THIRD AMENDMENT TO ATWOOD OCEANICS BENEFIT EQUALIZATION PLAN

Exhibit 10.26

THIRD AMENDMENT TO

ATWOOD OCEANICS BENEFIT EQUALIZATION PLAN

THIS AMENDMENT, by Atwood Oceanics, Inc., a Texas corporation (the “Sponsor”),

W I T N E S S E T H:

WHEREAS, the Sponsor has previously executed the Plan known as “Atwood Oceanics Benefit Equalization Plan” (the “Plan”);

WHEREAS the Sponsor has the right to amend the Plan; and

WHEREAS, the Sponsor has determined that the Plan should be amended in the manner hereinafter set forth;

NOW, THEREFORE, the Plan is amended as follows:

1. The recitals are amended in their entirety to read as follows:

WHEREAS, the Sponsor desires to establish a program that will compensate for certain limits on elective deferrals and employer matching contributions imposed on certain executives and other highly compensated managers under the Atwood Oceanics Retirement Plan and the Atwood Oceanics Pacific Retirement Plan;

WHEREAS, the Sponsor desires to provide the opportunity for certain executives and other highly compensated managers to accumulate supplemental funds for retirement or special needs prior to retirement through the deferral of portions of their compensation; and

WHEREAS, the plan hereby established is intended to constitute an unfunded plan of deferred compensation for a select group of management or highly compensated employees;

2. Section 3.1 is amended, effective January 1, 2005, in its entirety to read as follows:

3.1 Deferral Agreements. A Deferral Agreement shall be an agreement in a form satisfactory to the Administrative Committee to prospectively receive one or more items of compensation from the Employer in a reduced amount and to have the Administrative Committee credit an amount equal to the amount of the reduction to the Member’s Account. The Deferral Agreement shall specify (i) whether any amounts shall be deferred under this Plan as 401(k) Spillover Deferrals, and (ii) the amount, if any, of the Member’s Regular Deferral. Any such Deferral Agreement shall be revocable or irrevocable in accordance with its terms, provided that no revocation shall be effective prior to the Deferral Agreement Effective Date that would apply if the revocation were treated as a new Deferral Agreement or permit payment to the Member of any amount deferred prior to the date of revocation. A Member shall be entitled to prospectively modify his Deferral Agreement at least once a year. The Administrative Committee shall establish and announce to the Members the rules governing the administration of Elective Deferrals, including any limitations upon the amount that may be deferred and the procedures for and any limitations upon a Member’s right to revoke or change his designation. Elective Deferrals may be made by periodic payroll deductions or by other methods, as determined from time to time by the Administrative Committee.

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3. Section 9.1 is amended, effective December 1, 2008, in its entirety to read as follows:

9.1 Sponsor’s Right to Amend. Subject to the limitations prescribed by Section 9.2, the Sponsor may at any time and from time to time modify or amend the Plan in whole or in part. In addition, the President of the Sponsor may at any time and from time to time modify or amend the Plan in any manner that is not expected to substantially increase the number of Members, materially increase the administrative costs of the Plan, or have a material financial effect on any Employer. Any amendment shall be made by an instrument in writing, executed by the appropriate officer, setting forth the nature of the amendment and its effective date.

IN WITNESS WHEREOF, Atwood Oceanics, Inc. has executed this Amendment this 4th day of December, 2008 to be effective October 1, 2008, except as otherwise specified or as otherwise required to comply with applicable provisions of the Code, any statute amending the Code, or any other applicable statute, regulation, or ruling.

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