Energy XXI Acquisition Corporation (Bermuda) Limited

EXHIBIT 10.11

Energy XXI Acquisition Corporation (Bermuda) Limited

August 31, 2005

Mr. David Dunwoody

3417 Milam

Houston, Texas 77002-9531

Dear David:

The board of Energy XXI Acquisition Corporation (Bermuda) Limited (the “Company”) has appointed you as a non-executive director. In addition, you are requested to Chair the Remuneration Committee and serve as a member of the Audit and Nomination Committees. I am writing to set out the terms of your appointment. It is agreed that this is a contract for services and is not a contract of employment.

Appointment

Your appointment will be for an initial term of three years commencing on August 31, 2005, unless otherwise terminated earlier by and at the discretion of either party upon one month’s written notice. Continuation of your contract of appointment is contingent on satisfactory performance and re-election at forthcoming AGM’s. Non-executive directors are typically expected to serve two three-year terms, although the board may invite you to serve an additional period.

Time Commitment

Overall we anticipate a time commitment of one to two days per month. This time commitment will include attendance at quarterly board meetings, the AGM, preparation for the meetings, the preparation for such meetings and incidental monthly board activities such as the approval of various resolutions. We plan to have quarterly board meetings (all board meetings will be held outside the U.S.) and concurrent with such meetings, a meeting of the Audit Committee to review the financial results of the Company. For the convenience and depending upon the agenda, we may arrange for certain of these board meetings to be telephonic. In addition, between board meetings, we will relay various board resolutions and other materials each month that require approval.

In addition to the above, we invite you to attend as many of the road show presentations as you wish. In particular, given that you live in the U.S., we hope that you might be able to attend some of the road show presentations in the U.S. We will ask Sunrise to coordinate this activity with you and your schedule.

By accepting this appointment, you have confirmed that you are able to allocate sufficient time to meet the expectations of your role. The agreement of the chairman should be

sought before accepting additional commitments that might impact on the time you are able to devote to your role as a non-executive director of the company.

Role

Non-executive directors have the same general legal responsibilities to the Company as any other director. The board as a whole is collectively responsible for the success of the company. The board:

All directors must take decisions objectively in the interest of the company.

In addition to these requirements of all directors, the role of the non-executive director has the following key elements:

Fees

We have arranged to transfer 25,000 shares of the Company to your name. This shall be your compensation for the initial term. The Company will reimburse you for all reasonable and properly documented expenses you incur in performing the duties of your office.

Outside Interests

It is accepted and acknowledged that you have business interests other than those of the company and have declared any conflicts that are apparent at present. In the event that

you become aware of any potential conflicts of interest, these should be disclosed to the chairman and company secretary as soon as apparent.

Confidentiality

All information acquired during your appointment is confidential to the Company and should not be released, either during your appointment or following termination (by whatever means), to third parties without prior clearance from the chairman.

Your attention is also drawn to the requirements under both legislation and regulation as to the disclosure of price sensitive information. Consequently you should avoid making any statements that might risk a breach of these requirements without prior clearance from the chairman.

Induction

Immediately after appointment, the Company will provide a comprehensive induction. This will include the information pack recommended by the Institute for Chartered Secretaries and Administrators (ICSA), available at www.icsa.org.uk. We will also arrange for meetings with senior management and the Company’s auditors. We will also offer to major shareholders the opportunity to meet you.

Review Process

The performance of individual directors and the whole board and its committees is evaluated annually. If, in the interim, there are any matters which cause you concern about your role, you should discuss them with the chairman as soon as is appropriate.

Insurance

The Company is arranging for directors’ and officers’ liability insurance and it is intended to maintain such cover for the full term of your appointment. As soon as this insurance is place, we shall provide a copy of the policy to you.

Independent Professional Advice

Occasions may arise when you consider that you need professional advice in the furtherance of your duties as a director. Circumstances may occur when it will be appropriate for you to seek advice from independent advisors at the Company’s expense. Under such circumstances, we request that you advise the chairman prior to engaging the advisor and the estimated costs thereof. The Company will reimburse the full cost of expenditure incurred.

Committees

There are three committees of the board currently: the audit, remuneration and nomination committees. Currently, the Audit committee is the most active committee. Just prior to a business combination, the remuneration committee will increase its level of activity as we will then begin to have employees once a business combination is completed.

Please sign this letter agreement, retain a copy for your files, and return a copy to me via PDF file.