Exhibit 4.1

DUNE ENERGY, INC.

AND

THE GUARANTORS NAMED HEREIN

AND

THE BANK OF NEW YORK MELLON,

as Trustee and Collateral Agent

SECOND SUPPLEMENTAL INDENTURE

Dated as of December 21, 2011

to Indenture

Dated as of May 15, 2007

10 ¹/2% Senior Secured Notes due 2012

This SECOND SUPPLEMENTAL INDENTURE, dated as of December 21, 2011 (this “Second Supplemental Indenture”) is entered into by and among DUNE ENERGY, INC., a Delaware corporation (the “Company”), the Guarantors and THE BANK OF NEW YORK MELLON, a national banking association, as Trustee (in such capacity, the “Trustee”) and Collateral Agent (in such capacity, the “Collateral Agent”), under the Indenture (as defined herein). Capitalized terms used herein and not otherwise defined shall have the meanings assigned to them in the Indenture.

WITNESSETH:

WHEREAS, the Company has issued its 10 ¹/2% Senior Secured Notes due 2012 (“Notes”) pursuant to an Indenture, dated as of May 15, 2007 (as supplemented by the First Supplemental Indenture, dated December 30, 2008, the “Indenture”) among the Company, the Guarantors listed therein and the Trustee and Collateral Agent;

WHEREAS, the Company has offered to exchange for common stock, par value $0.001 per share, and other consideration any and all outstanding Notes (the “Offer”);

WHEREAS, in connection with the Offer, the Company has requested that the Holders of Notes deliver their consents with respect to the deletion of certain provisions of the Indenture;

WHEREAS, Section 9.02(a) of the Indenture provides that the Company, the Guarantors and the Trustee and Collateral Agent may amend, modify or supplement the Indenture, with the written consent of the Holder or Holders of a majority in aggregate principal amount of the then outstanding Notes;

WHEREAS, Section 9.02(b) of the Indenture provides that the Holders holding at least 75% in aggregate principal amount of the Notes may release all or substantially all of the Collateral otherwise than in accordance with the terms of the Indenture and the Collateral Agreements;

WHEREAS, the Holders of at least 75% in aggregate principal amount of the Notes have duly consented to the proposed modifications set forth in this Second Supplemental Indenture in accordance with Section 9.02 of the Indenture;

WHEREAS, the Company has heretofore delivered, or is delivering contemporaneously herewith, to the Trustee and Collateral Agent (i) an Officers’ Certificate stating that the execution of this Second Supplemental Indenture pursuant to Article Nine under the Indenture is authorized or permitted thereunder and (ii) an Opinion of Counsel stating that the execution of this Second Supplemental Indenture pursuant to Article Nine under the Indenture is authorized or permitted thereunder and that this Second Supplemental Indenture is a valid and enforceable obligation of the Company; and

WHEREAS, all acts and requirements necessary to authorize the execution and delivery of this Second Supplemental Indenture and to make this Second Supplemental Indenture valid and binding have been complied with or performed.

NOW, THEREFORE, in consideration of the foregoing and notwithstanding any provision of the Indenture which, absent this Second Supplemental Indenture, might operate to limit such action, the parties hereto, intending to be legally bound hereby, agree as follows:

ARTICLE ONE

AMENDMENTS

SECTION 1.01 Amendments.

(a) Subject to Section 2.01 hereof, the Indenture is hereby amended by deleting in their entireties Sections 4.04, 4.06, 4.08, 4.09, 4.10, 4.11, 4.12, 4.13, 4.14, 4.17, 4.18, 4.19, 4,20, 4.21, 4.22, 4.23, 4.24, 4.25, 6.01(4), 6.01(5), 6.01(6), 6.01(7), 6.01(8), 6.01(9), 6.01(10) and Articles Five and Twelve and, in each case, inserting the words “Intentionally Omitted” in lieu thereof.

(b) Effective as of the date hereof, none of the Company, the Trustee and Collateral Agent or other parties to or beneficiaries of the Indenture shall have any rights, obligations or liabilities under such Articles, Sections or Clauses and such Articles, Sections or Clauses shall not be considered in determining whether an Event of Default has occurred or whether the Company has observed, performed or complied with the provisions of the Indenture.

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SECTION 1.02 Amendment of Definitions. Subject to Section 2.01 hereof, the Indenture is hereby amended by deleting any definitions from the Indenture with respect to which references would be eliminated as a result of the amendments of the Indenture pursuant to Section 1.01 hereof. To the extent any clause, definition, paragraph, Section or Article of the Indenture has been deleted from the Indenture pursuant to Article One of this Second Supplemental Indenture, any reference in any provision of the Indenture, any Note or any Subsidiary Guarantee to such clause, definition, paragraph, Section or Article shall be disregarded in, and be deemed eliminated from, such provisions.

ARTICLE TWO

MISCELLANEOUS

SECTION 2.01 Effect of Second Supplemental Indenture. Except as amended hereby, all of the terms of the Indenture and Notes issued thereunder shall remain and continue in full force and effect and are hereby confirmed in all respects. From and after the date of this Second Supplemental Indenture, all references to the Indenture (whether in the Indenture or in any other agreements, documents or instruments) shall be deemed to be references to the Indenture as amended and supplemented by this Second Supplemental Indenture, and every Holder of Notes heretofore or hereafter authenticated and delivered shall be bound by the Indenture as so amended and supplemented.

SECTION 2.02 Effectiveness. The provisions of this Second Supplemental Indenture shall be effective only upon execution and delivery of this instrument by the parties hereto. Notwithstanding the foregoing sentence, the provisions of this Second Supplemental Indenture shall become operative only at such time as 75% in principal aggregate amount of Notes are accepted for purchase by the Company pursuant to the Offer, with the result that the amendments to the Indenture effective by this Second Supplemental Indenture shall be deemed to be revoked retroactively to the date hereof if such purchase shall not occur.

SECTION 2.03 Governing Law. THE LAW OF THE STATE OF NEW YORK SHALL GOVERN AND BE USED TO CONSTRUE THIS SECOND SUPPLEMENTAL INDENTURE.

SECTION 2.04 No Representations by Trustee. The recitals contained herein shall be taken as the statement of the Company, and the Trustee assumes no responsibility for the correctness or completeness of the same. The Trustee makes no representations as to the validity or sufficiency of this Second Supplemental Indenture.

(Signature page follows)

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IN WITNESS WHEREOF, the parties hereto have caused this Second Supplemental Indenture to be duly executed as of the date first above written.

Signature Page to Second Supplemental Indenture