**EXHIBIT 4.3.3**     **FIRST SUPPLEMENTAL INDENTURE**, dated as of January 2, 2008 (this “*First SupplementalIndenture*”), between **Encore Acquisition Company**, a Delaware corporation (the “*Company*”), and **WellsFargo Bank, National Association**, as trustee (the “*Trustee*”).     WHEREAS, the Company and the Trustee have heretofore entered into an Indenture dated as ofJuly 13, 2005 (the “*Indenture*”) relating to the Company’s 6% Senior Subordinated Notes due 2015;and     WHEREAS, EAP Operating, Inc., a Delaware corporation and a Subsidiary Guarantor, has filed aCertificate of Conversion under Delaware law to convert to a limited liability company formed underthe 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 bebinding upon each Subsidiary Guarantor and its successors and assigns; and     WHEREAS, Section 4.10 of the Indenture provides that the Company shall cause each RestrictedSubsidiary that Incurs any Indebtedness (other than Indebtedness Incurred pursuant to and incompliance with the last cause of Section 4.03(b)(16), to, at the same, execute and deliver to theTrustee a Guaranty Agreement pursuant to which such Restricted Subsidiary will Guarantee payment ofthe 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 theIndenture without the consent of any Holder to add Guarantees of any series of Securities aspermitted by the terms of the Indenture; and     WHEREAS, all acts and things necessary to make this First Supplemental Indenture a valid andbinding agreement in accordance with the Indenture have been done or performed;     NOW, THEREFORE, in consideration of the premises, agreements and obligations set forth hereinand for other good and valuable consideration, the receipt and sufficiency of which are herebyacknowledged, the parties hereto hereby agree, for the equal and proportionate benefit of allHolders of the Notes, as follows:     SECTION 1. Capitalized Terms. Capitalized terms used in this First SupplementalIndenture and not otherwise defined herein shall have the respective meanings assigned to suchterms in the Indenture.     SECTION 2. Guarantees. EAP Operating, LLC hereby agrees, jointly and severally withthe Subsidiary Guarantors, to guarantee the Company’s obligations under the Notes on the terms andsubject to the conditions set forth in Article 10 of the Indenture and to be bound by all otherapplicable provisions of the Indenture.     SECTION 3. Continuing Effect of Indenture. Except as expressly provided herein, allof the terms, provisions and conditions of the Indenture and the Notes outstanding thereunder shallremain in full force and effect.
 

 
     SECTION 4. Construction of First Supplemental Indenture. This First SupplementalIndenture is executed as and shall constitute an indenture supplemental to the Indenture and shallbe construed in connection with and as part of the Indenture.     SECTION 5. Trust Indenture Act Controls. If any provision of this First SupplementalIndenture limits, qualifies or conflicts with another provision of this First SupplementalIndenture or the Indenture that is required to be included by the Trust Indenture Act of 1939 as inforce at the date as of which this First Supplemental Indenture is executed, the provision requiredby said Act shall control.     SECTION 6. Trustee Disclaimer. The recitals contained in this First SupplementalIndenture shall be taken as the statements of the Company, and the Trustee assumes noresponsibility for their correctness. The Trustee makes no representations as to the validity orsufficiency of this First Supplemental Indenture.     SECTION 7. Governing Law. **THIS FIRST SUPPLEMENTAL INDENTURE SHALL BE GOVERNED BY, ANDCONSTRUED IN ACCORDANCE WITH, THE LAWS OF THE STATE OF NEW YORK.**     SECTION 8. Counterparts. This First Supplemental Indenture may be executed in anynumber of counterparts, each of which so executed shall be deemed to be an original, but all suchcounterparts shall together constitute but one and the same instrument.[The remainder of this page is intentionally left blank]
 

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