Document:

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                                                                     EXHIBIT 4.4

                          THIRD SUPPLEMENTAL INDENTURE

         THIRD SUPPLEMENTAL INDENTURE (this "SUPPLEMENTAL INDENTURE"), dated as
of January 4, 1999, among (i) GREY WOLF DRILLING COMPANY L.P., a Texas limited
partnership, GREY WOLF LLC, a Louisiana limited liability company, and GREY WOLF
HOLDINGS COMPANY, a Nevada corporation (collectively, the "NEW GUARANTORS"),
each a subsidiary of GREY WOLF, INC. (formerly "DI Industries, Inc."), a Texas
corporation (the "COMPANY"), (ii) the Company, (iii) the Guarantors (the
"EXISTING GUARANTORS") under the Indenture referred to below, and (iv) CHASE
BANK OF TEXAS, NATIONAL ASSOCIATION (formerly "Texas Commerce Bank National
Association"), a national banking association, as trustee under the Indenture
referred to below (the "TRUSTEE").

                                   WITNESSETH:

         WHEREAS, the Company has heretofore executed and delivered to the
Trustee an Indenture (as such may be amended from time to time, the
"INDENTURE"), dated as of June 27, 1997, providing for the issuance of an
aggregate principal amount of $175,000,000 of 8-7/8% Senior Notes due 2007 (the
"SECURITIES");

         WHEREAS, Murco Drilling Corporation became a Guarantor under the
Indenture pursuant to the Supplemental Indenture dated as of March 31, 1998;

         WHEREAS, the parties to the Indenture entered into that certain Second
Supplemental Indenture dated May 8, 1998, which amended the Indenture to permit
the execution and delivery of the Series B Indenture by the Existing Guarantors
and the issuance of guarantees of the Series B Notes;

         WHEREAS, SECTION 11.08 of the Indenture provides that the Company is
required to cause the New Guarantors to execute and deliver to the Trustee a
supplemental indenture pursuant to which the New Guarantors shall jointly and
severally and unconditionally and irrevocably guarantee all of the Company's
Obligations under the Securities and the Indenture pursuant to a Guarantee
contained in the Indenture on the terms and conditions set forth herein; and

         WHEREAS, pursuant to SECTION 10.01 of the Indenture, the Trustee, the
Company and the Existing Guarantors are authorized to execute and deliver this
Supplemental Indenture;

         NOW THEREFORE, in consideration of the foregoing and for other good and
valuable consideration, the receipt of which is hereby acknowledged, the New
Guarantors, the Company, the Existing Guarantors and the Trustee mutually
covenant and agree for the equal and ratable benefit of the holders of the
Securities as follows:

         1. Definitions. (a) Capitalized terms used herein without definition
shall have the meanings assigned to them in the Indenture.

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            (b) For all purposes of this Supplemental Indenture, except as
otherwise herein expressly provided or unless the context otherwise requires:
(i) the terms and expressions used herein shall have the same meanings as
corresponding terms and expressions used in the Indenture; and (ii) the words
"herein," "hereof" and "hereby" and other words of similar import used in this
Supplemental Indenture refer to this Supplemental Indenture as a whole and not
to any particular section hereof.

         2. Agreement to Guarantee. The New Guarantors hereby agree, jointly and
severally and unconditionally and irrevocably, with all other Guarantors, to
guarantee the Company's Obligations under the Securities and the Indenture on
the terms and subject to the conditions set forth in ARTICLE 11 of the Indenture
and to be bound by all other applicable provisions of the Indenture. From and
after the date hereof, the New Guarantors shall be Guarantors for all purposes
under the Indenture and the Securities.

         3. Ratification of Indenture; Supplemental Indentures Part of
Indenture. Except as expressly amended hereby, the Indenture is in all respects
ratified and confirmed and all of the terms, conditions and provisions thereof
shall remain in full force and effect. This Supplemental Indenture shall form a
part of the Indenture for all purposes, and every Holder of Securities
heretofore or hereafter authenticated shall be bound hereby.

         4. Governing Law. THIS SUPPLEMENTAL INDENTURE SHALL BE GOVERNED BY, AND
CONSTRUED IN ACCORDANCE WITH, THE LAWS OF THE STATE OF NEW YORK BUT WITHOUT
GIVING EFFECT TO APPLICABLE PRINCIPLES OF CONFLICTS OF LAW TO THE EXTENT THAT
THE APPLICATION OF THE LAWS OF ANOTHER JURISDICTION WOULD BE REQUIRED THEREBY.

         5. Trustee Makes No Representation. The Trustee makes no representation
as to the validity or sufficiency of this Supplemental Indenture.

         6. Counterparts. The parties may sign any number of copies of this
Supplemental Indenture. Each signed copy shall be an original, but all of them
together represent the same agreement.

         7. Effect of Headings. The Section headings herein are for convenience
only and shall not effect the construction thereof.

                         [SIGNATURES ON FOLLOWING PAGE.]

                                       2
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         IN WITNESS WHEREOF, the parties hereto have caused this Supplemental
Indenture to be duly executed as of the date first above written.

                                          GREY WOLF DRILLING COMPANY L.P.

                                          By: GREY WOLF HOLDINGS COMPANY,
                                              its general partner

                                          By:
                                             -----------------------------------
                                             Donald J. Guedry, Jr.
                                             Vice President and Treasurer

                                          GREY WOLF LLC

                                          By:
                                             -----------------------------------
                                             Donald J. Guedry, Jr.
                                             Vice President and Treasurer

                                          GREY WOLF HOLDINGS COMPANY

                                          By:
                                             -----------------------------------
                                             Donald J. Guedry, Jr.
                                             Vice President and Treasurer

                                          GREY WOLF, INC.

                                          By:
                                             -----------------------------------
                                             Donald J. Guedry, Jr.
                                             Vice President and Treasurer

                                          GREY WOLF INTERNATIONAL, INC.
                                          DI ENERGY, INC.
                                          MURCO DRILLING CORPORATION

                                          By:
                                             -----------------------------------
                                             Donald J. Guedry, Jr.
                                             Vice President and Treasurer of
                                             each of the foregoing companies

                                          CHASE BANK OF TEXAS, NATIONAL
                                          ASSOCIATION, as Trustee

                                          By:
                                             -----------------------------------
                                          Name:
                                               ---------------------------------
                                          Title:
                                                --------------------------------

                                       3<PAGE>

                                                                     EXHIBIT 4.6

                             SUPPLEMENTAL INDENTURE

         SUPPLEMENTAL INDENTURE (this "SUPPLEMENTAL INDENTURE"), dated as of
January 4, 1999, among (i) GREY WOLF DRILLING COMPANY L.P., a Texas limited
partnership, GREY WOLF LLC, a Louisiana limited liability company, and GREY WOLF
HOLDINGS COMPANY, a Nevada corporation (collectively, the "NEW GUARANTORS"),
each a subsidiary of GREY WOLF, INC. (formerly "DI Industries, Inc."), a Texas
corporation (the "COMPANY"), (ii) the Company, (iii) the Guarantors (the
"EXISTING GUARANTORS") under the Indenture referred to below, and (iv) CHASE
BANK OF TEXAS, NATIONAL ASSOCIATION, a national banking association, as trustee
under the Indenture referred to below (the "TRUSTEE").

                                   WITNESSETH:

         WHEREAS, the Company has heretofore executed and delivered to the
Trustee an Indenture (as such may be amended from time to time, the
"INDENTURE"), dated as of May 8, 1998, providing for the issuance of an
aggregate principal amount of $75,000,000 of 8-7/8% Senior Notes due 2007, (the
"SENIOR NOTES");

         WHEREAS, SECTION 11.8 of the Indenture provides that the Company is
required to cause the New Guarantors to execute and deliver to the Trustee a
supplemental indenture pursuant to which the New Guarantors shall jointly and
severally and unconditionally and irrevocably guarantee all of the Company's
Obligations under the Senior Notes and the Indenture pursuant to a Guarantee
contained in the Indenture on the terms and conditions set forth herein; and

         WHEREAS, pursuant to SECTION 10.1 of the Indenture, the Trustee, the
Company and the Existing Guarantors are authorized to execute and deliver this
Supplemental Indenture;

         NOW THEREFORE, in consideration of the foregoing and for other good and
valuable consideration, the receipt of which is hereby acknowledged, the New
Guarantors, the Company, the Existing Guarantors and the Trustee mutually
covenant and agree for the equal and ratable benefit of the holders of the
Senior Notes as follows:

         1. Definitions. (a) Capitalized terms used herein without definition
shall have the meanings assigned to them in the Indenture.

            (b) For all purposes of this Supplemental Indenture, except as
otherwise herein expressly provided or unless the context otherwise requires:
(i) the terms and expressions used herein shall have the same meanings as
corresponding terms and expressions used in the Indenture; and (ii) the words
"herein," "hereof" and "hereby" and other words of similar import used in this
Supplemental Indenture refer to this Supplemental Indenture as a whole and not
to any particular section hereof.

         2. Agreement to Guarantee. The New Guarantors hereby agree, jointly and
severally and unconditionally and irrevocably, with all other Guarantors, to
guarantee the Company's

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Obligations under the Senior Notes and the Indenture on the terms and subject to
the conditions set forth in ARTICLE 11 of the Indenture and to be bound by all
other applicable provisions of the Indenture. From and after the date hereof,
the New Guarantors shall be Guarantors for all purposes under the Indenture and
the Senior Notes.

         3. Ratification of Indenture; Supplemental Indentures Part of
Indenture. Except as expressly amended hereby, the Indenture is in all respects
ratified and confirmed and all the terms, conditions and provisions thereof
shall remain in full force and effect. This Supplemental Indenture shall form a
part of the Indenture for all purposes, and every Holder of Senior Notes
heretofore or hereafter authenticated and delivered shall be bound hereby.

         4. Governing Law. THIS SUPPLEMENTAL INDENTURE SHALL BE GOVERNED BY, AND
CONSTRUED IN ACCORDANCE WITH, THE LAWS OF THE STATE OF NEW YORK BUT WITHOUT
GIVING EFFECT TO APPLICABLE PRINCIPLES OF CONFLICTS OF LAW TO THE EXTENT THAT
THE APPLICATION OF THE LAWS OF ANOTHER JURISDICTION WOULD BE REQUIRED THEREBY.

         5. Trustee Makes No Representation. The Trustee makes no representation
as to the validity or sufficiency of this Supplemental Indenture.

         6. Counterparts. The parties may sign any number of copies of this
Supplemental Indenture. Each signed copy shall be an original, but all of them
together represent the same agreement.

         7. Effect of Headings. The Section headings herein are for convenience
only and shall not effect the construction thereof.

                         [SIGNATURES ON FOLLOWING PAGE.]

                                        2

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         IN WITNESS WHEREOF, the parties hereto have caused this Supplemental
Indenture to be duly executed as of the date first above written.

<Table>
<S>                                                            <C>
GREY WOLF DRILLING COMPANY L.P.                                GREY WOLF INTERNATIONAL, INC.
                                                               DI ENERGY, INC.
By:   GREY WOLF HOLDINGS COMPANY,                              MURCO DRILLING CORPORATION
      its general partner

      By:                                                      By:
         ------------------------------------------               ----------------------------------------
         Donald J. Guedry, Jr.                                    Donald J. Guedry, Jr.
         Vice President and Treasurer                             Vice President and Treasurer of each
                                                                  of the foregoing companies

                                                               CHASE BANK OF TEXAS, NATIONAL
GREY WOLF LLC                                                    ASSOCIATION, as Trustee

By:                                                            By:
   ------------------------------------------------               ----------------------------------------
   Donald J. Guedry, Jr.                                       Name:
   Vice President and Treasurer                                     --------------------------------------
                                                               Title:
                                                                     -------------------------------------

GREY WOLF HOLDINGS COMPANY

By:
   ------------------------------------------------
   Donald J. Guedry, Jr.
   Vice President and Treasurer

GREY WOLF, INC.

By:
   ------------------------------------------------
   Donald J. Guedry, Jr.
   Vice President and Treasurer
</Table>

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