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                                                                     EXHIBIT 4.3

                                 AMENDMENT NO. 1
                               TO RIGHTS AGREEMENT

         This Amendment No. 1 (the "Amendment") to the Rights Agreement (the
"Rights Agreement") dated as of July 14, 1998 between Parker Drilling Company, a
Delaware corporation (the "Company"), and Norwest Bank Minnesota, N.A. (the
"Rights Agent") is effective as of September 22, 1998.

                                    RECITALS

         The Company desires to amend the Rights Agreement to revise the
redemption provisions of Section 24(b) and remove the restrictions on redeeming
the Rights Agreement if the Board of Directors is not comprised of Continuing
Directors, and certifies that the Amendment complies with the terms of Section
29 of the Rights Agreement.

         NOW, THEREFORE, in consideration of the premises and the mutual
agreements herein set forth, the parties hereto agree as follows:

         1. Section 24(b) of the Rights Agreement is hereby amended to read as
follows:

                  "(b) The Board of Directors of the Company may, at its option,
         at any time prior to the Shares Acquisition Date redeem all but not
         less than all the then outstanding Rights at a redemption price of one
         cent ($.01) per Right then outstanding, appropriately adjusted to
         reflect any adjustment in the number of Rights outstanding pursuant to
         Section 12(i) herein (such redemption price being hereinafter referred
         to as the "Redemption Price"). Any such redemption of the Rights by the
         Board of Directors may be made effective at such time, on such basis
         and with such conditions as the Board of Directors in its sole
         discretion may establish."

         2. Section 1, Certain Definitions, is hereby amended to delete the
definitions of "Transaction" and "Transaction Person."

         IN WITNESS WHEREOF, the parties hereto have caused this Amendment No. 1
to the Rights Agreement to be duly executed, effective as of the day and year
first above written.

                                             PARKER DRILLING COMPANY


                                             By    /s/ James J. Davis
                                               ---------------------------------
                                                James J. Davis
                                                Senior Vice President -- Finance


                                             NORWEST BANK MINNESOTA, N.A.,
                                             As Rights Agent


                                             By       /s/ Barbara M. Novak
                                               ---------------------------------
                                               Name:  Barbara M. Novak
                                               Title: Vice President