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                                                                     EXHIBIT 4.1

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                            NABORS INDUSTRIES, INC.,

                                   as Issuer,

                                       and

                             NABORS INDUSTRIES LTD.,

                                  as Guarantor,


                             ZERO COUPON CONVERTIBLE

                           SENIOR DEBENTURES DUE 2021


                          SECOND SUPPLEMENTAL INDENTURE

                          DATED AS OF OCTOBER 25, 2004


                 J.P. MORGAN TRUST COMPANY, NATIONAL ASSOCIATION
                        (as successor to Bank One, N.A.),

                                   as Trustee


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                 This SECOND SUPPLEMENTAL INDENTURE (this "Second Supplemental
Indenture"), dated as of October 25, 2004, is among Nabors Industries, Inc., a
Delaware corporation, as issuer (the "COMPANY"), Nabors Industries, Ltd., a
Bermuda exempted company, as guarantor (the "GUARANTOR"), and J.P. Morgan Trust
Company, National Association (as successor to Bank One, N.A.), a national
banking association, as trustee (the "TRUSTEE").

                             RECITALS OF THE COMPANY

                  WHEREAS, the Company and the Trustee entered into an
Indenture, dated as of February 5, 2001, as amended and supplemented by the
First Supplemental Indenture thereto, dated as of June 21, 2002, and this Second
Supplemental Indenture (as so amended and supplemented, the "Indenture"),
pursuant to which the Company issued $1,381,200,000 in aggregate principal
amount at maturity of Zero Coupon Convertible Senior Debentures due 2021 (each a
"Security", collectively the "Securities");

                  WHEREAS, the Company and the Guarantor desire to execute this
Second Supplemental Indenture to add additional covenants by the Company for the
benefit of the Holders and to amend Sections 3.07 and 3.10 of the Indenture in
certain respects;

                  WHEREAS, Section 9.01(4) of the Indenture provides that the
Company and the Guarantor may enter into one or more supplemental indentures
without the written consent of any Holders to make any change that does not
adversely affect the right of any Holder;

                  WHEREAS, the Board of Directors of each of the Company and of
the Guarantor (or a duly authorized committee thereof) has duly adopted
resolutions authorizing the Company and the Guarantor, respectively, to execute
and deliver this Second Supplemental Indenture; and

                  WHEREAS, all the conditions and requirements necessary to make
this Second Supplemental Indenture, when duly executed and delivered, a valid
and binding agreement in accordance with its terms for the purposes herein
expressed, have been performed and fulfilled.


                  NOW, THEREFORE, THIS SECOND SUPPLEMENTAL INDENTURE
WITNESSETH:

                  For and in consideration of the premises provided for herein
by the Holders thereof, it is mutually covenanted and agreed, for the equal and
proportionate benefit of all Holders of the Securities, as follows:

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                                    ARTICLE 1

                              RELATION TO INDENTURE


         SECTION 1.1 RELATION TO INDENTURE.

                  This Second Supplemental Indenture constitutes an integral
part of the Indenture.

         SECTION 1.2 DEFINITIONS.

                  For all purposes of this Second Supplemental Indenture, except
as expressly provided for or unless the context otherwise requires:

                  (1) Capitalized terms used but not defined in this Second
Supplemental Indenture shall have the respective meanings assigned to them in
the Indenture; and

                  (2) All references in this Second Supplemental Indenture to
Articles and Sections, unless otherwise specified, refer to the corresponding
Articles and Sections of this Second Supplemental Indenture.

                                    ARTICLE 2

                           REDEMPTION AND REPURCHASES


         SECTION 2.1 EXCHANGE ARRANGEMENT ON CALL FOR REDEMPTION.

                  Section 3.07 of the Indenture is hereby amended by deleting it
in its entirety and substituting in place thereof the following:

                  Section 3.07. [INTENTIONALLY OMITTED].

         SECTION 2.2 EFFECT OF REPURCHASE NOTICE OR FUNDAMENTAL CHANGE
REPURCHASE NOTICE.

                  The last paragraph of Section 3.10 of the Indenture is hereby
amended by deleting it in its entirety and substituting in place thereof the
following:

                  There shall be no repurchase of any Securities pursuant to
         Section 3.08 hereof or repurchase pursuant to Section 3.09 hereof if
         there has occurred (prior to, on or after, as the case may be, the
         giving, by the Holders of such Securities, of the required Repurchase
         Notice or Option to Elect Repurchase Upon a Fundamental Change, as the


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         case may be) and is continuing an Event of Default (other than a
         default in the payment of the Purchase Price or Fundamental Change
         Purchase Price, as the case may be, with respect to such Securities).


                                    ARTICLE 3

                              ADDITIONAL COVENANTS


         SECTION 3.1 PAYMENT OF PURCHASE PRICE IN CASH.

                  The following new Section 4.12 is hereby added to the
Indenture:

                  SECTION 4.12. PAYMENT OF PURCHASE PRICE IN CASH.

                  The Company and the Guarantor covenant and agree for the
         benefit of each Holder that in any Company Notice issued pursuant to
         Section 3.08 of the Indenture, the Company shall in all circumstances
         elect to pay the Purchase Price solely in cash.

         SECTION 3.2 CONVERSION PAYMENTS IN CASH.

                  The following new Section 4.13 is hereby added to the
Indenture:

                  SECTION 4.13. CONVERSION PAYMENTS IN CASH.

                  (a) The Company and the Guarantor covenant and agree for the
         benefit of each Holder that any written notice issued by the Company
         pursuant to Section 11.02 of the Indenture shall in all circumstances
         specify that the Company shall make payment solely in cash for all
         Securities submitted for conversion unless the Full Cash Price (as
         defined below) for a Security is greater than the Principal Amount
         thereof, in which case the Company shall (x) pay in cash the percentage
         of the Full Cash Price equal to the quotient obtained by dividing the
         Principal Amount of such Security by the Full Cash Price for such
         Security, and (y) pay the remaining portion of the payment for such
         Securities either, at the option of the Company, (i) by delivery of a
         number of shares of Common Stock equal to the quotient obtained by
         dividing (A) the excess of the Full Cash Price for such Security over
         the Principal Amount of such Security by (B) the Sale Price of the
         Common Stock for the Trading Day immediately prior to the related
         Conversion Date (and cash in lieu of fractional shares of Common Stock)
         or (ii) in cash. The "FULL CASH PRICE" shall be equal to the Sale Price
         of the Common Stock on the Trading Day immediately prior to the related
         Conversion Date, multiplied by the Conversion Rate in effect on such
         Trading Day.


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                  (b) The calculation set forth in Section 4.13(a) shall be made
         by the Company and the Guarantor. The Trustee shall have no duty to
         make the calculation set forth in Section 4.13(a) and takes no
         responsibility for any calculation made by the Company or the Guarantor
         pursuant to Section 4.13(a). Each Exchange Agent (other than the
         Company or one of its Affiliates) shall have the same protection under
         this Section 4.13(b) as the Trustee.


                                    ARTICLE 4

                            MISCELLANEOUS PROVISIONS


         SECTION 4.1 RATIFICATION OF INDENTURE.

                  Except as expressly modified or amended hereby, the Indenture
continues in full force and effect and is in all respects confirmed and
preserved.

         SECTION 4.2 EFFECTIVENESS.

                  This Second Supplemental Indenture shall be effective as of
the date first written above.

         SECTION 4.3 CONFLICT WITH THE TRUST INDENTURE ACT.

                  If any provision of this Second Supplemental Indenture
modifies or excludes any provision of the Trust Indenture Act that is required
under such Act to be part of and govern this Second Supplemental Indenture, the
latter provision of the Trust Indenture Act shall control. If any provision
hereof modifies or excludes any provision of the Trust Indenture Act that may be
so modified or excluded, the latter provision of the Trust Indenture Act shall
be deemed to apply to this Second Supplemental Indenture, as so modified or
excluded, as the case may be.

         SECTION 4.4 SECURITIES DEEMED CONFORMED.

                  As of the date hereof, the provisions of each Security then
outstanding shall be deemed to be conformed, without the necessity for any
reissuance or exchange of such Security or any other action on the part of the
Holders, the Company, the Guarantor or the Trustee, so as to reflect this Second
Supplemental Indenture.

         SECTION 4.5 NO ADDITIONAL TRUSTEE OBLIGATIONS.

                  No duties, responsibilities or liabilities are assumed, or
shall be construed to be assumed, by the Trustee by reason of this Second
Supplemental Indenture. This Second


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Supplemental Indenture is executed and accepted by the Trustee subject to all
the terms and conditions set forth in the Indenture with the same force and
effect as if those terms and conditions were repeated at length herein and made
applicable to the Trustee with respect hereto.

         SECTION 4.6 SUCCESSORS.

                  All agreements of the Company, the Guarantor and the Trustee
in this Second Supplemental Indenture and in the Indenture shall bind their
respective successors.

         SECTION 4.7 BENEFITS OF SECOND SUPPLEMENTAL INDENTURE.

                  Nothing in this Second Supplemental Indenture, express or
implied, shall give to any Person, other than the parties hereto and their
successors hereunder and the Holders, any benefit or any legal or equitable
right, remedy or claim under this Second Supplemental Indenture.

         SECTION 4.8 GOVERNING LAW.

                  THE LAW OF THE STATE OF NEW YORK SHALL GOVERN AND BE USED TO
CONSTRUE AND ENFORCE THIS SECOND SUPPLEMENTAL INDENTURE.

         SECTION 4.9 COUNTERPARTS.

                  This Second Supplemental Indenture may be executed in any
number of counterparts, each of which shall be an original, but all such
counterparts shall together constitute but one and the same instrument.

         SECTION 4.10 TRUSTEE.

                  The Trustee is not responsible in any manner whatsoever for or
in respect of the validity or sufficiency of this Second Supplemental Indenture
or for or in respect of the recitals contained herein, which are made solely by
the Company and the Guarantor.


                            [SIGNATURE PAGE FOLLOWS]


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                  IN WITNESS WHEREOF, the parties hereto have cause this Second
Supple mental Indenture to be duly executed as of the first day and year first
written above.


                                           ISSUER:

                                           NABORS INDUSTRIES, INC.

                                           By: /s/ BRUCE P. KOCH
                                              ----------------------------------
                                                  Bruce P. Koch
                                                  Vice President-Finance and
                                                    Chief Financial Officer


                                           GUARANTOR:

                                           NABORS INDUSTRIES LTD.

                                           By: /s/ DANIEL MCLACHLIN
                                              ----------------------------------
                                                Daniel McLachlin
                                                Vice President - Administration


                                           TRUSTEE:

                                           J.P. MORGAN TRUST COMPANY,
                                           NATIONAL ASSOCIATION (as successor
                                           to Bank One, N.A.), as Trustee

                                           By: /s/ MARY JANE HENSON
                                              ----------------------------------
                                              Name: Mary Jane Henson
                                              Title: Vice President


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