FIRST AMENDMENT TO ATWOOD OCEANICS, INC. AMENDED AND RESTATED 2007 LONG-TERM INCENTIVE PLAN

EXHIBIT 10.3

FIRST AMENDMENT TO

ATWOOD OCEANICS, INC.

AMENDED AND RESTATED 2007 LONG-TERM INCENTIVE PLAN

WHEREAS, Atwood Oceanics, Inc., a Texas corporation (the “Company”), has established and maintains the Atwood Oceanics, Inc. Amended and Restated 2007 Long-Term Incentive Plan (the “Plan”); and

WHEREAS, pursuant to Section 10.1 of the Plan, the Company has the right to amend the Plan at any time by action of the Board of Directors of the Company (the “Board”), subject to prior approval by the Company’s stockholders to the extent such approval is determined to be required by applicable legal and/or stock exchange requirements; and

WHEREAS, the Company desires to amend the Plan to remove the requirement that both the Company and the participant execute the applicable award agreement; and

WHEREAS, this amendment is not a material modification that is subject to prior stockholder approval;

NOW, THEREFORE, the Plan is amended as follows:

1. Section 2.4 of the Plan is hereby replaced with the following sentence:

“‘Award Notice’ means any written notice of grant that establishes the terms, conditions, restrictions, and/or limitations applicable to an Award in addition to those established by the Plan and by the Committee’s exercise of its administrative powers.”

2. The fourth sentence of Section 5.1 of the Plan is hereby replaced with the following sentence:

“Each grant of an Option shall be evidenced by an Award Notice which shall set forth the terms and conditions of such Option and be in such form as the Committee may from time to time approve subject to the requirements of Section 5.2.”

3. The fifth sentence of Section 7.1 of the Plan is hereby replaced with the following sentence:

“Each grant of a SAR shall be evidenced by an Award Notice which shall set forth the terms and conditions of such SAR and be in such form as the Committee may from time to time approve, subject to the requirements of the Plan.”

4. The second sentence of Section 8.1 of the Plan is hereby replaced with the following sentence:

“Each Award of Performance Units shall be evidenced by an Award Notice which shall set forth the terms and conditions of such Performance Units and be in such form as the Committee may from time to time approve, subject to the requirements of Section 8.2.”

5. The term “Award Agreement” is hereby replaced with the term “Award Notice” throughout the Plan.

This First Amendment to the Plan shall be effective as of the date it is originally approved by the Board.