Dune Energy, Inc.
                         3050 Post Oak Blvd., Suite 695
                                Houston, TX 77056

                                                               December 28, 2006

      Re:   Tender Offer for American Natural Energy Corporation 8% Convertible
            Debentures Due September 30, 2006 (the "Debentures")

Dear Debenture Holder:

      Dune Energy, Inc. ("Dune") is a United States oil and natural gas
exploration and development company whose common stock is traded on the American
Stock Exchange under the symbol "DNE". Dune hereby tenders its offer to purchase
the above-referenced Debentures registered in your name for and in consideration
of such number of newly-issued shares of Dune's common stock, $.001 par value,
equal to fifty-five percent (55%) of the outstanding principal amount of the
Debentures registered to you, as determined after 5:00pm, New York City time, on
January 31, 2007 and upon and subject to the other terms and conditions set
forth in the Offer to Purchase Statement (the "Offer to Purchase") and the
related Letter of Transmittal enclosed herewith.

      Please review such Offer to Purchase carefully with your legal and tax
advisers. A copy of the Offer to Purchase and the Letter of Transmittal are
attached as exhibits to that tender offer statement on Schedule TO filed by Dune
with the U.S. Securities and Exchange Commission, or SEC, on December 28, 2006.

      If you agree to tender the Debentures registered to you in accordance with
such terms and conditions, please carefully follow the following instructions:

      1.    Complete and sign the enclosed Letter of Transmittal where
            information and signatures are required on pages 2 and 3 thereof.
            Your signature must have a Medallion Signature Guaranty to be
            effective;

      2.    Complete and sign the enclosed Transfer Form. Your signature must
            have a Medallion Signature Guaranty to be effective, which may be
            affixed next to your signature on the Transfer Form.

      3.    Mail to Computershare Trust Company of Canada, as Depositary (the
            "Depositary") in the enclosed pre-addressed envelope for receipt



Debenture Holders
December 28, 2006
Page 2 of 2

            prior to January 31, 2007, the signed Letter of Transmittal,
            Transfer Form and the original Debentures certificate previously
            issued to you.

      If you have any questions about the above procedures, please contact Luce
Lafontaine at the office of the Depositary at telephone number (604) 661-0203.

      If you and other debenture-holders validly tender (and not properly
withdraw) Debentures with no less than $6,000,000 outstanding principal amount
by the above date, as it may be extended, and the other conditions to the tender
offer, as set forth in the enclosed Offer to Purchase, are satisfied, the
Depositary will send to you, promptly after the closing the number of Dune
shares to which you are entitled.

      If Debentures are not tendered by the above date, as it may be extended,
or the other conditions to closing are not satisfied, or Dune otherwise
terminates the tender offer, the Depositary will notify you of such fact and
return to you the Debentures registered to you, as well as the signed
instruments previously mailed by you to the Depositary.

      In addition to the foregoing, upon any extension of the offering period,
material change in the terms or conditions of the tender offer, or termination
of the tender offer, Dune will make a public announcement of such action in the
form of a release posted in Business Wire, Dow Jones News Service or another
comparable news service, as well as supplement its statement on Schedule TO
filed with the SEC.

      If you require any information about Dune, you are directed to the Offer
to Purchase and its public filings, as set forth at the SEC website at
www.sec.gov.

                                              By Order Of the Board of Directors


                                              /s/ Richard M. Cohen
                                              ----------------------------------
                                              Richard M. Cohen
                                              Secretary, Dune Energy, Inc.