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                                                                    EXHIBIT 10.4

                     THIRD AMENDMENT TO FINANCING AGREEMENT


       Third Amendment to Financing Agreement dated as of this 10th day of
February, 1999 (the "Amendment"), by and among Energy Partners, Ltd., a Delaware
corporation (the "Borrower"), and Energy Income Fund, L.P., a Delaware limited
partnership ("EIF"), to that certain Financing Agreement dated as of April 15,
1998, as amended by the First Amendment to Financing Agreement dated as of June
19, 1998, and as further amended by the Second Amendment to Financing Agreement
dated as of August 31, 1998 (as amended, the "Agreement").

                                    RECITALS

       WHEREAS, pursuant to the Agreement, EIF agreed to make loans to Borrower
for the purposes and subject to the terms and conditions set forth therein;

       WHEREAS, Section 11.2(a) of the Agreement provides that the parties
thereto may amend or modify the Agreement by a written instrument duly executed
by the parties;

       WHEREAS, Borrower and EIF desire to increase the maximum aggregate amount
to be funded under the Agreement from Twenty Million Dollars ($20,000,000) to
Twenty-Five Million Dollars ($25,000,000);

       WHEREAS, Borrower and EIF desire to amend the Agreement in certain other
respects.

       NOW, THEREFORE, in consideration of the foregoing, and other good and
valuable consideration, the receipt and sufficiency of which are hereby
acknowledged, the parties agree as follows:

       1. All capitalized terms used herein shall have the meanings assigned to
them in the Agreement unless expressly defined otherwise in this Amendment.

       2. Except as otherwise specifically provided herein, all terms and
conditions of the Agreement shall apply to the interpretation and enforcement of
this Amendment as if explicitly set forth herein.

       3. Section 1.1 is amended by deleting the defined terms listed below and
their respective accompanying definitions:

          "Chevron Final Payment Date"

       4. Section 1.1 is further amended by adding the following new definition
in the appropriate alphabetical order:

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              "Development Financing" shall have the meaning set forth in
          Section 2.1(d) of this Agreement.

       5. Section 1.1 is further amended by replacing the existing definitions
with the definition listed below for such defined term:

              "Additional Financings" shall have the meaning set forth in
          Section 2.1(e).

       6. Subsections 2.1(b) through (e) are amended to read as follows:

              (b) Subject to the terms and conditions set forth in this
          Agreement, EIF agrees to make a loan to Borrower (the "Bay Marchand
          Financing") in the aggregate principal amount of up to Ten Million
          Dollars ($10,000,000) for the following purposes:

                  (i) up to Nine Million Three Hundred Thousand Dollars
              ($9,200,000) to finance the acquisition of a 20% interest in the
              Bay Marchand Properties;

                  (ii) up to Five Hundred Thousand Dollars ($500,000) for
              working capital; and

                  (iii) up to Three Hundred Thousand Dollars ($300,000) to
              finance payment of costs and expenses to EIF.

              (c) Subject to the terms and conditions set forth in this
          Agreement, EIF agrees to make a loan to Borrower (the "Hughes-Rawls
          Financing") in the principal amount of up to Two Hundred Twenty
          Thousand Four Hundred One Dollars ($220,401) to finance certain costs
          associated with Borrower's obligations under the Hughes-Rawls
          Agreement.

              (d) Subject to the terms and conditions set forth in this
          Agreement and EIF's prior written approval. EIF agrees to make a loan
          to Borrower (the "Development Financing") in the principal amount of
          up to Five Million Dollars ($5,000,000) to finance development costs
          associated with the Chevron Properties, Bay Marchand Properties or
          Hughes-Rawls Properties.

              (e) In the event that the Chevron Financing, Bay Marchand
          Financing and Hughes-Rawls Financing do not fund an amount equal to
          the entire principal amount of Twenty Million Dollars ($20,000,000)
          contemplated in Subsections (a) through (c) above and subject to the
          terms and conditions set forth in this Agreement, EIF agrees to make
          additional loans to Borrower ("Additional Financings") to finance
          costs relating to Borrower's obligations under the


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          Proposed Oil and Gas Agreements that satisfy certain conditions set
          forth in Section 6.2 ("Approved Transactions"); provided, however,
          that the aggregate principal amount funded under this Agreement
          pursuant to Subsections (a) through (c) above shall not exceed Twenty
          Million Dollars ($20,000,000). The Chevron Financing, Bay Marchand
          Financing, Hughes-Rawls Financing, Development Financing and any
          Additional Financings are collectively referred to as the
          "Development Loan" herein.

       8. Section 2.1 is further amended by changing the current subsection
2.1(e) to subsection 2.1(f).

       9. Section 6.2(i) is amended by adding the following new provisions:

          (xii)  Amendments to the Security Instruments in form and substance
                 satisfactory to ElF and its counsel; and

          (xiii) First Allonge to Development Note.

       10. THIS AMENDMENT IS TO BE CONSTRUED UNDER THE LAWS OF THE COMMONWEALTH
OF MASSACHUSETTS.

       11. Except as expressly amended hereby, the Agreement remains in full
force and effect. Any references to the Agreement in the Loan Documents shall
refer to the Agreement as amended hereby.

       12. This Amendment shall be of no force and effect until receipt and
execution of this Amendment by EIF in its offices in Longmeadow, Massachusetts.


                            (Signature page follows.)



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       IN WITNESS WHEREOF, the parties have executed this Amendment as of the
date first written above.

                                      ENERGY PARTNERS, LTD.


                                      By: /s/ RICHARD A. BACHMANN
                                          -------------------------------------
                                          Richard A. Bachmann
                                          President and Chief Executive Officer


                                      ENERGY INCOME FUND, L.P.

                                      By: EIF General Partner, L.L.C.,
                                          its General Partner

                                          By: /s/ ROBERT D. GERSHEN
                                              ---------------------------------
                                              Robert D. Gershen
                                              A Managing Director


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