**EXHIBIT 4.4.4**     **SECOND SUPPLEMENTAL INDENTURE**, dated as of January 2, 2008 (this “*Second 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 ofNovember 16, 2005 (the “*Original Indenture*”), as supplemented by the First Supplemental Indenturedated as of November 23, 2005 (together with the Original Indenture, the “*Indenture*”) relating tothe Company’s 7.25% Senior Subordinated Notes due 2017; 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 10.03 of the Indenture states that Article 10 of the Indenture shall bebinding upon each Subsidiary Guarantor and its successors and assigns; and     WHEREAS, Section 4.15 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 4.08(b)(16) of the Indenture, to, at the same time,execute and deliver to the Trustee a Guarantee Agreement pursuant to which such RestrictedSubsidiary will Guarantee payment of the Notes on the same terms and condition as those set forthin 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 Second 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 Second 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 Second Supplemental Indenture. This Second 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 Second SupplementalIndenture limits, qualifies or conflicts with another provision of this Second 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 Second Supplemental Indenture is executed, the provisionrequired by said Act shall control.     SECTION 6. Trustee Disclaimer. The recitals contained in this Second 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 SECOND SUPPLEMENTAL INDENTURE SHALL BE GOVERNED BY,AND CONSTRUED IN ACCORDANCE WITH, THE LAWS OF THE STATE OF NEW YORK.**     SECTION 8. Counterparts. This Second 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 Second Supplemental Indenture to beduly executed, as of the day and year first above written.      ENCORE ACQUISITION COMPANY