Exhibit 3.1

CERTIFICATE OF DESIGNATION

OF

CONVERTIBLE PREFERRED STOCK

OF

DUNE ENERGY, INC.

To Be Designated

Series C Convertible Preferred Stock

Pursuant to Section 151(g) of the

General Corporation Law of the State of Delaware

The undersigned DOES HEREBY CERTIFY that the following resolution was duly adopted by the Board of Directors (the “Board of Directors”) of Dune Energy, Inc., a Delaware corporation (the “Corporation”), at a meeting duly convened and held, at which a quorum was present and acting throughout:

RESOLVED, that pursuant to the authority conferred on the Board of Directors by the Corporation’s Certificate of Incorporation, the issuance of a series of convertible preferred stock, par value $0.001 per share, of the Corporation that shall consist of 250,000 shares of convertible preferred stock be, and the same hereby is, authorized; and the President and Chief Executive Officer of the Corporation be, and he hereby is, authorized and directed to execute and file with the Secretary of State of the State of Delaware a Certificate of Designation of such convertible preferred stock of the Corporation fixing the designations, powers, preferences and rights of the shares of such series, and the qualifications, limitations or restrictions thereof (in addition to the designations, powers, preferences and rights, and the qualifications, limitations or restrictions thereof set forth in the Certificate of Incorporation that may be applicable to the Corporation’s preferred stock), as follows:

1. Number of Shares; Designation. A total of 250,000 shares of convertible preferred stock, par value $0.001 per share, of the Corporation are hereby designated as Series C Preferred Stock (the “Series”). Shares of the Series (“Series C Preferred Shares”) will be issued pursuant to the terms of an offer to exchange any and all of the Corporation’s outstanding 10 ¹/2% Senior Secured Notes due 2012 as set forth in an Offering Memorandum and Disclosure Statement, dated November 14, 2011 (the “Offering Memorandum”), a copy of which will be provided to any stockholder of the Corporation upon request therefor. Capitalized terms used herein and not otherwise defined have the respective meanings set forth in the Offering Memorandum.

2. Rank. The Series shall, with respect to rights (including to redemption payments) upon liquidation, dissolution or winding-up of the affairs of the Corporation, rank:

3. Dividends. Dividends may be declared and paid on the Series C Preferred Shares from funds legally available therefor as and when determined by the Board of Directors. The Series shall, with respect to the payment of dividends, rank pari passu with the Common Stock.

4. Liquidation.

(a) The liquidation value per Series C Preferred Share, in case of the voluntary or involuntary liquidation, dissolution or winding-up of the affairs of the Corporation, shall equal $0.0001 (the “Liquidation Value”).

(b) In the event of any voluntary or involuntary liquidation, dissolution or winding-up of the Corporation (a “Liquidation Event”), the holders of Series C Preferred Shares (i) shall not be entitled to receive the Liquidation Value of such shares held by them until the liquidation value of all Senior Liquidation Shares shall have been paid in full, and (ii) shall be entitled to receive the Liquidation Value of such shares held by them in preference to and in priority over any distributions upon the Junior Liquidation Shares. Upon payment in full of the Liquidation Value to which the holders of Series C Preferred Shares are entitled for such shares, such holders will not be entitled to any further participation in any distribution of assets by the Corporation with respect to their Series C Preferred Shares.

(c) The Corporation shall, no later than the date on which a Liquidation Event occurs, deliver a written notice of any Liquidation Event, stating the payment date or dates when and the place or places where the amounts distributable in such circumstances shall be payable, not less than 30 days prior to any payment date stated therein, to each holder of Series C Preferred Shares.

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5. Conversion.

(a) Mandatory Conversion. At such time as the Corporation receives the acceptance of filing of an Amendment to the Corporation’s Certificate of Incorporation from the Secretary of State of the State of Delaware, pursuant to which the total number of shares of Common Stock that the Corporation shall have authority to issue will be increased to 4,200,000,000 (the “Recapitalization Time”), each Series C Preferred Share shall mandatorily convert into such number of fully paid and non-assessable shares of Common Stock (the “Conversion Shares”) as is determined in accordance with the terms hereof (the “Mandatory Conversion”).

(b) Number of Conversion Shares. The number of Conversion Shares to be delivered by the Corporation to a holder for each Series C Preferred Share pursuant to the Mandatory Conversion shall be 14,149.595545; provided, however, that the number of Conversion Shares issued shall never, when combined with all other then outstanding shares of Common Stock and shares of Common Stock that have been subscribed for or otherwise committed to be issued, exceed the number of shares of Common Stock then authorized to be issued by the Corporation, and in the event that there are insufficient shares of Common Stock authorized to permit the full Mandatory Conversion, the Corporation will promptly take all such actions necessary so as to permit the full Mandatory Conversion as soon as practicable after the Corporation becomes aware of such insufficiency; provided further, that no fractional Conversion Shares shall be delivered upon the Mandatory Conversion, and any fractional shares resulting from the Mandatory Conversion shall be rounded to the nearest whole Conversion Share, with fractional Conversion Shares equal to or greater than 0.5 Conversion Shares being rounded up to the next nearest whole Conversion Share and fractional Conversion Shares less than 0.5 Conversion Shares being rounded down to the next nearest whole Conversion Share.

(c) Delivery of Conversion Shares. The Corporation shall, no later than the close of business on the third Business Day following the Recapitalization Time, issue and deliver or cause to be delivered to such holder of Series C Preferred Shares the number of Conversion Shares determined pursuant to paragraph 5(b) above.

6. Status of Shares. All Series C Preferred Shares that are at any time converted pursuant to paragraph 5 above, and all Series C Preferred Shares that are otherwise reacquired by the Corporation and subsequently canceled by the Board of Directors, shall be retired and shall not be subject to reissuance.

7. Voting Rights. Each share of the Series shall entitle the holder thereof to 1 vote, voting together with the Common Stock as a single class, and shall be entitled to notice of any stockholders’ meeting in accordance with the Bylaws of the Corporation.

8. Restrictions and Limitations.

So long as any Series C Preferred Shares remain outstanding, the Corporation shall not, without the vote or written consent by the holders of at least a majority of the outstanding Series C Preferred Shares, voting together as a single class, alter, modify or amend (whether by merger or otherwise) the terms of the Series in any way.

In the event that the holders of at least a majority of the outstanding Series C Preferred Shares agree to allow the Corporation to alter or change the rights, preferences or privileges of the Series pursuant to applicable law, no such change shall be effective to the extent that, by its terms, such change applies to less than all of the Series C Preferred Shares then outstanding.

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9. Certain Definitions. As used in this Certificate, the following term shall have the following respective meaning:

“Capital Stock” of any person or entity means any and all shares, interests, rights to purchase, warrants, options, participations or other equivalents of or interests in the common stock or preferred stock of such person or entity, including, without limitation, partnership and membership interests.

(Signature page follows)

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IN WITNESS WHEREOF, the Corporation has caused this Certificate to be duly executed on its behalf by its undersigned President and Chief Executive Officer as of December 21, 2011.

Signature Page to Certificate of Designation -

Series C Convertible Preferred Stock