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                                                                     EXHIBIT 4.1


                       FIRST AMENDMENT TO RIGHTS AGREEMENT


                  This Amendment, dated as of October 19, 1998 (the
"Amendment"), is between Bayard Drilling Technologies, Inc., a Delaware
corporation (the "Company"), and Norwest Bank Minnesota, N.A., a national
banking association (the "Rights Agent"),

                              W I T N E S S E T H:

                  WHEREAS, the Company and the Rights Agent are parties to a
Rights Agreement dated as of August 21, 1998 (the "Agreement"); and

                  WHEREAS, pursuant to Section 27 of the Agreement, the Company
and the Rights Agent desire to amend the Agreement set forth below.

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

                  Section 1. Amendments to Section 1.

                  (a) The definition of "Beneficial Owner" is amended by adding
the following after the words "provided however" in the proviso immediately
following subparagraph (iii) of such definition:

         notwithstanding anything to the contrary contained in this Agreement,
         no Person shall, as a result of the Bayard Stockholder Agreements, be
         deemed to be the "Beneficial Owner" of or to "beneficially own" any
         shares of Common Stock owned by any other Person; and provided further,
         however

                  (b) The definition of Expiration Date is amended by deleting
such definition in its entirety and substituting the following:

                  "Expiration Date" shall mean the earliest of (i) the Final
         Expiration Date, (ii) the time at which the Rights are redeemed as
         provided in Section 23 hereof, (iii) the time at which the Rights
         expire pursuant to Section 13(d) hereof, (iv) the time at which all
         Rights then outstanding and exercisable are exchanged pursuant to
         Section 24 hereof and (v) immediately prior to the "Effective Time" as
         such term is defined in the Merger Agreement. Upon the Expiration Date,
         the Rights shall expire.

                  (c) The definition of "Acquiring Person" is amended by adding
the following at the end of the definition:



                                        

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         Notwithstanding anything in this definition of "Acquiring Person" to
         the contrary, Parent and any Affiliate or Associate thereof shall not
         be or become an Acquiring Person unless and until Parent, together with
         all Affiliates and Associates thereof, becomes the Beneficial Owner of
         20% or more of the shares of Common Stock then outstanding; provided,
         however, that none of Parent and such Affiliates and Associates shall
         become an Acquiring Person if such Person, together with all Affiliates
         and Associates of such Person, shall become the Beneficial Owner of 20%
         or more of the shares of Common Stock then outstanding solely as a
         result of a reduction in the number of shares of Common Stock
         outstanding due to the repurchase of Common Stock by the Company,
         unless and until such time as such Person or any Affiliate or Associate
         thereof shall purchase or otherwise become the Beneficial Owner of
         additional shares of Common Stock constituting 1% or more of the then
         outstanding shares of Common Stock or any other Person (or Persons) who
         is (or collectively are) the Beneficial Owner of shares of Common Stock
         constituting 1% or more of the then outstanding shares of Common Stock
         shall become an Affiliate or Associate of such Person unless, in either
         such case, such Person, together with all Affiliates and Associates of
         such Person, is not then the Beneficial Owner of 15% or more of the
         shares of Common Stock then outstanding; provided, however, that this
         sentence shall terminate at the time of the termination of the Company
         Stock Option Agreement unless at or prior to the time of such
         termination, Parent has exercised the option granted thereby so as to
         become the Beneficial Owner of 15% or more of the shares of Common
         Stock then outstanding.

                  (d) The following definitions are added to Section 1 of the
Agreement:

                  "Company Stock Option Agreement" shall mean the Stock Option
         Agreement dated as of October 19, 1998 between Parent and the Company
         providing for, among other things, the grant of an option to purchase
         up to 3,620,595 shares of Common Stock and any amendment to such
         Company Stock Option Agreement that is entered into by the Company at a
         time when the Rights Agreement may be amended.

                  "Bayard Stockholder Agreements" shall mean those agreements
         dated as of October 19, 1998 among Parent and the Subject Stockholders
         providing for among other things, the agreement of the Subject
         Stockholders to vote their shares of Common Stock in favor of the
         Merger and approval and adoption of the Merger Agreement and the
         transactions contemplated thereby and any amendment to such Stockholder
         Agreements that are entered into by the Company at a time when the
         Rights Agreement may be amended.

                  "Merger" shall mean the merger of Merger Sub with and into the
         Company in accordance with the General Corporation Law of the State of
         Delaware and upon the terms and subject to the conditions set forth in
         the Merger Agreement.



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                  "Merger Agreement" shall mean the Agreement and Plan of
         Merger, dated as of October 19, 1998, among Parent, Merger Sub, and the
         Company and any amendment to such Merger Agreement that is entered into
         by the Company at a time when the Rights Agreement may be amended.

                  "Merger Sub" shall mean Nabors Acquisition Corp. VII, a
         Delaware corporation, which is a wholly owned subsidiary of Parent.

                  "Parent" shall mean Nabors Industries, Inc., a Delaware
         corporation.

                  "Subject Stockholders" (individually, a Subject Stockholder)
         shall mean those stockholders of the Company that are parties to any
         Bayard Stockholder Agreement.

                  Section 2. New Section 35.

                  The following is added as a new Section 35:

                  Section 35. Merger Agreement, etc. Except to the extent caused
         by Parent's becoming the Beneficial Owner of any Common Stock other
         than in accordance with the Merger Agreement or the Company Stock
         Option Agreement, none of the execution or delivery of the Merger
         Agreement, the conversion of shares of Common Stock into the right to
         receive common stock of Parent in accordance with Article II of the
         Merger Agreement and the consummation of the Merger or any other
         transaction contemplated by the Merger Agreement, the Company Stock
         Option Agreement or the Bayard Stockholder Agreements in accordance
         with the terms of such agreements, shall cause (i) the Rights to become
         exercisable, (ii) Parent or any of its Subsidiaries to be deemed an
         Acquiring Person, (iii) any such event to be a Flip-In Event or
         Flip-Over Event or (iv) a Stock Acquisition Date, Flip-In Trigger Date
         or the Distribution Date to occur upon any such event.

                  Section 3. Severability. If any term, provision, covenant or
restriction of this Amendment is held by a court of competent jurisdiction or
other authority to be invalid, void or unenforceable, the remainder of the
terms, provisions, covenants and restrictions of this Amendment shall remain in
full force and effect and shall in no way be affected, impaired or invalidated.

                  SECTION 4. GOVERNING LAW. THIS AMENDMENT SHALL BE DEEMED TO BE
A CONTRACT MADE UNDER THE LAWS OF THE STATE OF DELAWARE AND FOR ALL PURPOSES
SHALL BE GOVERNED BY AND CONSTRUED IN ACCORDANCE WITH THE LAWS OF SUCH STATE
APPLICABLE TO CONTRACTS MADE AND TO BE PERFORMED ENTIRELY WITHIN SUCH STATE.


 
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                  Section 5. Counterparts. This Amendment may be executed in any
number of counterparts and each of such counterparts shall for all purposes be
deemed to be an original, and all such counterparts shall together constitute
but one and the same instrument.

                  Section 6. Effect of Amendment. Except as expressly modified
herein, the Agreement shall remain in full force and effect.

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

                                BAYARD DRILLING TECHNOLOGIES, INC.


                                By /s/ JAMES E. BROWN
                                  ------------------------------
                                   Name:  James E. Brown
                                   Title: President


                                NORWEST BANK MINNESOTA, N.A.


                                By /s/ JOHN BAKER
                                  ------------------------------
                                   Name:  John Baker
                                   Title: Account Manager


 
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