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Exhibit 4.1.2

     FIRST SUPPLEMENTAL INDENTURE, dated as of January 2, 2008 (this “First Supplemental Indenture”), between Encore Acquisition Company, a Delaware corporation (the “Company”), and Wells Fargo Bank, National Association, as trustee (the “Trustee”).

     WHEREAS, the Company and the Trustee have heretofore entered into an Indenture dated as of April 2, 2004 (the “Indenture”) relating to the Company’s 6.25% Senior Subordinated Notes due 2014; and

     WHEREAS, EAP Operating, Inc., a Delaware corporation and a Subsidiary Guarantor, has filed a Certificate of Conversion under Delaware law to convert to a limited liability company formed under the laws of Delaware, effective as of December 31, 2007, named EAP Operating, LLC; and

     WHEREAS, Section 11.03 of the Indenture states that Article 10 of the Indenture shall be binding upon each Subsidiary Guarantor and its successors and assigns; and

     WHEREAS, Section 4.10 of the Indenture provides that the Company shall cause each Restricted Subsidiary that Incurs any Indebtedness (other than Indebtedness Incurred pursuant to and in compliance with the last cause of Section 4.03(b)(16), to, at the same, execute and deliver to the Trustee a Guaranty Agreement pursuant to which such Restricted Subsidiary will Guarantee payment of the Securities on the same terms and condition as those set forth in the Indenture; and

     WHEREAS, Section 9.01 provides that the Company and the Trustee may amend or supplement the Indenture without the consent of any Holder to add Guarantees of any series of Securities as permitted by the terms of the Indenture; and

     WHEREAS, all acts and things necessary to make this First Supplemental Indenture a valid and binding agreement in accordance with the Indenture have been done or performed;

     NOW, THEREFORE, in consideration of the premises, agreements and obligations set forth herein and for other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the parties hereto hereby agree, for the equal and proportionate benefit of all Holders of the Notes, as follows:

     SECTION 1. Capitalized Terms. Capitalized terms used in this First Supplemental Indenture and not otherwise defined herein shall have the respective meanings assigned to such terms in the Indenture.

     SECTION 2. Guarantees. EAP Operating, LLC hereby agrees, jointly and severally with the Subsidiary Guarantors, to guarantee the Company’s obligations under the Notes on the terms and subject to the conditions set forth in Article 10 of the Indenture and to be bound by all other applicable provisions of the Indenture.

     SECTION 3. Continuing Effect of Indenture. Except as expressly provided herein, all of the terms, provisions and conditions of the Indenture and the Notes outstanding thereunder shall remain in full force and effect.

     SECTION 4. Construction of First Supplemental Indenture. This First Supplemental Indenture is executed as and shall constitute an indenture supplemental to the Indenture and shall be construed in connection with and as part of the Indenture.

     SECTION 5. Trust Indenture Act Controls. If any provision of this First Supplemental Indenture limits, qualifies or conflicts with another provision of this First Supplemental Indenture or the Indenture that is required to be included by the Trust Indenture Act of 1939 as in force at the date as of which this First Supplemental Indenture is executed, the provision required by said Act shall control.

     SECTION 6. Trustee Disclaimer. The recitals contained in this First Supplemental Indenture shall be taken as the statements of the Company, and the Trustee assumes no responsibility for their correctness. The Trustee makes no representations as to the validity or sufficiency of this First Supplemental Indenture.

     SECTION 7. Governing Law. THIS FIRST SUPPLEMENTAL INDENTURE SHALL BE GOVERNED BY, AND CONSTRUED IN ACCORDANCE WITH, THE LAWS OF THE STATE OF NEW YORK.

     SECTION 8. Counterparts. This First Supplemental Indenture may be executed in any number of counterparts, each of which so executed shall be deemed to be an original, but all such counterparts shall together constitute but one and the same instrument.

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