EXHIBIT 4.1

CERTIFICATE OF ADJUSTMENT
OF
ATWOOD OCEANICS, INC.

TO:     Continental Stock Transfer & Trust Company, Rights Agent

17 Battery Place

New York, NY 10004-1123

Attention: Vivina Mendez

Facsimile: 212-616-7616

Atwood Oceanics, Inc., a corporation organized and existing under the laws of the State of Texas (the “Company”), does hereby certify as follows:

1.    The Company is a party to the Rights Agreement (the “Rights Agreement”) entered into as of October 18, 2002, between the Company and Continental Stock Transfer & Trust Company (the “Rights Agent”). The Rights Agreement was previously modified by a Certificate of Adjustment dated March 17, 2006.

         2.    On June 11, 2008, the Company announced that its Board of Directors declared a two-for-one stock split to be effected in the form of a 100% stock dividend (the “Stock Split”), pursuant to which, on July 11, 2008 (the “Split Date”), the Company will distribute to each holder of record of Common Stock, par value $1.00 per share, of the Company (“Common Stock”) at the close of business on June 27 , 2008 (the “Record Date”), one additional share of Common Stock for each outstanding share of Common Stock held of record by such holder on the Record Date (and with one Right, as defined in the Rights Agreement, attached to each such additional share of Common Stock).

         3.    In accordance with the Rights Agreement, as previously modified, each share of Common Stock is currently accompanied by a one two-thousandth of a share of Series A Junior Participating Preferred Stock purchase right (a “Right”). Subject to the terms and conditions of the Rights Agreement, each Right, after it becomes exercisable pursuant to the terms of the Rights Agreement, and until such time as it expires or is redeemed, entitles the holder to purchase Series A Junior Participating Preferred Stock from the Company at a Purchase Price (as defined in the Rights Agreement) of $150.00, before giving effect to the Stock Split.

         4.    As a result of the Stock Split and pursuant to Section 11(n) of the Rights Agreement, effective as of July 11, 2008, (a) each outstanding share of Common Stock (including shares issued in respect of the Stock Split) will continue to have one Right associated with it, and (b) each Right, after it becomes exercisable pursuant to the terms of the Rights Agreement, and until such time as it expires or is redeemed, will, subject to the terms and conditions of the Rights Agreement, entitle the holder to purchase one four-thousandth of a share of Series A Junior Participating Preferred Stock from the Company at a Purchase Price of $150.00.

         5.    Pursuant to Section 11(n) of the Rights Agreement, the number of outstanding Rights will be deemed increased by 100% such that each Common Share outstanding immediately after the Stock Split shall have issued with respect to it one Right upon the Split Date.

         6.    Pursuant to Section 23 of the Rights Agreement, the Redemption Price of each Right will be deemed decreased by one-half from $0.005 to $0.0025 upon the Split Date.

         7.    Upon and following the Split Date, pursuant to the Certificate of Designations setting forth the rights, preferences and limitations of the Preferred Shares, as a result of the Stock Split, each Preferred Share shall be entitled to an aggregate dividend of 4000 multiplied times the dividend declared per Common Share. If no dividend is declared in a quarter, the Preferred Shares are entitled to a minimum preferential quarterly dividend of $0.01 per share. In the event of liquidation, the holder of the Preferred Shares will be entitled to the greater of a minimum preferential liquidation payment of $1.00 per share and an aggregate payment of 4000 multiplied times the payment made per Common Share. Each Preferred Share will have 4000 votes, voting together with the Common Shares. Finally, in the event of any merger, consolidation or other transaction in which Common Shares are exchanged, each Preferred Share will be entitled to receive 4000 multiplied times the amount received per Common Share.

         8.    Pursuant to the requirements of Section 12 of the Rights Agreement, this Certificate of Adjustment is being delivered to Continental Stock Transfer & Trust Company as rights agent under the Rights Agreement and as transfer agent for the Common Stock.

IN WITNESS WHEREOF, the undersigned has executed this Certificate of Adjustment this 25th day of June, 2008.

ATWOOD OCEANICS, INC.

By:   /s/ James M. Holland   

       James H. Holland
       Senior Vice President and Secretary