<PAGE>

EXHIBIT 10.2

                               FIRST AMENDMENT TO
                              ENERGY PARTNERS, LTD.
            AMENDED AND RESTATED 2000 LONG TERM STOCK INCENTIVE PLAN

            The Energy Partners, Ltd. Amended and Restated 2000 Long Term Stock
Incentive Plan (the "Plan") is hereby amended, effective as of May 13, 2004, in
the following respects:

            1.    Subsection (b) of Section 2 of the Plan is amended to read in
      its entirety as follows:

                  "(b) `Award' means any Option, Performance Share, Restricted
            Share or Restricted Share Unit granted to an Eligible Person under
            the Plan."

            2.    Subsections (m), (n) and (o) of Section 2 of the Plan are
      renumbered as subsections (n), (o) and (p), respectively, and a new
      subsection (m) is added to read in its entirety as follows:

                  "(m) `Restricted Share Unit' means a right, granted under
            Section 5(e), to receive Shares or cash at the end of a specified
            deferral period."

            3.    Subsection (b) of Section 4 of the Plan is amended to read in
      its entirety as follows:

                  "(b) Subject to adjustment as provided in Section 4(c) hereof,
            (i) the maximum number of Shares with respect to which Options may
            be granted during any calendar year to any Eligible Person under
            this Plan shall be 200,000 Shares, and (ii) the maximum number of
            Shares reserved for issuance in connection with Awards of Restricted
            Shares and Restricted Share Units shall be limited to 20% of the
            number of Shares reserved for issuance pursuant to Section 4(a)
            hereof."

            4.    The second sentence of subsection (c)(i) of Section 5 of the
      Plan is amended to read as follows:

                  "Performance objectives may vary from Eligible Person to
            Eligible Person and shall be based upon one or more of the following
            performance criteria as the Committee may deem appropriate: total
            stockholder return, earnings, earnings per share, increase in
            reserves per share, increase in value of proved reserves and other
            reserve-based measures, operating income, net income, pro forma net
            income, return on stockholders' equity, return on designated assets,
            net asset value, economic value added, revenues, expenses, operating
            profit margin, operating cash flow, cash flow per share, and net
            profit margin."

<PAGE>

            5.    A new subsection (e) is added to Section 5 of the Plan to read
      in its entirety as follows:

                  "(e) Restricted Share Units. The Committee is authorized to
            grant Restricted Share Units to Eligible Persons on the following
            terms and conditions:

                        (i) Award and Restrictions. Delivery of Shares or cash,
                  as the case may be, will occur upon expiration of the deferral
                  period specified for Restricted Share Units by the Committee
                  (or, if permitted by the Committee, as elected by the Eligible
                  Person). In addition, Restricted Share Units shall be subject
                  to such restrictions as the Committee may impose, if any
                  (including, without limitation, the achievement of performance
                  criteria if deemed appropriate by the Committee), at the date
                  of grant or thereafter, which restrictions may lapse at the
                  expiration of the deferral period or at earlier or later
                  specified times, separately or in combination, in installments
                  or otherwise, as the Committee may determine.

                        (ii) Forfeiture. Except as otherwise determined by the
                  Committee at date of grant or thereafter, upon termination of
                  employment during the applicable deferral period or portion
                  thereof to which forfeiture conditions apply (as provided in
                  the Award Agreement evidencing the Restricted Share Units), or
                  upon failure to satisfy any other conditions precedent to the
                  delivery of Shares or cash to which such Restricted Share
                  Units relate, all Restricted Share Units that are at that time
                  subject to deferral or restriction shall be forfeited;
                  provided, however, that the Committee may provide, by rule or
                  regulation or in any Award Agreement, or may determine in any
                  individual case, that restrictions or forfeiture conditions
                  relating to Restricted Share Units will be waived in whole or
                  in part in the event of terminations of employment resulting
                  from specified causes, and the Committee may in other cases
                  waive in whole or in part the forfeiture of Restricted Share
                  Units.

                        (iii) Dividend Equivalents. Unless otherwise determined
                  by the Committee at date of grant, Dividend Equivalents on the
                  specified number of Shares covered by a Restricted Share Unit
                  shall be either (A) paid with respect to such Restricted Share
                  Unit at the dividend payment date in cash or in unrestricted
                  Shares having a Fair Market Value equal to the amount of such
                  dividends, or (B) deferred with respect to such Restricted
                  Share Unit and the amount or value thereof automatically
                  deemed reinvested in additional Restricted Share Units or
                  other Awards, as the Committee shall determine or permit the
                  Participant to elect."

                                      -2-