Exhibit 10.71 First Amendment to REGISTRATION RIGHTS AGREEMENT THIS FIRST AMENDMENT TO REGISTRATION RIGHTS AGREEMENT (this "Agreement") is entered into as of March 5, 2001, by and among Brigham Exploration Company, a Delaware corporation (the "Company"), and the parties listed on Schedule A hereto. RECITALS WHEREAS, pursuant to that certain Registration Rights Agreement dated as of November 1, 2000 (the "Original Agreement"), by and among the Company and DLJMB Funding III, Inc., a Delaware corporation and DLJ ESC II, L.P., a Delaware Limited Partnership (the "Initial Investors"), the Company provided certain registration rights to the Initial Investors regarding shares of the Company's common stock issuable upon conversion of warrants issued by the Company to the Initial Investors; WHEREAS, each of the Initial Investors and DLJ Merchant Banking Partners III, L.P., a Delaware Limited Partnership, and DLJ Offshore Partners III, C.V., a Netherlands Antilles Limited Partnership (collectively hereinafter referred to as the "Investors"), and the Company are parties to that certain Securities Purchase Agreement dated as of March 5, 2001 (the "New Securities Purchase Agreement"); WHEREAS, each of the Investors is a party to a certain Warrant Certificate (the "New Warrant Certificate") dated as of March 5, 2001, by and between the Company and each of such Investors; WHEREAS, the New Warrant Certificates were executed and delivered in connection with the consummation of transactions contemplated by the new Securities Purchase Agreement; WHEREAS, pursuant to the New Warrant Certificates, each of the Investors has been issued a warrant (the "New Warrant") to purchase shares of the Company's common stock, par value $.01 per share; and WHEREAS, to induce the Investors to enter into the New Warrant Certificates and the new Securities Purchase Agreement, the Company has agreed to provide registration rights under the Original Agreement with respect to the shares issuable upon exercise of the New Warrants. 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: Section 1. Amendments to the Original Agreement. (a) The "RECITALS" section of the Original Agreement is amended by deleting such section entirely and replacing it with the following: " WHEREAS, each of DLJMB Funding III, Inc. ("MB") and DLJ ESC II, L.P. ("ESC") (MB and ESC are sometimes hereinafter referred to collectively as the "Initial Investors") 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, and each of the Initial Investors and DLJ Merchant Banking Partners III, L.P. ("MBP") and DLJ Offshore Partners III, C.V. ("Offshore") (the Initial Investors, MBP and Offshore are sometimes hereinafter referred to collectively as the "Investors") is a party to a certain Warrant Certificate (the "New Warrant Certificate") dated as of March 5, 2001, by and between the Company and such Investor; WHEREAS, the Warrant Certificates were executed and delivered to the Initial Investors 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 Initial Investors, and the New Warrant Certificates were executed and delivered in connection with the consummation of transactions contemplated by that certain Securities Purchase Agreement dated as of March 5, 2001 by and among the Company and the Investors; WHEREAS, pursuant to the Warrant Certificates, each 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"), and pursuant to the New Warrant Certificates, each Holder (as defined below) has been issued a warrant (the "New Warrant") to purchase shares of the Company's Common Stock; WHEREAS, to induce the Initial Investors to enter into the Warrant Certificates, and the Investors to enter into the New Warrant Certificates and the Securities Purchase Agreements described above, the Company has agreed to grant the registration and other rights contained in this Agreement;" (b) The definition of Registrable Securities in Section 1.(d) of the Original Agreement is amended by deleting such Section 1.(d) entirely and replacing it with the following: " (d) "Registrable Securities" means (i) the Common Stock of the Company issuable or issued upon exercise of the Warrants or the New 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, New 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" (c) Schedule A to the Original Agreement is amended by deleting such Schedule A entirely and replacing it with Schedule A to this Agreement. Section 2. No Other Changes. Except as explicitly amended by this Amendment, the terms, conditions, rights and obligations under the Original Agreement shall remain in full force and effect. Section 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. 2 IN WITNESS WHEREOF, the parties hereto have executed this Amendment as of the date set forth above. 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 DLJMB FUNDING III, INC. /s/ Steven A. Webster ---------------------------------------- Name: Steven A. Webster Title: Attorney-in-Fact Address: 277 Park Avenue New York, New York 10172 Attention: Nicole Arnaboldi, Ivy Dodes Telefax: 212-892-7272 DLJ ESC II, L.P. By: DLJ LBO Plans Management Corporation ---------------------------------------- General Partner /s/ Steven A. Webster ---------------------------------------- Name: Steven A. Webster Title: Attorney-in-Fact Address: c/o DLJ LBO Plans Management Corporation 277 Park Avenue New York, New York 10172 Attention: Ivy Dodes/Nicole Arnaboldi Telefax: 212-892-7272 3 DLJ Merchant Banking Partners III, L.P. By: DLJ Merchant Banking III, Inc. Managing General Partner /s/ Steven A. Webster ---------------------------------------- Name: Steven A. Webster Title: Attorney-in-Fact Address: DLJ Merchant Banking Partners III, L.P. 277 Park Avenue New York, New York 10072 Attention: Nicole Arnaboldi, Ivy Dodes Telefax: 212-892-7272 DLJ Offshore Partners III, C.V. By: DLJ Merchant Banking III, Inc. Managing General Partner /s/ Steven A. Webster ---------------------------------------- Name: Steven A. Webster Title: Attorney-in-Fact Address: c/o DLJ Offshore Management N.V. John B. Gorsiraweg 14 Willemstad, Curacao Netherlands, Antilles Fax: 011-599-961-4129 4 Schedule A to Registration Rights Agreement Number of Shares Holder Name November 1, 2000 March 5, 2001 - ----------- ---------------- ------------- DLJ MB Funding III, Inc., 6,036,667 141,869 a Delaware corporation DLJ ESC II, LP, 630,000 371,789 a Delaware limited partnership DLJ Merchant Banking Partners III, L.P. -0- 1,527,154 DLJ Offshore Partners III, C.V -0- 64,451 --------- --------- TOTAL 6,666,667 2,105,263 5