of such Losses in such proportion as is appropriate to reflect the
relative fault of the indemnifying party on the one hand and of the indemnified
party on the other in connection with the Violations that resulted in such
Losses as well as any other relevant equitable considerations; provided, that,
in no event shall any contribution by a Holder under this Section 10(d) exceed
the gross proceeds before expenses and commissions to each such Holder, except
in the case of willful fraud by such Holder. The relative fault of the
indemnifying party and of the indemnified party shall be determined by reference
to, among other things, whether the Violation resulting in such Losses relates
to information supplied by the indemnifying party or by the indemnifying party
and the parties= relative intent, knowledge, access to information, and
opportunity to correct or prevent such Violation.

         (5) Notwithstanding the foregoing, to the extent that the provisions on
indemnification and contribution contained in the underwriting agreement entered
into in connection with the underwritten public offering are in conflict with
the foregoing provisions, the provisions in the underwriting agreement shall
control.

         (6) The obligations of the Company and Holders under this Section 10
shall survive the completion of any offering of Registrable Securities and the
termination of Registration Rights pursuant to Section 15.

         11. REPORTS UNDER THE ACT

         With a view to making available to the Holders the benefits of SEC Rule
144 promulgated under the Act and any other rule or regulation of the SEC that
may at an time permit a Holder to sell securities of the Company to the public
without registration or pursuant to a registration on Form S-3, the Company
agrees to use commercially reasonable efforts to:

         (1) Make and keep public information available, as those terms are
understood and defined in SEC Rule 144, at all times after the effective date of
the first registration statement filed by the Company for the offering of its
securities to the general public;

         (2) File with the SEC in a timely manner all reports and other
documents required of the Company under the Act and the 1934 Act; and

         (3) Furnish to any Holder, so long as the Holder owns any Registrable
Securities, promptly upon request (i) a written statement by the Company that it
has complied with the reporting requirements of the 1934 Act (at any time after
the date on which it becomes subject to such reporting requirements), or that it
qualifies as a registrant whose securities may be resold pursuant to Form S-3
(at any time after it so qualifies), (ii) a copy of the most recent annual or
quarterly report of the Company and such other reports and documents so filed by
the Company, and (iii) such other information as may be reasonably requested in
availing any Holder of any rule or regulation of the SEC that permits the
selling of any such securities without registration or pursuant to such Form
S-3.


                                       8


         12. ASSIGNMENT OF REGISTRATION RIGHTS

         The rights to cause the Company to register Registrable Securities
pursuant to this Agreement may be assigned by a Holder to a transferee or
assignee of such securities who shall, upon such transfer or assignment, be
deemed a AHolder@ under this Agreement; provided that the Company is, within a
reasonable period of time after such transfer, furnished with written notice of
the name and address of such transferee or assignee and the securities with
respect to which such registration rights are being assigned; provided, further,
that such assignment shall be effective only if immediately following such
transfer the further disposition of such securities by the transferee or
assignee is restricted under the Act and that such transferee or assignee is (a)
a partner or retired partner of any Holder that is a partnership, (b) a member
of the immediate family or a trust for the benefit of any Holder that is an
individual, (c) an entity controlling, controlled by or under common control
with any Holder that is not an individual, (d) a transferee or assignee that
after the transfer or assignment holds (i) 10% of the Registrable Securities of
the transferor, or (ii) Registrable Securities prior to the transfer, or (e) a
constituent member of any Holder that is a limited liability company.

         13. LIMITATIONS ON SUBSEQUENT REGISTRATION RIGHTS

         From and after the date of this Agreement, the Company shall not,
without the prior written consent of the Holders of 25% of the Registrable
Securities then outstanding, enter into any agreement with any holder or
prospective holder of any securities of the Company that would allow such holder
or prospective holder to (a) include such securities in any registration filed
under Section 2, 3 or 4, unless under the terms of such agreement such holder or
prospective holder may include such securities in any such registration only to
the extent that the inclusion of its securities will not reduce the amount of
the Registrable Securities of the Holders which is included or (b) make a demand
registration which could result in such registration statement being declared
effective prior to 180 days of the effective date of any registration effected
pursuant to Section 2.

         14. "MARKET STANDOFF" AGREEMENT

         The Holders hereby agree that they shall not, to the extent requested
by the Company and an underwriter of Common Stock (or other securities) of the
Company, sell or otherwise transfer or dispose (other than to donees who agree
to be similarly bound) of any Registrable Securities for 180 days following the
effective date of a registration statement of the Company filed under the Act;
provided, however, that the foregoing shall not be effective unless all officers
and directors of the Company (whether or not pursuant to this Agreement) enter
into similar agreements and the Company has used all reasonable efforts to
obtain similar agreements from all holders of at least 1% of the Company=s then
outstanding Common Stock.

         To enforce the foregoing covenant, the Company may impose stop-transfer
instructions with respect to the Registrable Securities of the Holders (and the
shares or securities of every other person subject to the foregoing restriction)
until the end of such period.


                                       9


         15. TERMINATION OF REGISTRATION RIGHTS

         The registration rights granted under Sections 2, 3 and 4 of this
Agreement shall terminate as to each Holders on the earlier of (a) the tenth
(10th) anniversary of the date of this Agreement and (b) the date on which all
Registrable Securities held by or issuable to such Holder (and its affiliates)
may be sold under Rule 144 during any 90 day period.

         15. MISCELLANEOUS

         15.1 NOTICES

         Any notice required or permitted under this Agreement shall be given in
writing and shall be deemed effectively given (a) upon personal delivery to the
party to be notified, (b) upon confirmation of receipt by fax by the party to be
notified, (c) one business day after deposit with a reputable overnight courier,
prepaid for overnight delivery and addressed as set forth in (d), or (d) three
days after deposit with the United States Post Office, postage prepaid,
registered or certified with return receipt requested and addressed to the party
to be notified at the address indicated for such party on the signature page, or
at such other address as such party may designate by 10 days= advance written
notice to the other parties given in the foregoing manner.

         15.2 AMENDMENTS AND WAIVERS

         Any term of this Agreement may be amended and the observance of any
term may be waived (either generally or in a particular instance and either
retroactively or prospectively) only with the written consent of the Company and
the holders of a majority of the Registrable Securities then outstanding.
Additional Holders may be added to this Agreement with such consent by amending
SCHEDULE A and adding a signature page executed by such additional Holder.

         15.3 GOVERNING LAW; JURISDICTION; VENUE

         This Agreement shall be governed by and construed under the laws of the
State of New York without regard to principles of conflict of laws. The parties
irrevocably consent to the jurisdiction and venue of the state and federal
courts located in New York City in connection with any action relating to this
Agreement.

         15.4 SUCCESSORS AND ASSIGNS

         The terms and conditions of this Agreement shall inure to the benefit
of and be binding on the respective successors and assigns of the parties as
provided herein.

         15.5. SEVERABILITY

         If one or more provisions of this Agreement are held to
beunenforceable under applicable law, such provision shall be excluded from
this Agreement, and the balance of this Agreement shall be interpreted as if
such provision were so excluded and shall be enforceable in accordance with its
terms.


                                       10


         15.6 ENTIRE AGREEMENT; COUNTERPARTS

         This Agreement constitutes the entire agreement between the parties
about its subject and supersedes all prior agreements. This Agreement may be
executed in two or more counterparts, which together shall constitute one
instrument.



                            [Signature page follows]


                                       11


         IN WITNESS WHEREOF, the parties have executed this Agreement as of the
date first above written.

                                       BRIGHAM EXPLORATION COMPANY


                                       By: /S/ KAREN E. LYNCH
                                          -------------------------------------
                                                Its: Vice President

                                       Address:

                                       Brigham Exploration Company
                                       6300 Bridge Point Parkway
                                       Building 2, Suite 500
                                       Austin, TX  78730
                                       Attention: Chief Financial Officer
                                       Fax:  512-427-3400

                                       DLJ MB FUNDING III, INC.


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

                                       Address:

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


                                       DLJ ESC II, LP

                                       By:      DLJ LBO Plans Management
                                                Corporation, its general partner


                                                By: /S/ IVY B. DODES
                                                   ----------------------------
                                                        Ivy B. Dodes
                                                        Principal
                                       Address:

                                       277 Park Avenue
                                       New York, New York 10172

                                       Attention: Michael Isikow
                                       Telefax: 212-892-2689


                                       12


                                   SCHEDULE A
                        TO REGISTRATION RIGHTS AGREEMENT


 HOLDER NAME                                     NUMBER OF SHARES
 -----------------------                         ----------------

 DLJ MB Funding III, Inc.,                           6,036,667
 a Delaware corporation

 DLJ ESC II, LP,                                       630,000
 a Delaware limited partnership


                                       13