FIRST AMENDMENT TO ATWOOD OCEANICS BENEFIT EQUALIZATION PLAN

Exhibit 10.24

FIRST 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 1.9 is amended to read in its entirety as follows:

1.9 Change in Control. “Change in Control” shall mean a change in the ownership or effective control of the Employer or in the ownership of a substantial portion of the assets of the Employer, in accordance with Section 409A of the Code and any rules and regulations promulgated thereunder.

2. Section 3.4 is amended by deleting the last sentence thereof.

3. Sections 6.1 and 6.2 are amended to read in their entirety as follows:

6.1 Time of Distribution. In the event of the Member’s Separation other than on account of death, each Member shall begin receiving his distribution six months following the Member’s Separation other than on account of death. In the event of a Change in Control, each Member shall receive a distribution as soon as practical after such Change in Control. In the event of Separation on account of death, each Beneficiary shall receive a distribution as soon as practical after the Member’s death.

6.2 Distribution Method. Distributions shall be paid in cash. Distributions made on account of Separation other than on account of death shall be made in equal annual installments for a period of five years. Distributions made on account of a Change in Control or Separation on account of death shall be made in the form of a single sum.

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IN WITNESS WHEREOF, Atwood Oceanics, Inc. has executed this Amendment this 14 day of December, 2005 to be effective January 1, 2005 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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