EXHIBIT 3.4

                          AMENDMENT TO RIGHTS AGREEMENT

         Amendment to Rights Agreement, dated as of October 23, 2001 ("Amendment
to Rights Agreement"), between Patterson-UTI Energy, Inc., a Delaware
corporation (the "Company"), and Continental Stock Transfer & Trust Company, a
New York corporation (the "Rights Agent").

                                   WITNESSED:

         WHEREAS, the Company and the Rights Agent entered into a Rights
Agreement dated as of January 2, 1997 (the "Rights Agreement"); and

         WHEREAS, the parties to the Rights Agreement desire to enter into this
Amendment to Rights Agreement to amend the Rights Agreement in certain respects.

         NOW, THEREFORE, in consideration of the premises and agreements
contained herein and in the Rights Agreement, the parties agree as follows:

         1. The words "one one-hundredth of a Preferred Share" wherever they
appear in the Rights Agreement or in any of the exhibits to the Rights Agreement
shall be deleted and in each such instance the words "one one-thousandth of a
Preferred Share" shall be substituted therefor.

         2. The dollar figure $166 appearing in the second line of Subsection
(b) of Section 7 of the Rights Agreement shall be deleted, and the dollar figure
$75 shall be substituted therefor and shall also be substituted wherever the
dollar figure $166 appears in the Rights Agreement or in any of the exhibits to
the Rights Agreement.

         3. The date January 2, 2007 appearing in the third to the last line of
Subsection (a) of Section 7 of the Rights Agreement shall be deleted, and the
date October 23, 2011 shall be substituted therefor, and such date shall also be
substituted for the date January 2, 2007 wherever that date appears in the
Rights Agreement or in any of the exhibits to the Rights Agreement.

         4. This Amendment to Rights Agreement may be executed in counterparts,
both of which shall be considered one and the same agreement.

         5. The Rights Agreement, as amended by this Amendment to Rights
Agreement, shall remain in full force and effect.



         IN WITNESS WHEREOF, the parties hereto have caused this Amendment to
Rights Agreement to be duly executed and attested, all as of the day and year
first above written.

Attest:                                PATTERSON-UTI ENERGY, INC.

By: /s/ Michelle R. Martini            By: /s/ Jonathan D. Nelson
    -------------------------------        -----------------------------------
                                           Jonathan D. Nelson, Chief Financial
                                           Officer

Attest:                                CONTINENTAL STOCK TRANSFER &
                                       TRUST COMPANY, as Rights Agent

By: /s/ Thomas Jennings                By: /s/ William F. Seegraber
    -------------------------------        -----------------------------------
    Thomas Jennings                        William F. Seegraber
    Asst. Secretary                        Vice President


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