Amendment to Rights Agreement

Exhibit 4.1

Amendment to Rights Agreement

          This Amendment to the Rights Agreement between Encore Acquisition Company, a Delaware corporation (the “Company”), and Mellon Investor Services LLC, a New Jersey limited liability company, as Rights Agent (the “Rights Agent”), dated as of October 28, 2008 (the “Rights Agreement”) is hereby adopted and dated as of October 31, 2009.

          WHEREAS, the Company and the Rights Agent entered into the Rights Agreement specifying the terms of the Rights (as defined therein);

          WHEREAS, Section 27 of the Rights Agreement permits the Company to amend the Rights Agreement so long as the Rights are then redeemable, and Section 23 of the Rights Agreement provides that the Board of Directors of the Company may redeem the Rights at any time before a Person becomes an Acquiring Person;

          WHEREAS, no Person is currently an Acquiring Person, and the Rights are currently redeemable;

          WHEREAS, the Company desires to amend the Rights Agreement in accordance with Section 27 of the Rights Agreement;

          WHEREAS, the Company proposes to enter into an Agreement and Plan of Merger, dated as of October 31, 2009 (the “Merger Agreement”), by and between the Company and Denbury Resources Inc., a Delaware corporation (“Denbury”);

          WHEREAS, the Board of Directors of the Company has determined it advisable and in the best interest of its stockholders to amend the Rights Agreement to enable the Company to enter into the Merger Agreement and consummate the transactions contemplated thereby without causing Denbury or any of its subsidiaries to become an “Acquiring Person” (as defined in the Rights Agreement).

          NOW, THEREFORE, in consideration of the premises and mutual agreements set forth herein and in the Rights Agreement, the parties hereby agree as follows:

          SECTION 1. DEFINITIONS. Capitalized terms used and not otherwise defined herein shall have the meaning assigned to such terms in the Rights Agreement.

          SECTION 2. AMENDMENTS TO RIGHTS AGREEMENT. The Rights Agreement is hereby amended as set forth in this Section 2.

     (a) The definition of “Acquiring Person” in Section 1 of the Rights Agreement is amended to add the following sentence at the end thereof:

“Notwithstanding anything in this Agreement to the contrary, none of Denbury or any Subsidiary, Affiliate or Associate of Denbury shall be deemed to be an Acquiring Person, either individually or collectively, as a result of any or all of the Merger Events.”

     (b) The definition of “Distribution Date” in Section 1 of the Rights Agreement is amended to add the following sentence at the end thereof:

“Notwithstanding anything in this Agreement to the contrary, a Distribution Date shall not be deemed to have occurred as the result of any or all of the Merger Events.”

     (c) The definition of “Flip-In Event” in Section 1 of the Rights Agreement is amended to add the following sentence at the end thereof:

“Notwithstanding anything in this Agreement to the contrary, none of the Merger Events shall be a Flip-In Event.”

     (d) The definition of “Flip-Over Event” in Section 1 of the Rights Agreement is amended to add the following sentence at the end thereof:

“Notwithstanding anything in this Agreement to the contrary, none of the Merger Events shall be a Flip-Over Event.”

     (e) The definition of “Stock Acquisition Date” in Section 1 of the Rights Agreement is amended to add the following sentence at the end thereof:

“Notwithstanding anything in this Agreement to the contrary, a Stock Acquisition Date shall not be deemed to have occurred as the result of any or all of the Merger Events.”

     (f) The definition of “Expiration Date” in Section 1 of the Rights Agreement is amended to replace the words “and (iv)” with “, (iv)” and to add at the end thereof the words “and (v) the Effective Time (as such term is defined in the Merger Agreement) of the Merger (as such term is defined in the Merger Agreement). The Company shall give the Rights Agent reasonable advance written notice of the Effective Time, provided, however, that if the Company is the surviving corporation under the Merger Agreement, the Company hereby agrees to promptly notify the Rights Agent, in writing, upon the occurrence of the Effective Time (as such term is defined in the Merger Agreement), which notice shall specify (i) that the Effective Time (as such term is defined the Merger Agreement) has occurred, and (ii) the date upon which the Rights established hereby expired and this Agreement terminated.”

     (g) The following definitions shall be added to Section 1 of the Rights Agreement:

“Denbury” shall mean Denbury Resources Inc., a Delaware corporation.

“Merger Agreement” shall mean the Agreement and Plan of Merger dated as of October 31, 2009 by and between the Company and Denbury.

“Merger Events” shall mean (i) the announcement of the Merger (as such term is defined in the Merger Agreement), (ii) the execution and delivery

of the Merger Agreement, (iii) the conversion of Common Stock into the right to receive the Merger Consideration (as such term is defined in the Merger Agreement) in accordance with Article II of the Merger Agreement or (iv) the consummation of the Merger (as such term is defined in the Merger Agreement) or any other transaction contemplated by the Merger Agreement.

          SECTION 3. MISCELLANEOUS.

     (a) The term “Agreement” as used in the Rights Agreement shall be deemed to refer to the Rights Agreement as amended hereby.

     (b) The foregoing amendment shall be effective as of the date first above written, and, except as set forth herein, the Rights Agreement shall remain in full force and effect and shall be otherwise unaffected hereby. Without limiting the foregoing, the Rights Agent shall not be subject to, nor required to interpret or comply with, or determine if any Person has complied with, the Merger Agreement, even though reference thereto may be made in this Amendment and the Rights Agreement.

     (c) This Amendment may be executed in two or more counterparts, each of which shall be deemed to be an original, but all for which together shall constitute one and the same instrument.

     (d) This Amendment shall be deemed to be a contract made under the laws of the State of Delaware and for all purposes shall be governed by and construed in accordance with the laws of such State applicable to contracts to be made and performed entirely within such State; provided, however, that all provisions regarding the rights, duties and obligations of the Rights Agent shall be governed by and construed in accordance with the laws of the State of New York applicable to contracts made and to be performed entirely within such State.

     (e) The undersigned officer of the Company, as an appropriate officer of the Company, (i) hereby certifies pursuant to Section 27 of the Rights Agreement that this Amendment is in compliance with the terms of such Section 27 and (ii) hereby directs the Rights Agent to execute and deliver this Amendment.

     IN WITNESS WHEREOF, the parties hereto have caused this Amendment to be duly executed as of the day and year first above written.