Walter Scott Jr.

Exhibit 10.33

EXECUTION COPY

December 12, 2005

Mr. Bobby S. Shackouls

717 Texas Avenue, Suite 2100

Houston, TX 77002

Dear Bobby:

This letter agreement sets forth our agreement regarding your anticipated appointment to the Board of Directors (the “Board”) of ConocoPhillips (“ConocoPhillips”) following the anticipated acquisition (the “Merger”) of Burlington Resources Inc. (the “Company”) by ConocoPhillips pursuant to the Agreement and Plan of Merger by and among the Company, ConocoPhillips, and Cello Acquisition Corp. dated as of December 12, 2005 (the “Merger Agreement”), as well as our agreements with respect to certain restrictive covenants you have agreed to be bound by in connection with the transaction and with respect to certain post-closing rights to an office and secretarial services that we will provide you.

In consideration of the restrictive covenants set forth below and in recognition of your record of expertise and leadership at the Company, ConocoPhillips and the Company agree, effective as of the Closing Date (as defined in the Merger Agreement) to your appointment to the Board as one of the Company nominees pursuant to Section 6.2 of the Merger Agreement, and further agree that ConocoPhillips shall cause you to be provided at the expense of ConocoPhillips or the Company with suitable office space and a secretary in the 717 Texas building consistent with the Company’s historical practice for retired Chairmen of the Company for not less than five years following the Closing Date; your current secretary shall continue to be your secretary during this period for so long as she remains employed, and, in the event of her retirement or other termination, her successor shall be reasonably satisfactory to you. Notwithstanding the foregoing, in the event that at any time during the five-year period following the Closing Date, you become engaged in a full-time executive capacity with an organization that does, or would ordinarily be expected to, provide secretarial services and office support to an individual performing your functions, your rights under this paragraph to an office and secretarial services shall immediately terminate. For the avoidance of doubt, the Company has advised ConocoPhillips that you are currently entitled to a car and club memberships, and we will honor that entitlement upon your termination of employment by transferring your car and club memberships to you upon such termination.

In consideration of the foregoing, you hereby agree and acknowledge that, effective as of the Closing Date, Section 7 of the letter agreement between you and the Company, dated as of July 7, 1999 is hereby amended such that the non-competition covenant set forth therein shall apply following your termination of employment as an officer of the Company for any reason from the date of such termination through the second anniversary of such termination.

If the Merger Agreement is terminated before the Closing Date, this letter agreement will be null and void. Otherwise, this letter agreement represents a binding agreement between us, and may not be amended without the written agreement of all parties hereto. Any dispute hereunder shall be resolved in accordance with the dispute resolution provisions of the Employment Agreement.

Date: December 12, 2005