Exhibit 99.1

                               THIRD AMENDMENT TO
                          REGISTRATION RIGHTS AGREEMENT


     This Third Amendment to Registration Rights Agreement (this "Amendment") is
entered  into  as  of  May 24, 2004, by and among Brigham Exploration Company, a
Delaware  corporation  (the  "Company"),  and  the  Credit  Suisse  First Boston
entities listed on Schedule A hereto (the "CSFB Entities").

                                   RECITALS

     WHEREAS,  pursuant  to that certain Registration Rights Agreement, dated as
of November 1, 2000 (the "Agreement," and as amended by the March 2001 Amendment
and  the  December  2002 Amendment described below, the "Amended Agreement"), by
and  among the Company, DLJMB Funding III, Inc., a Delaware corporation, and DLJ
ESC  II,  L.P., a Delaware limited partnership (collectively, the "November 2000
Investors"),  the  Company  provided certain registration rights to the November
2000  Investors  regarding  shares  of  the Company's Common Stock issuable upon
exercise  of  warrants  issued  by  the  Company to the November 2000 Investors;

     WHEREAS,  pursuant  to  that certain First Amendment to Registration Rights
Agreement,  dated  March  5, 2001 (the "March 2001 Amendment"), by and among the
Company, each of the November 2000 Investors, DLJ Merchant Banking Partners III,
L.P.,  a  Delaware  limited  partnership, and DLJ Merchant Banking III, Inc., as
Advisory  General  Partner  on  behalf  of  DLJ  Offshore  Partners III, C.V., a
Netherlands  Antilles  limited  partnership  (collectively,  the  "March  2001
Investors"),  the  Company  provided  certain  registration  rights  under  the
Agreement  to  the March 2001 Investors regarding shares of the Company's Common
Stock issuable upon exercise of warrants issued by the Company to the March 2001
Investors;

     WHEREAS,  pursuant  to that certain Second Amendment to Registration Rights
Agreement, dated December 21, 2002 (the "December 2002 Amendment"), by and among
the  Company  and  the  CSFB Entities, the Company provided certain registration
rights  under the Amended Agreement to the CSFB Entities other than the November
2000  Investors  (collectively,  the  "December  2002  Investors") regarding (i)
shares  of  the Company's Common Stock acquired by them pursuant to that certain
Omnibus  Agreement  dated  as of December 20, 2002, by and among the Company and
the  December  2002  Investors,  and  (ii)  shares of the Company's Common Stock
issuable  upon  exercise  of  warrants  represented  by  the  respective Warrant
Certificates  dated as of December 20, 2002, by and between the Company and each
of  the  December  2002  Investors;

     WHEREAS,  the  Company  proposes  to  register  equity  securities  on  a
registration  statement  on  Form  S-3  and has asked the CSFB Entities to waive
their right to have their Registrable Securities (as such term is defined in the
Amended  Agreement)  on  that  registration  statement;

     WHEREAS,  to induce the CSFB Entities to grant that waiver, the Company and
the  CSFB  Entities  have  agreed to amend the Amended Agreement as set forth in
this  Amendment;



     NOW, THEREFORE, for and in consideration of the foregoing, and other good
and valuable consideration, the sufficiency of which are hereby acknowledged,
the parties hereto, intending to be legally bound, do hereby agree as follows:

     1. AMENDMENTS. The Amended Agreement is amended by adding a new Section 16
to read as follows:

          "16.  RIGHTS  RELATING  TO  THE COMPANY'S SHELF REGISTRATION STATEMENT

               16.1  SHELF  REGISTRATION  STATEMENT

               For purposes of this Section 16,  the  following  terms  have the
following meanings:

               (a) "REPURCHASE TRANSACTION" means a transaction in which the
Company issues the Company's Common Stock under the Shelf Registration Statement
in an underwritten offering and uses the net sales proceeds to repurchase
Registrable Securities at the same net purchase price as the primary shares sold
in the offering.

               (b) "SHELF REGISTRATION STATEMENT" means the Company's
registration statement on Form S-3 filed with the SEC pursuant to which the
Company is registering an aggregate of $200 million of securities delayed or
continuous basis under Rule 415 under the Act.

               16.2 OBLIGATION TO EFFECT A REPURCHASE TRANSACTION

               (a) If the Company shall receive a written request from the
Holders of at least 25% of the Registrable Securities owned by the Holders on
the date of such notice (the "Triggering Holders") that the Company effect a
Repurchase Transaction covering at least 25% of the Registrable Securities owned
by the Holders on the date of such notice (a "Trigger Notice"), then within ten
days after its receipt of the Trigger Notice, the Company will either (i) give
written notice of such request to all Holders (the "Company Notice") or (ii)
give written notice to the Triggering Holders of the Company's decision to defer
the Repurchase Transaction pursuant to Section 16.3 (the "Deferral Notice"). If
the Company gives the Deferral Notice, then at the end of the Deferral Period
described in Section 16.3, unless the Triggering Holders have withdrawn the
Trigger Notice, the Company will give the Company Notice to all Holders.

               (b) The Holders shall have three business days after receipt of
the Company Notice to advise the Company if such Holders will participate in the
Repurchase Transaction and the number of shares of Company's Common Stock they
desire to sell in the Repurchase Transaction (the "Participating Holder
Notice"), provided that any Holder who is not a Triggering Holder and who does
not timely furnish a Participating Holder Notice will be deemed to have opted
not to participate in the Repurchase Transaction.

               (c) The Company shall prepare and file with the SEC a prospectus
supplement to the Shelf Registration Statement, and such other filings as may be
necessary in order to implement the Repurchase Transaction, no later than ten
days after the deadline for receipt of the Participating Holder Notice;
provided, however if the Company is unable to prepare and file the prospectus
supplement and other filings within the ten days required herein as a direct
result of events beyond the control of the Company, the Company will promptly
notify the CSFB Entities in writing



describing  the reason for the delay in filing and providing an estimate of when
the  filing  will  be  made  and  the  Company will make such filings as soon as
practicable  thereafter.

               (d) The Company shall use its reasonable best efforts, without
incurring unreasonable expense, to cause the prospectus supplement to be
declared effective by the SEC no later than three weeks after it is filed with
the SEC.

               16.3 DEFERRAL NOTICE

               Notwithstanding the foregoing, if the Company shall furnish to
the Triggering Holders within 10 days after its receipt of the Trigger Notice 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 the Repurchase Transaction
to proceed at that time and it is therefore essential to defer the giving of the
Company Notice, the Company shall have the right to defer such notice for up to
2 periods of not more than 30 days each; provided, however, that the Company may
not use this right more than once (for a total of up to 60 days) in any 12-month
period. Notwithstanding any other provision of this Agreement, Section 2(c) will
not apply to a Repurchase Transaction.

               16.4 APPLICABILITY OF OTHER PROVISIONS OF THIS AGREEMENT

               (a) If the Holders deliver a Trigger Notice at a time when the
Company is not engaging (or actively preparing to engage) in an underwritten
offering of the Company's Common Stock, then the Holders' right will be subject
to all of the terms of this Agreement applicable to a request for registration
under Section 2, including without limitation the last sentence of Section 8(a),
except as otherwise provided in this Section 16. Upon completion of Repurchase
Transaction, the Company will be deemed to have effected a registration pursuant
to Section 2.

               (b) If the Holders deliver a Trigger Notice at a time when the
Company is engaging (or actively preparing to engage) in an underwritten
offering of Company's Common Stock, and if the Holders deliver the Trigger
Notice within the time limits provided for exercising piggyback registration
rights under Section 3, then (i) the requirement in Section 16.2 that the
Trigger Notice cover at least 25% of the Registrable Securities shall not apply
and (ii) the exercise of the Holders' rights will be subject to all of the terms
of this Agreement applicable to a request for registration under Section 3,
including without limitation the last sentence of Section 8(b), except as
otherwise provided in this Section 16. Upon completion of the Repurchase
Transaction, the Company will not be deemed to have effected a registration
pursuant to Section 2.

               16.5 LOCKUP AGREEMENT

               For 120 days following the date of the Company's purchase of
Registrable Securities in a Repurchase Transaction, to the extent requested by
the Company and an underwriter of the Company's Common Stock, (i) the Holders
shall not sell, or otherwise transfer or dispose (other than to donees who agree
to be similarly bound), of any Registrable Securities, and (ii) the Holders
shall not make any demand for, or exercise any right with respect to, the
registration of any Registrable Securities; provided, however that the foregoing
shall not be effective unless all of the Officers and Directors (other than any
Director designated by the CSFB Entities) of the Company (whether or not
pursuant to this Amendment) enter into similar agreements and the Company has
used all reasonable efforts to obtain similar agreements from all holders of at
least 5% of the then outstanding Company's



Common Stock. Notwithstanding the foregoing, any Officer who has a Section
10(b)(5)-1 sales program in effect with the Company as of the date of this
Amendment shall be exempt from the lock-up provisions of this Section 16.5 to
the extent of the sales of the Company's Common Stock provided in such sales
program during the lock-up period. At the request of the Company, the Holders
will enter into a lock-up agreement in customary form relating to the foregoing
covenants. To enforce the foregoing covenants, the Company may impose
stop-transfer instructions with respect to the Registrable Securities of the
Holders until the end of such period. Notwithstanding any other provision of
this Agreement, Section 14 ("Market Standoff" Agreement) will not apply to a
Repurchase Transaction.

               16.6 UNDERWRITER

               Unless the Company is engaging (or actively preparing to engage)
in an underwritten offering as described in Section 16.4(b), in the event that
the Company plans to issue the Company's Common Stock in a marketed transaction
as part of a Repurchase Transaction, the Triggering Holders shall provide the
Company with the names of: (i) up to three reputable national or regional
underwriters who have indicated a willingness to underwrite the Company's
offering that will be part of the Repurchase Transaction in which event the
Company shall have the right to substitute one underwriter acceptable to the
Company for one of the underwriters named by the Triggering Holders; or (ii)
four or more reputable national or regional underwriters who have indicated a
willingness to underwrite the Company's offering that will be part of the
Repurchase Transaction in which event the Company shall have the right to
substitute two underwriters acceptable to the Company for two of the
underwriters named by the Triggering Holders. The Company shall use its best
efforts to enter into an underwriting agreement in customary form with such
underwriters. Notwithstanding any provision of this Section 16.6 to the
contrary, for purposes of this Section 16.6, the Triggering Holders shall have
the right to name Credit Suisse First Boston as an underwriter and Credit Suisse
First Boston shall be deemed by the Triggering Holders and the Company to be an
underwriter acceptable to the Company. Any failure of the Triggering Holders to
provide underwriter information to the Company, or any failure by such
underwriter(s) to proceed with the offering on customary terms, shall relieve
the Company of its obligation to file the prospectus supplement within the
timeframe set forth in this Section 16, though the Company shall still be
obligated to use its reasonable best efforts to effect the Repurchase
Transaction as soon as practicable. To the extent this Section 16.6 is
inconsistent with Section 8(a), this Section 16.6 shall control.

               16.7 LIMITATION ON NUMBER OF SHARES

               (a) The Holders shall not sell more than 50% of the Registrable
Securities in Repurchase Transactions during the 12 months following the date
the Shelf Registration Statement is declared effective, and the Company shall
have no obligation to effect Repurchase Transactions in excess of that amount
during that 12-month period. For purposes of this Section 16.7, the term
Registrable Securities refers to the Registrable Securities outstanding on the
date the Shelf Registration Statement is declared effective.

               (b) The Company shall have no obligation to effect a Repurchase
Transaction with respect to more shares of Company's Common Stock than are then
registered under the Shelf Registration Statement.



               16.8 TERMINATION OF RIGHTS

               The Holders shall not have any rights under this Section 16 until
the Shelf Registration Statement is declared effective. All of the Holders'
rights under this Section 16 shall terminate when the Company withdraws the
Shelf Registration Statement or deregisters all of the shares of the Company's
Common Stock registered thereunder, provided that the Company shall not (i)
withdraw the Shelf Registration Statement or deregister all or a portion of the
shares of the Company's Common Stock registered thereunder until after 12 months
following the date the Shelf Registration Statement is declared effective; or
(ii) deregister any shares of the Company's Common Stock after it receives a
Trigger Notice until the Repurchase Transaction contemplated by that Trigger
Notice has been completed.

               16.9 PURCHASE AGREEMENT

               The repurchase of the Registrable Securities by the Company in a
Repurchase Transaction would be documented by a stock purchase agreement to be
entered into simultaneously with the underwriting agreement for the underwritten
offering of Company Common Shares as described above. The stock purchase
agreement shall contain representations and warranties by the Holders which are
typical of similar transactions and relate to: (i) due organization, valid
existence and good standing (where available) of Holders; (ii) Holders' power
and authority to execute and deliver the stock purchase agreement and consummate
the transactions and perform their obligations thereunder; (iii) the validity
and legally binding obligation of Holders; (iv) no conflict or violation of
other agreements of Holders; (v) Holders are the record and beneficial owners of
the shares and convey them free and clear of any lien, claims or encumbrances;
(vi) Holders have made their own independent investigation concerning the
Company and made informed decisions regarding the sale of their shares pursuant
to the stock purchase agreement; and (vii) no approval of any government entity
is required by the Holders in connection with the execution and delivery of the
stock purchase agreement by the Holders or consummation of the transactions
contemplated by the stock purchase agreement. In addition, the Company shall
make representations and warranties to the Holders which are typical of similar
transactions and relate to: (i) due organization, valid existence and good
standing of Company; (ii) power and authority to execute and deliver the stock
purchase agreement and consummate the transactions and perform its obligations
thereunder; (iii) due authorization by all necessary corporate action; (iv) the
validity and legally binding obligation of the Company; (v) no conflict or
violation of other agreements of the Company; and (vi) no approval of any
government entity is required by the Company in connection with the execution
and delivery of the stock purchase agreement by the Company or consummation of
the transactions contemplated by the stock purchase agreement."

     2. NO OTHER CHANGES. Except as explicitly amended by this Amendment, the
terms, conditions, rights and obligations under the Amended Agreement shall
remain in full force and effect.

     3. COUNTERPARTS. This Amendment may be executed by the parties hereto in
any number of counterparts, each of which shall be deemed an original, but all
of which shall constitute one and the same agreement.



     IN  WITNESS  WHEREOF, the parties hereto have executed this Amendment as of
the  date  set  forth  above.


BRIGHAM  EXPLORATION  COMPANY

By:     /s/  Eugene B. Shepherd, Jr.
        ----------------------------
Name:   Eugene B. Shepherd, Jr.
        -----------------------
Title:  Chief  Financial  Officer
        -------------------------


DLJ  MB  FUNDING  III,  INC.

        By:    /s/  Robert  Cabes
           -------------------------
               ROBERT  CABES
               Attorney-in-Fact


DLJ  ESC  II,  LP

By:     DLJ  LBO  PLANS  MANAGEMENT  CORPORATION,
        its  general  partner

        By:    /s/  Robert  Cabes
           -------------------------
               ROBERT  CABES
               Attorney-in-Fact


DLJ  MERCHANT  BANKING  PARTNERS  III,  L.P.

By:     DLJ  MERCHANT  BANKING  III,  INC.,
        its  Managing  General  Partner


        By:    /s/  Robert  Cabes
           -------------------------
               ROBERT  CABES
               Attorney-in-Fact


DLJ MERCHANT BANKING III, INC., AS ADVISORY
GENERAL PARTNER ON BEHALF OF
DLJ OFFSHORE PARTNERS III, C.V.


        By:    /s/  Robert  Cabes
           -------------------------
               ROBERT  CABES
               Attorney-in-Fact



DLJ MERCHANT BANKING III, INC.,
AS ADVISORY GENERAL PARTNER ON BEHALF OF
DLJ OFFSHORE PARTNERS III-1, C.V. AND AS
ATTORNEY-IN-FACT FOR DLJ MERCHANT BANKING III, L.P.,
AS ASSOCIATE GENERAL PARTNER OF
DLJ OFFSHORE PARTNERS III-1, C.V.


        By:    /s/  Robert  Cabes
           -------------------------
               ROBERT  CABES
               Attorney-in-Fact


DLJ MERCHANT BANKING III, INC., AS ADVISORY
GENERAL PARTNER ON BEHALF OF
DLJ OFFSHORE PARTNERS III-2, C.V. AND
AS ATTORNEY-IN-FACT FOR DLJ MERCHANT BANKING III, L.P.,
AS ASSOCIATE GENERAL PARTNER OF
DLJ OFFSHORE PARTNERS III-2, C.V.


        By:    /s/  Robert  Cabes
           -------------------------
               ROBERT  CABES
               Attorney-in-Fact


DLJ MB PARTNERSIII GMBH & CO. KG

By:     DLJ MERCHANT BANKING III, L.P.,
        its Managing Limited Partner

        By:    DLJ  MERCHANT  BANKING  III,  INC.,
               its  General  Partner

               By:    /s/  Robert  Cabes
                  -------------------------
                      ROBERT  CABES
                      Attorney-in-Fact



MILLENNIUM PARTNERS II, L.P.

By:     DLJ MERCHANT BANKING III, INC.,
        its Managing General Partner


        By:    /s/  Robert  Cabes
           -------------------------
               ROBERT  CABES
               Attorney-in-Fact


MBP III PLAN INVESTORS, L.P.

By:     DLJ LBO PLANS MANAGEMENT CORPORATION,
        its Managing General Partner

        By:    /s/  Robert  Cabes
           -------------------------
               ROBERT  CABES
               Attorney-in-Fact



                                              SCHEDULE A
                         TO THIRD AMENDMENT TO REGISTRATION RIGHTS AGREEMENT

DLJ Merchant Banking Partners III, L.P.

DLJ MB Funding III, Inc

DLJ ESC II, LP

DLJ Merchant Banking III, Inc., as Advisory General Partner on behalf of DLJ
Offshore Partners III, C.V.

DLJ Merchant Banking III, Inc., as Advisory General Partner on behalf of DLJ
Offshore Partners III-1, C.V. and as attorney-in-fact for DLJ Merchant Banking
III, L.P., as Associate General Partner of DLJ Offshore Partners III-1, C.V.

DLJ Merchant Banking III, Inc., as Advisory General Partner on behalf of DLJ
Offshore Partners III-2, C.V. and as attorney-in-fact for DLJ Merchant Banking
III, L.P., as Associate General Partner of DLJ Offshore Partners III-2, C.V.

DLJ MB PartnersIII GmbH & Co. KG

Millennium Partners II, L.P.

MBP III Plan Investors, L.P.