First Amendment to 2004 Stock Incentive Plan

EXHIBIT 10.2

FIRST AMENDMENT TO THE

REMINGTON OIL AND GAS CORPORATION

2004 STOCK INCENTIVE PLAN

April 13, 2005

WHEREAS, Remington Oil and Gas Corporation (the “Company”) has heretofore adopted the Remington Oil and Gas Corporation 2004 Stock Incentive Plan (the “Plan”);

WHEREAS, the Company reserved the right to amend the Plan and any awards pursuant to Section 1.5 of the Plan (subject to the restrictions on amendment set forth therein); and

WHEREAS, the Company, acting through its Board of Directors has determined that the Plan should be amended to change the definitions of “Change in Control,” “Cause” and “Common Stock” under the Plan;

NOW THEREFORE, the Plan is hereby amended as follows:

1. The definition of a “Change in Control” in Section 1.2 of the Plan is hereby amended by deleting subparagraph (ii) thereof and inserting the following:

“(ii) The acquisition or holding of direct or indirect beneficial ownership (as defined under Rule 13d-3 of the Exchange Act) of securities of the Company representing the aggregate 30% or more of the total combined voting power of the Company’s then issued and outstanding voting securities by any person, entity or group of associated persons or entities acting in concert, other than an employee benefit plan of the Company or of any subsidiary of the Company, or any entity holding such securities for or pursuant to the terms of any such plan. The Directors may, by a majority vote, determine the acquisition of 30%-49.9% is not a hostile action and therefore does not trigger a change of control.”

2. The definition of “Cause” in Section 1.2 of the Plan is hereby amended to read as follows:

      “Cause” for termination of any Participant who is an eligible employee in either the Company’s Employee Severance Plan or Executive Severance Plan (the “Severance Plans”) shall mean termination of the Participant for “Cause” as defined in such Severance Plans or termination of employment by the Participant for “Good Reason” as defined in such Severance Plans, the relevant portions of which are incorporated herein by reference. If a Participant is not an eligible employee in either of the Severance Plans, “Cause” means (i) the willful commission by a Participant of a criminal or other act that causes or is likely to cause substantial economic damage to the Company or an Affiliate or substantial injury to the business reputation of the Company or Affiliate; (ii) the commission by a Participant of an act of fraud in the performance of such Participant’s duties on behalf of the Company or an Affiliate; or (iii) the continuing willful failure of a Participant to perform the duties of such Participant to the Company or an Affiliate (other than such failure resulting from the Participant’s incapacity due to

physical or mental illness) after written notice thereof (specifying the particulars thereof in reasonable detail) and a reasonable opportunity to be heard and cure such failure are given to the Participant by the Committee. For purposes of the Plan, no act, or failure to act, on the Participant’s part shall be considered “willful” unless done or omitted to be done by the Participant not in good faith and without reasonable belief that the Participant’s action or omission was in the best interest of the Company or an Affiliate, as the case may be.

3. The definition of “Common Stock” in Section 1.2 of the Plan is hereby amended to read as follows:

“Common Stock” means the common stock of the Company, par value $.01 per share.

4. As amended hereby, the Plan is ratified and affirmed in all respects.

REMINGTON OIL AND GAS CORPORATION