SECOND AMENDMENT TO ATWOOD OCEANICS BENEFIT EQUALIZATION PLAN

Exhibit 10.25

SECOND 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. Section 1.2 is amended in its entirety to read as follows:

1.2 Active Member. “Active Member” shall mean an individual designated as such by the President of the Sponsor.

2. Section 1.18 is amended in its entirety to read as follows:

1.18 Eligible Class. “Eligible Class” shall mean, with respect to a Plan Year, all Employees who receive compensation from the Sponsor in excess of the dollar limit in effect with respect to the Retirement Plan for such Plan Year under section 401(a)(17) of the Code.

3. Section 2.1 is amended in its entirety to read as follows:

2.1 Designation of Active Members by President. The President of the Sponsor may designate from time to time such members of the Eligible Class as he shall from time to time determine to be Active Members, provided that there shall not be more than 20 Active Members at any time. An Active Member shall continue as such until the earlier of (i) the date the individual ceases to be a member of the Eligible Class, or (ii) the date specified by the President of the Sponsor as the date on which the individual shall no longer be an Active Member.

4. Section 2.2 is amended in its entirety to read as follows:

2.2 Commencement of Participation. An Employee shall become a Member on the later of (i) the effective date of the adoption of the Plan by such individual’s Employer, or (ii) the date on which such individual is first designated as an Active Member by the President of the Sponsor.

5. Section 2.4 is amended in its entirety to read as follows:

2.4 Recommencement of Participation by Former Members. A former Member shall again become a Member on the date, if any, on which such individual is again designated as an Active Member by the President of the Sponsor.

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IN WITNESS WHEREOF, Atwood Oceanics, Inc. has executed this Amendment this 4th day of December, 2008 to be effective October 1, 2008, 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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