1 EXHIBIT 10.39.1 AMENDMENT TO REGISTRATION RIGHTS AGREEMENT This AMENDMENT TO REGISTRATION RIGHTS AGREEMENT (the "Amendment") dated as of March 26, 1999, among Brigham Exploration Company, a Delaware corporation (the "Company"), Joint Energy Development Investments II Limited Partnership, a Delaware limited partnership ("JEDI-II"), and ECT Merchant Investments Corp. ("ECT Merchant"), amends the Registration Rights Agreement dated as of August 20, 1998 among the Company, JEDI-II and Enron Capital & Trade Resources Corp., a Delaware corporation ("ECT"). NOW, THEREFORE, in consideration of the mutual covenants and agreements set forth herein and for good and valuable consideration, the receipt of which is hereby acknowledged, the parties agree as follows: ARTICLE I MODIFICATION OF DEFINITION OF WARRANTS AND WARRANT SHARES Section 1.01. Definition of Warrant. "Warrants" means the Warrants issued by the Company to JEDI-II and ECT Merchant as of the date hereof for the purchase of an aggregate of 1,000,000 shares of Common Stock, evidenced as of the date hereof by Warrant Certificates Nos. A-3 and A-4, and any Warrants issued upon the transfer thereof or in substitution therefor, as the same may be amended from time to time. Section 1.02. Definition of Warrant Shares. "Warrant Shares" shall mean the shares of Common Stock and other securities receivable upon exercise of the Warrants. ARTICLE II MISCELLANEOUS Section 2.01 Execution in Counterparts. This Amendment may be executed in any number of counterparts and by different parties on separate counterparts and all of such counterparts shall together constitute one and the same instrument. Section 2.02 Governing Law. This Amendment and the rights and obligations of the parties hereunder shall be construed in accordance with and be governed by the laws of the State of Texas and the United States of America. Section 2.01 Descriptive Headings, etc. The descriptive headings of the sections of this Amendment are inserted for convenience only and shall not be deemed to affect the meaning or construction of any of the provisions hereof. 2 IN WITNESS WHEREOF, the parties have executed this Amendment to Registration Rights Agreement as of the date first written above. BRIGHAM EXPLORATION COMPANY By:/s/ Karen E. Lynch -------------------------------------------- Karen E. Lynch Vice President JOINT ENERGY DEVELOPMENT INVESTMENTS II LIMITED PARTNERSHIP By: Enron Capital Management II Limited Partnership, its General Partner By: Enron Capital II Corp., its General Partner By: /s/ Mark J. Warner -------------------------------------- Mark J. Warner Agent and Attorney-in-fact ECT MERCHANT INVESTMENTS CORP. By: /s/ Mark Warner -------------------------------------- Name: Mark Warner -------------------------------------- Title: Agent and Attorney in Fact -------------------------------------- -2-