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.