<PAGE>
 
                                                                  EXHIBIT 10(hh)


                              EXCHANGE AGREEMENT


  THIS EXCHANGE AGREEMENT (this "Agreement") is made and entered into as of
January 3, 1996, by and among BAKER HUGHES INCORPORATED, a Delaware corporation
("BHI"), and TUBOSCOPE VETCO INTERNATIONAL CORPORATION, a Delaware corporation
(the "Company").

                              W I T N E S S E T H:
                              - - - - - - - - - - 

  WHEREAS, D.O.S. Ltd., a Bermuda corporation ("D.O.S. Ltd."), is to be merged
with a wholly-owned subsidiary ("Sub") of the Company (the "Merger") pursuant to
an Agreement and Plan of Merger dated as of January 3, 1996 among the Company,
Sub and D.O.S. Ltd. (the "Merger Agreement");

  WHEREAS, the Board of Directors of the Company has determined that it is in
the best interests of the Company and its shareholders to improve its capital
structure by issuing shares of the Company's Common Stock, par value $.01 per
share ("Common Stock"), and warrants to purchase Common Stock, in exchange for
the outstanding shares of the Company's Redeemable Series A Convertible
Preferred Stock, par value $.01 per share ("Preferred Stock");

  WHEREAS, the Company will issue to BHI, and BHI will acquire, on the terms and
subject to the conditions set forth herein, 1,500,000 shares (the "Shares") of
the Company's Common Stock and warrants (the "Warrants") to purchase 1,250,000
shares of Common Stock (the Shares and the Warrants are collectively referred to
herein as the "Securities"), in exchange for the 100,000 shares of Preferred
Stock held by BHI (the "BHI Preferred Stock").

  NOW, THEREFORE, in consideration of and subject to the mutual agreements,
terms and conditions herein contained and for other good and valuable
consideration, the receipt and adequacy of which are hereby acknowledged, the
parties hereto agree as follows:


                                   ARTICLE I.

                                  DEFINITIONS

  Capitalized terms used herein without definitions shall have the meanings
assigned to such terms in the Merger Agreement.
<PAGE>
 
                                                                  EXHIBIT 10(hh)

                                  ARTICLE II.

                             EXCHANGE OF SECURITIES

  2.1    Exchange.  At the Closing, the Company will issue, sell, transfer,
convey and deliver to BHI (i) the Shares as evidenced by the delivery of a
certificate or certificates evidencing the Shares in good delivery form and (ii)
the Warrants as evidenced by the delivery of the Warrant Certificate in the form
set forth on Appendix I, subject to the terms and conditions set forth herein,
in exchange (the "Exchange") for the delivery, conveyance and transfer to the
Company of the BHI Preferred Stock as evidenced by the delivery of the share
certificate or certificates representing such shares of Preferred Stock, duly
endorsed in blank for transfer, together with such other documentation
evidencing the transfer as may be reasonably requested by the Company.

  2.2    Suspension of Dividend.  BHI agrees that the cash dividends otherwise
due and owing on March 31, June 30, September 30 and December 31, 1996 pursuant
to Paragraph 2 of the Certificate of Designation of Series A Convertible
Preferred Stock of Tuboscope Corporation (the "Certificate of Designation")
shall not be due and owing; provided, that if the Exchange contemplated in
                            ---------                                     
Section 2.1 hereof is not consummated for any reason, such cash dividends shall
be paid for all such periods, notwithstanding the provisions of this paragraph,
and any quarterly payments which may not have been made owing to this paragraph
shall be made at the time of the next quarterly payment called for in the
Certificate of Designation, together with interest on such quarterly payments
for the period from the date on which they would otherwise have been due to the
date of payment at an interest rate equal to the prime rate as announced from
time to time by Texas Commerce Bank National Association.

  2.3    Closing.  The closing of the Exchange shall take place at the Closing
on the Closing Date.  The Exchange shall be deemed to be made as of the
Effective Time.


                                  ARTICLE III.

                         REPRESENTATIONS AND WARRANTIES
                                 OF THE COMPANY

  The Company warrants and represents to BHI as follows:

  3.1    Organization.  The Company is a corporation duly organized, validly
existing and in good standing under the laws of the State of Delaware with
corporate power and authority to own, operate and lease its properties and to
carry on its business as now conducted.

                                       2
<PAGE>
 
                                                                  EXHIBIT 10(hh)

  3.2    Authorization, Execution and Enforceability.  The Company has full
power and authority to enter into this Agreement and the capacity and authority
to make the representations, warranties, covenants and agreements herein.  The
execution, delivery and performance by the Company of this Agreement have been
duly and validly authorized and are within the corporate powers of the Company.
This Agreement has been duly executed and delivered by the Company and
constitutes its valid and binding agreement, enforceable in accordance with its
terms, subject to the effect of bankruptcy, insolvency, reorganization,
moratorium or other similar laws relating to or affecting the rights of
creditors, and the effect of general principles of equity, including without
limitation concepts of materiality, reasonableness, good faith and fair dealing
and the possible unavailability of specific performance or injunctive relief
regardless of whether considered in a proceeding in equity or at law.  The
Shares to be issued by the Company to BHI hereunder, as of the Closing will be
duly and validly authorized and, when issued and delivered against payment
therefor as provided herein, will be duly and validly issued and fully paid and
non-assessable.  When executed by the Company and delivered in accordance with
their terms, the Warrants will constitute valid and binding obligations of the
Company, enforceable in accordance with their terms, subject to the effect of
bankruptcy, insolvency, reorganization, moratorium or other similar laws
relating to or affecting the rights of creditors, and the effect of general
principles of equity, including without limitation concepts of materiality,
reasonableness, good faith and fair dealing and the possible unavailability of
specific performance or injunctive relief regardless of whether considered in a
proceeding in equity or at law.  The shares of Common Stock reserved for
issuance upon exercise of the Warrants will be as of the Closing duly authorized
and reserved for such purpose, and, if and when the Warrants are exercised in
accordance with the rights provided for therein, the shares of Common Stock
issuable upon such exercise will be validly issued, fully paid and non-
assessable, and the issuance of such shares will not be subject to any
preemptive or similar rights.

  3.3    Capital Structure as of Closing Date.  Except as contemplated by this
Agreement, the representations and warranties set forth in Section 3.2(b) of the
Merger Agreement will be true and correct as of the Closing Date, except that to
the extent such representations and warranties speak as of an earlier date, they
will be true and correct as of such earlier date.

  3.4    Consents and Approvals; No Violations.

          (a) No consent, action, approval or authorization of, or registration,
declaration or filing with, any governmental department, commission, agency or
other instrumentality or any other person or entity is required to authorize, or
is otherwise required in connection with, the execution and delivery of this
Agreement by the Company or its performance of the terms hereof, including
without limitation, the issuance of the Shares and Warrants or the exercise of
the Warrants, or the validity or enforceability hereof or thereof against the
Company as to which the failure to obtain or make would have a Company Material
Adverse Effect (as defined below) or would materially adversely affect the
consummation of the transactions contemplated hereby,

                                       3
<PAGE>
 
                                                                  EXHIBIT 10(hh)

except for the filing of a notification report by the Company and BHI under the
Hart-Scott-Rodino Antitrust Improvements Act of 1976, as amended (the "HSR
Act"), and the expiration or termination of the applicable waiting period with
respect thereto.  As used in this Agreement, "Company Material Adverse Effect"
shall mean any effect that is, individually or in the aggregate, materially
adverse to the business, operations, assets, condition (financial or otherwise)
or results of operations of the Company and its Subsidiaries taken as a whole
except for general economic changes that may affect the industries of the
Company or any of its Subsidiaries generally.

          (b) The execution and delivery of this Agreement does not, and the
consummation of the transactions contemplated hereby and compliance with the
provisions hereof will not, conflict with, or result in any violation of, or
default (with or without notice or lapse of time, or both) under, or give rise
to a right of termination, cancellation or acceleration of any obligation or to
the loss of a material benefit under, or result in the creation of any lien,
security interest, charge or encumbrance upon any of the properties or assets of
the Company or any of its Subsidiaries under, any provision of (i) the
Certificate of Incorporation or Bylaws of the Company or any provision of the
comparable charter or organizational documents of any of its Subsidiaries, (ii)
any loan or credit agreement, note, bond, mortgage, or indenture applicable to
the Company or any of its Subsidiaries, (iii) any other agreement, instrument,
permit, concession, franchise or license applicable to the Company or any of its
Subsidiaries or (iv) any judgment, order, decree, statute, law, ordinance, rule
or regulation applicable to the Company or any of its Subsidiaries or any of
their respective properties or assets, other than, in the case of clause (iii),
any such conflicts, violations, defaults, rights, liens, security interests,
charges or encumbrances that, individually or in the aggregate, would not have a
Company Material Adverse Effect, materially impair the ability of the Company to
perform its obligations hereunder or prevent the consummation of any of the
transactions contemplated hereby.

          3.5  Form 10K and Proxy.  The representations and warranties set forth
in Section 3.2(e) of the Merger Agreement are true and correct.  The Company's
Annual Report on Form 10K for the year ended December 31, 1995 (the "Annual
Report") and the Proxy Statement related to the Company's meeting of
stockholders at which the Merger Agreement is to be considered (the "Proxy
Statement") will comply in all material respects with the requirements of the
Securities Act of 1933, as amended, and the Securities Exchange Act of 1934, as
amended, (as applicable) and the rules and regulations of the Securities and
Exchange Commission thereunder applicable, and neither the Annual Report, as of
the date it is filed, or the Proxy Statement, as of the Effective Time, will
contain any untrue statement of a material fact or omit to state a material fact
required to be stated therein or necessary to make the statements therein, in
light of the circumstances under which they were made, not misleading.

                                       4
<PAGE>
 
                                                                  EXHIBIT 10(hh)

          3.6  Antidilution Provisions.  The issuance or exercise of the
Warrants granted hereunder will not cause an antidilution adjustment to the
warrants granted to SCF-III, L.P ("SCF") pursuant to that certain Subscription
Agreement and Warrant dated as of January 3, 1996 by and between the Company and
SCF.


                                  ARTICLE IV.

                     REPRESENTATIONS AND WARRANTIES OF BHI

          BHI represents and warrants to the Company as follows:

          4.1  Organization, Authorization, Execution and Enforceability.  BHI
is a corporation duly organized, validly existing and in good standing under the
laws of the State of Delaware with power and authority to own, operate and lease
its properties and to carry on its business as now conducted.  BHI has full
power and authority to enter into this Agreement and the capability and
authority to make the representations, warranties, covenants and agreements
herein.  The execution, delivery and performance by BHI of this Agreement have
been duly and validly authorized and are within the corporate powers of BHI.
This Agreement has been duly executed and delivered by BHI and constitutes its
valid and binding agreement, enforceable in accordance with its terms, subject
to the effect of bankruptcy, insolvency, reorganization, moratorium or other
similar laws relating to or affecting the rights of creditors, and the effect of
general principles of equity, including without limitation concepts of
materiality, reasonableness, good faith and fair dealing and the possible
unavailability of specific performance or injunctive relief regardless of
whether considered in a proceeding in equity or at law.

          4.2  Consents and Approvals.  No consent, action, approval or
authorization of, or registration, declaration or filing with, any governmental
department, commission, agency or other instrumentality or any other person or
entity is required to authorize, or is otherwise required in connection with,
the execution and delivery of this Agreement by BHI or its performance of the
terms hereof, including without limitation, the transfer of the Preferred Stock
and the exchange of the Shares and the Warrants, or the validity or
enforceability hereof or thereof against BHI as to which the failure to obtain
or make would have a Company Material Adverse Effect or would materially
adversely affect the consummation of the transactions contemplated hereby,
except for the filing of a notification report by the Company and BHI under the
HSR Act and the expiration or termination of the applicable waiting period with
respect thereto.

          4.3 Stock ownership.

          (a) BHI is the lawful owner, of record and beneficially, of the entire
right title and interest in and to the BHI Preferred Stock, free and clear of
all Encumbrances, except such Encumbrances as may arise under applicable federal
and

                                       5
<PAGE>
 
                                                                  EXHIBIT 10(hh)

state securities laws and regulations.  As used in this Section 4.3,
"Encumbrances" shall mean any claim, lien, pledge, option, change, easement,
security interest, mortgage, right of way, encumbrance, restrictions, equities,
reservation, adverse claims or other similar right or interest of any nature
created by, through or under BHI or any of its affiliates.

          (b) Delivery of the BHI Preferred Stock pursuant hereto will vest good
and marketable title in the Company, free and clear of all Encumbrances.

          4.4  Accredited Investor.  BHI is an "accredited investor" as defined
in Rule 501 of Regulation D promulgated pursuant to the Securities Act of 1933,
as amended.


                                   ARTICLE V.

                            COVENANTS OF THE COMPANY

          The Company further agrees, except as set forth in or contemplated by
this Agreement or as otherwise approved by BHI in writing, that:

          5.1 Registration Rights.

          (a) Reference is made to that certain Agreement for the Purchase and
Sale of the Baker Hughes Tubular Services Eastern Hemisphere Division of Baker
Hughes Incorporated dated as of October 1, 1991 by and between the Company and
BHI (the "Purchase Agreement"). BHI represents and warrants that it is, as of
the date of this Agreement,  the sole Holder of Registrable  Securities (as such
capitalized terms are defined in the Purchase Agreement) and that the only
registration rights BHI has, as of the date hereof, with respect to equity
securities of the Company are as provided in the Purchase Agreement.  The
Company represents and warrants that the Company has not granted any outstanding
registration rights or agreed to grant any registration rights to any person or
entity except for the registration rights to be granted pursuant to Section 5.12
of the Merger Agreement and registration rights granted under the Outstanding
Registration Rights Agreements (as such term is defined in Exhibit D to the
Merger Agreement).

          (b) If the Closing occurs, the Purchase Agreement shall automatically
be amended as follows:

          (i) Section 1.1 of the Purchase Agreement shall be amended to add the
following definitions (except with respect to the definition of Registrable
Securities, which shall be substituted for the definition in Section 1.1):

                                       6
<PAGE>
 
                                                                  EXHIBIT 10(hh)

          "DOS Registrable Securities" means the securities subject to the
registration rights to be provided by Buyer pursuant to Section 5.12 of the
Agreement and Plan of Merger dated as of January 3, 1996 among the Buyer, Grow
Acquisition Limited and D.O.S. Ltd.

          "Exchange Agreement" means the Exchange Agreement dated as of January
3, 1996 by and among BHI and Buyer.

          "Junior Registrable Securities" means the 1,500,000 shares of Common
Stock acquired pursuant to the Exchange Agreement and the shares of Common Stock
for which the Warrants are exercisable and any Common Stock or other security of
Buyer issued as a dividend or other distribution with respect to, or in exchange
for, or in replacement of, such shares of Common Stock or the Warrants. The
rights of the Holders of Junior Registrable Securities shall be subordinate to
the rights of Holders of Senior Registrable Securities and shall be subordinate
to the rights of the holders of DOS Registrable Securities and pari passu with
                                                               -----------    
respect to all registration rights (other than registration rights relating to
the DOS Registrable Securities) granted by the Buyer after October 1, 1991
unless otherwise expressly subordinated with the written agreement of the
Holders. Notwithstanding the foregoing, if the Holders make a request for
Registration pursuant to Section 8.3 and request that all Registrable Securities
be included in such Registration  then the Junior Registrable Securities shall
be, for purposes of such Registration, superior to registration  rights (other
than registration rights relating to the DOS Registrable Securities) granted by
the Buyer after October 1, 1991 and all such other registration rights (other
than registration rights relating to the DOS Registrable Securities) shall rank
subordinate to the rights of Holders of the Junior Registrable Securities.

          "Registrable Securities" means Senior Registrable Securities and
Junior Registrable Securities.  Notwithstanding the foregoing, any particular
Registrable Security shall cease to be a Registrable Security at such time as
(i) it has been effectively registered under the 1933 Act and sold or
transferred in accordance with the Registration statement covering it, (ii) it
has been distributed to the public pursuant to Rule 144 (or any similar
provision then in force) under the 1933 Act, or (iii) it has been transferred
and a new certificate or other evidence of ownership for it has been delivered
by or on behalf of the Buyer and such certificate and the shares evidenced
thereby are not subject to any stop transfer order or similar restriction on
resale.

          "Senior Registrable Securities" means the 1,686,047 shares of Common
Stock owned by BHI as of the date hereof and any Common Stock or other security
of Buyer issued as a dividend or other distribution with

                                       7
<PAGE>
 
                                                                  EXHIBIT 10(hh)

respect to, or in exchange for, or in replacement of, such shares of Common
Stock.  The rights of the Holders of Senior Registrable Securities shall be
senior to the rights of Holders of Junior Registrable Securities and to the
rights of the holders of DOS Registrable Securities.

          "Warrants" means those certain Warrants for the purchase of an
aggregate of 1,250,000 shares (subject to adjustment as provided therein) of
Common Stock issued to Buyer pursuant to the Exchange Agreement.

          (ii) A new sentence shall be added to the end of Section 8.3(b) as
follows:

          Notwithstanding the foregoing, the Buyer shall be entitled to postpone
for a reasonable period of time (not exceeding 90 days) the filing (but not the
preparation) of any registration statement otherwise required to be prepared and
filed by it pursuant hereto if (i) at the time the Buyer receives a request for
such registration, the Buyer is in possession of material non-public information
that would be required to be disclosed in a registration statement but that has
not been and will otherwise not be disclosed to the public and the Buyer deems
disclosure not to be in the best interests of the Buyer and its stockholders
(and the Buyer so notifies the Holders requesting a Registration within 5
Business Days of such request), or (ii) the Buyer determines (and the Buyer so
notifies the Holders requesting a Registration within 5 Business Days of such
request) that in its judgment, such registration and offering would materially
interfere with any financing, acquisition, corporate reorganization or other
material transaction involving the Buyer that prior to such request the Board of
Directors of the Buyer had agreed by resolution to pursue.

          (iii)  The third and fourth sentences of Section 8.2(c) of the
Purchase Agreement shall be amended by deleting such sentences and adding to the
end of Section 8.2(c):

          Notwithstanding any other provisions of this Section 8.2, if the
underwriter determines that marketing factors require a limitation on the amount
of shares of Common Stock to be Registered, then the underwriter may limit the
amount of Registrable Securities to be included in the Registration and
underwriting, and the amount of securities to be offered shall be reduced first
from the Common Stock being offered for the account of persons or entities
entitled to include Common Stock in such offering and whose rights to include
Common Stock in the offering rank subordinate to the rights of the Holders of
Junior Registrable Securities and then, if the offering size shall require
further reduction, from the Common Stock being offered for the account of the
Holders of Junior Registrable Securities and

                                       8
<PAGE>
 
                                                                  EXHIBIT 10(hh)

such other persons and entities entitled to include Common Stock in such
offering and whose rights to include such Common Stock rank pari passu to the
                                                            ----------       
registration rights of the Holders  of Junior Registrable Securities (allocated
pro rata in proportion to their respective number of shares to be registered),
and then, if  the offering size shall require further reduction,  from the
Common Stock being offered for the account of the holders of DOS Registrable
Securities and such other persons or entities entitled to include Common Stock
in such offering and whose rights to include Common Stock in the offering rank
subordinate to the rights of the Holders of Senior Registrable Securities and
senior to the rights of Junior Registrable Securities and then, if the offering
size shall require further reduction, from the Common Stock being offered for
the account of the Holders of Senior Registrable Securities and such other
persons and entities entitled to include Common Stock in such offering and whose
rights to include such Common Stock rank pari passu to the registration rights
                                         ----------                           
of the Holders of Senior Registrable Securities (allocated pro rata in
proportion to their respective number of shares to be registered), to the extent
necessary to reduce the total amount of securities to be included in such
offering to the amount recommended by such managing underwriter or underwriters
prior to any reduction of the securities to be sold by the Company: provided,
however, that such limitation shall not exclude more than 50% of the aggregate
amount of the Senior Registrable Securities of Holders sought to be registered
by Holders in such Registration; and provided, further, however the provisions
of this Section 8.2 are subject to the rights and obligations of certain
stockholders of the Buyer as set forth in the Stockholders' Agreement.

          (iv) A new Section 8.3(d) shall be added as follows:

          Notwithstanding any other provisions of this Section 8.3, if any other
person or entity participates in an underwritten offering pursuant to this
Section 8.3 and if the underwriter determines that marketing factors require a
limitation on the amount of shares of Common Stock to be Registered, then the
underwriter may limit the amount of Registrable Securities to be included in the
Registration and underwriting, and the amount of securities to be offered shall
be reduced first from the Common Stock being offered for the account of persons
or entities entitled to include Common Stock in such offering and whose rights
to include Common Stock in the offering rank subordinate to the rights of the
Holders of Junior Registrable Securities and then, if the offering size shall
require further reduction, from the Common Stock being offered for the account
of the Holders of Junior Registrable Securities and such other persons and
entities entitled to include Common Stock in such offering and whose rights to
include such Common Stock rank pari passu to the registration rights of the
                               ----------                                  
Holders  of Junior Registrable Securities (allocated pro rata in proportion to
their respective number of

                                       9
<PAGE>
 
                                                                  EXHIBIT 10(hh)

shares to be registered), and then, if  the offering size shall require further
reduction,  from the Common Stock being offered for the account of the Company
and the holders of DOS Registrable Securities and such other persons or entities
entitled to include Common Stock in such offering and whose rights to include
Common Stock in the offering rank subordinate to the rights of the Holders of
Senior Registrable Securities and senior to the rights of Junior Registrable
Securities (in whatever proportion or order they have agreed among themselves)
and then, if the offering size shall require further reduction, from the Common
Stock being offered for the account of the Holders of Senior Registrable
Securities and such other persons and entities entitled to include Common Stock
in such offering and whose rights to include such Common Stock rank pari passu
                                                                    ----------
to the registration rights of the Holders of Senior Registrable Securities
(allocated pro rata in proportion to their respective number of shares to be
registered).  If the number of Junior Registrable Securities are limited as a
result of the application of the immediately preceding sentence or Section
8.3(c) with the result that less than  75% of the Registrable Securities
requested to be included in such Registration  are sold, then the number of
Registrations that may be requested by Holders under Section 8.3  shall be
increased by one.

          (v) A new Section 8.3(e) shall be added as follows:

          Any written request or notice by a Holder pursuant to Section 8.2 or
8.3 to include Registrable Securities in a Registration must specify what
portion of such Registrable Securities that are proposed to be included in a
Registration constitute Senior Registrable Securities and what portion
constitute Junior Registrable Securities in order for such request or notice to
be effective.

          5.2  Obtaining Consents.  The Company will use its reasonable best
efforts to obtain, and to assist BHI in obtaining, all consents, resignations,
authorizations and approvals and making all filings necessary for the
consummation of the transactions contemplated by this Agreement, if any,
required under any applicable law or regulation.

          5.3  Satisfaction of Closing Conditions.  The Company shall use its
reasonable best efforts to satisfy the conditions to Closing set forth in
Article VII relating to the Company in an expeditious manner.  The Company shall
not be required to institute or defend any action in any court or before any
administrative body or take action to divest or hold separate any assets of it
or any of its affiliates in connection with satisfying such conditions.

          5.4  Delivery of Documents at Closing.  At the Closing, subject to
satisfaction of the conditions set forth in Article VII, the Company shall
execute and deliver to BHI all documents required to be delivered by the Company
pursuant to Section 7.1.

                                       10
<PAGE>
 
                                                                  EXHIBIT 10(hh)

                                  ARTICLE VI.

                                COVENANTS OF BHI

          BHI further agrees, except as set forth in or contemplated by this
Agreement or as otherwise approved by the Company in writing, as follows:

          6.1  Obtaining Consents.  BHI will use its reasonable best efforts to
obtain, and to assist the Company in obtaining, all consents, authorizations and
approvals and making all filings necessary for the consummation of the
transactions contemplated by this Agreement, if any, required under any
applicable law or regulation.

          6.2  Satisfaction of Closing Conditions.  BHI shall use its reasonable
best efforts to satisfy the conditions to Closing set forth in Article VII
relating to BHI in an expeditious manner.  BHI shall not be required to
institute or defend any action in any court or before any administrative body or
take action to divest or hold separate any assets of it or any of its affiliates
in connection with satisfying such conditions.

          6.3  Delivery of Documents at Closing.  At the Closing, subject to
satisfaction of the conditions set forth in Article VII, BHI shall execute and
deliver to the Company the documents contemplated to be delivered by BHI
pursuant to Section 7.2.

          6.4  Disposition of Securities.  BHI agrees that it will not, until
December 31, 1997 (the period from the date of this Agreement to December 31,
1997, the "Lock-up Period"), offer to sell, contract to sell, or otherwise sell,
dispose of, loan, pledge or grant any rights with respect to (collectively, a
"Disposition") any of the Shares, the Warrants or the Warrant Shares.  The
foregoing restriction does not apply to (i) any Disposition that may be effected
in a tender or exchange offer made to all holders of a class or series of the
Company's securities, (ii) any Disposition, conversion or exchange of the Shares
or Warrant Shares for other securities, cash or property in connection with a
merger, consolidation, recapitalization, redemption or other reclassification
involving the Company or the Company's securities, (iii) any Disposition in
connection with a disposition or other transfer of all or substantially all of
the assets of BHI, provided the transferee agrees to be bound by this Section
6.4 or (iv) any Disposition to an affiliate of BHI that agrees to be bound by
this Section 6.4.  Such restriction shall not apply to any securities BHI may
hold as a result of any transaction described in clause (i) or (ii) above
following such transaction.  The foregoing restriction has been expressly agreed
to preclude BHI, among other things, from engaging in any hedging or other
transaction which is designed to or reasonably expected to lead to or result in
a Disposition of any of the Shares, the Warrants or the Warrant Shares during
the Lock-up Period, even if such shares would be disposed of by someone other
than BHI.  Furthermore, BHI has also agreed and consented to the entry of stop
transfer instructions with the Company's transfer agent against the transfer of
the Shares except in

                                       11
<PAGE>
 
                                                                  EXHIBIT 10(hh)

compliance with this restriction.  An exercise of the Warrants shall not
constitute a Disposition of the Shares, the Warrants or the Warrant Shares.


                                  ARTICLE VII.

                           CONDITIONS TO THE CLOSING;
                       TERMINATION, AMENDMENT AND WAIVER

          7.1  Conditions to Obligation of BHI.  The obligation of BHI to effect
the transactions contemplated by this Agreement is subject to the following
conditions:

          (a) Representations and Warranties of the Company.  Except as
contemplated by this Agreement, (i) the representations and warranties of the
Company hereunder shall be made again at the Closing and shall be true in all
material respects as of the Closing Date, except that to the extent such
representations and warranties speak as of an earlier date, they will be true
and correct as of such earlier date, (ii) the Company shall have performed (or
caused to have been performed) in all respects all covenants required of it (and
its subsidiaries) by this Agreement as of the Closing and (iii) the Company
shall have furnished BHI at the Closing with a certificate of the President of
the Company to such effect.

          (b) Third Party Consents and Approvals.  The Company shall have made
all filings with, and obtained all required consents, approvals, permits and
authorizations  in connection with the execution and delivery of this Agreement
and the transactions contemplated hereby from any governmental entity except
where the failure to obtain such consents, approvals, permits and authorizations
would not be reasonably likely to result in a Company Material Adverse Effect
(assuming the transactions contemplated by this Agreement have taken place) or
to materially adversely affect the consummation of the transactions contemplated
hereby.

          (c) Stock and Warrant Certificates.  The Company shall have delivered
to BHI at the Closing one or more stock certificates representing the Shares in
good delivery form and certificates representing the Warrants in the form set
forth on Appendix I.

          (d) Conditions Precedent to Merger.  All of the conditions precedent
to the consummation of the Merger as set forth in Sections 6.1 and 6.3 of the
Merger Agreement shall have been satisfied as of the Closing Date; and all
conditions precedent set forth in Section 6.2 of the Merger Agreement shall have
been satisfied or waived by the Company as of the Closing Date, provided that
any such waiver shall not be materially adverse to BHI as a holder of Preferred
Stock exchanging the Preferred Stock for Securities.

                                       12
<PAGE>
 
                                                                  EXHIBIT 10(hh)

          7.2  Conditions to Obligations of the Company.  In addition to the
satisfaction of the conditions referred to in subparagraph (b) of Section 7.1
hereof, the obligations of the Company to effect the transactions contemplated
by this Agreement shall be subject to the following conditions:

          (a) Representations and Warranties of BHI.  Except as contemplated in
this Agreement, (i) the representations and warranties of BHI hereunder shall be
made again at the Closing and shall be true in all material respects as of the
Closing Date, except that to the extent such representations and warranties
speak as of an earlier date, they will be true and correct as of such earlier
date, (ii) BHI shall have performed in all material respects all covenants
required of it by this Agreement as of the Closing Date and (iii) BHI shall have
furnished the Company at the Closing with a certificate of one of its authorized
representatives to such effect.

          (b) Delivery of BHI Preferred Stock.  BHI shall have delivered the
share certificate or certificates representing the BHI Preferred Stock, together
with such other documentation evidencing the transfer as may be reasonably
requested by the Company as specified in Section 2.1 hereof.

          (c) Conditions Precedent to Merger.  All of the conditions precedent
to the consummation of the Merger as set forth in Sections 6.1, 6.2 and 6.3 of
the Merger Agreement shall have been satisfied, or waived by a party having the
right to waive such condition under the Merger Agreement, as of the Closing
Date.

          7.3  Termination of Agreement.  Anything herein to the contrary
notwithstanding, this Agreement and the transactions contemplated herein may be
terminated at any time before the Closing as follows:

          (a) Mutual Consent. By the mutual consent of the Company and BHI.

          (b) Expiration Date. By the Company or BHI if the Closing shall not
have occurred by December 31, 1996.

          (c) Termination of Merger Agreement. By the Company or BHI if the
Merger Agreement shall have been terminated.

          (d) Amendment of Merger Agreement.  By BHI if an amendment or
modification of the Merger Agreement is made which is materially adverse to BHI
as a holder of Preferred Stock exchanging the Preferred Stock for Securities.

          7.4  Effect of Termination and Failure of Conditions.  In the event of
termination of this Agreement as provided in Section 7.3, or of the failure of a
condition resulting in BHI, or the Company not performing its or their
obligations hereunder pursuant to the terms of Section 7.1 or 7.2, as the case
may be, this Agreement shall forthwith become void

                                       13
<PAGE>
 
                                                                  EXHIBIT 10(hh)

and there shall be no liability on the part of any party hereto with respect
thereto except that nothing herein shall relieve any party from liability for
any breach hereof.


                                 ARTICLE VIII.

                                 MISCELLANEOUS

          8.1  Headings.  The descriptive headings of the several Articles and
Sections of this Agreement are inserted for convenience only and do not
constitute a part of the Agreement.

          8.2  Entire Agreement.  This Agreement, the documents to be executed
hereunder, and the exhibits attached hereto constitute the entire agreement
between the parties hereto pertaining to the subject matter hereof and supersede
all prior agreements, understandings, negotiations and discussions, whether oral
or written, of the parties pertaining to the subject matter hereof.
Notwithstanding the foregoing, except as specifically provided in this Agreement
if the Closing occurs, the Purchase Agreement shall continue in full force and
effect, including specifically sections 8.11 and 8.12 of the Purchase Agreement.

          8.3  Waiver.  At any time prior to the Closing, any party hereto may
(a) extend the time for the performance of any of the obligations or other acts
of any other party hereto or (b) waive compliance with any of the agreements of
any other party or with any conditions to its own obligations. Any agreement on
the part of a party hereto to any such extension or waiver shall be valid if set
forth in an instrument in writing signed on behalf of such party. The
consummation of the transactions contemplated hereby shall not be deemed a
waiver of the right any party may have hereunder with respect to any other
party's representations, warranties, covenants or agreements contained in or
related to this Agreement being incorrect, untrue or breached.

          8.4  Amendment.  This Agreement may not be amended except by an
instrument in writing signed by each of the parties hereto.  No supplement,
alteration or modification of this Agreement shall be binding unless executed in
writing by the parties hereto.

          8.5  Further Actions. Each party shall execute and deliver such other
certificates, agreements and other documents and take such other actions as may
reasonably be requested by the other parties in order to consummate or implement
the transactions contemplated by this Agreement.

          8.6  Assignment. Except as otherwise expressly provided herein,  the
terms and conditions of this Agreement shall inure to the benefit of and be
binding upon the respective successors and assigns of the Company and BHI.  The
Company may not assign or delegate any of its rights or duties hereunder,
without the prior written consent of BHI.  BHI may not assign or delegate any of
its rights or duties hereunder without the prior

                                       14
<PAGE>
 
                                                                  EXHIBIT 10(hh)

written consent of the Company, which consent shall not be unreasonably
withheld; but in any event BHI shall remain responsible for any assignee's
performance.  Any assignment or delegation made without such consent shall be
void.

          8.7  Independent Covenants.  The covenants contained herein are
independent and separate, and in the event that any provision contained herein
is declared invalid or illegal, the other provisions hereof shall not be
affected or impaired thereby and shall remain valid and enforceable.

          8.8  Remedies and Certain Rights.  In the event of a breach or
threatened breach by any party hereto of the provisions of this Agreement, any
other party hereto shall be entitled to specific performance.

          8.9  Governing Law.  This Agreement and the other documents delivered
pursuant hereto and the legal relations between the parties shall be governed
and construed in accordance with the laws of the State of Delaware, without
giving effect to principles of conflict of laws.

          8.10  Counterparts.  This Agreement may be executed in any number of
counterparts, each of which when so executed shall be deemed an original but all
of which together shall constitute one and the same instrument.

          8.11  Withholding or Granting of Consent.  Except as otherwise
provided in this Agreement, each party hereto may, with respect to any consent
or approval that it is entitled to grant pursuant to this Agreement or any other
document or instrument or agreement delivered or entered into pursuant hereto,
grant or withhold such consent or approval in its sole and uncontrolled
discretion, with or without cause, and subject to such conditions as it shall
deem appropriate.

          8.12  Notices.  Any notice or communication required or permitted
hereunder shall be in writing and either delivered personally, telegraphed or
telecopied or sent by certified or registered mail, postage prepaid, and shall
be deemed to be given, dated and received when so delivered personally,
telegraphed or telecopied or, if mailed, five business days after the date of
mailing to the following address or telecopy number, or to such other address or
addresses as such person may subsequently designate by notice given hereunder.

          if to Tuboscope Vetco International:

               Tuboscope Vetco International Corporation
               2835 Holmes Road
               Houston, TX  77051
               Telecopy:  (713) 799-5183
               Attn:  General Counsel

                                       15
<PAGE>
 
                                                                  EXHIBIT 10(hh)

with a copy to:

        Latham & Watkins
        650 Town Center Drive, 20th Floor
        Costa Mesa, CA  92626
        Telecopy:  (714) 755-8290
        Attn:  Patrick Seaver

if to Baker Hughes Incorporated:

        Baker Hughes Incorporated
        3900 Essex Lane, Suite 1200
        Houston, TX  77027
        Attn:  General Counsel

with a copy to:

        Baker & Botts, L.L.P.
        3000 One Shell Plaza
        Houston, Texas 77002
        Telecopy: (713) 229-1522
        Attn: J. David Kirkland, Jr.

          IN WITNESS WHEREOF, each of the parties hereto has executed this
Agreement as of the date first above written.

                              BAKER HUGHES INCORPORATED


Date:  March 13, 1996           By:     /s/  LAWRENCE O'DONNELL, III
       --------------                   ----------------------------

                                        Name: Lawrence O'Donnell, III
                                              -----------------------
         
                                        Title:     Vice President
                                                   --------------
         
         
                                        TUBOSCOPE VETCO INTERNATIONAL
                                          CORPORATION

Date:  March 13, 1996           By:     /s/  MARTIN I. GREENBERG
       --------------                   ------------------------

                                        Name: Martin I. Greenberg
                                              -------------------
                               
                                        Title:     Vice President
                                                   --------------

                                       16
<PAGE>
 
                                                                      APPENDIX I
                                                           TO EXCHANGE AGREEMENT


                   TUBOSCOPE VETCO INTERNATIONAL CORPORATION

               WARRANT FOR THE PURCHASE OF SHARES OF COMMON STOCK
                           EXPIRING DECEMBER 31, 2000

NO. __                                                          1,250,000 SHARES



          BY THIS WARRANT (this "Warrant"), Tuboscope Vetco International
Corporation, a Delaware corporation (the "Company"), certifies that, for good
and valuable consideration, the receipt and sufficiency of which are hereby
acknowledged, Baker Hughes Incorporated, a Delaware corporation (along with its
registered assigns, the "Holder"), is entitled to subscribe for and purchase
from the Company, subject to the terms and conditions set forth herein, at any
time or from time to time prior to 5:00 p.m. (Houston, Texas time) on December
31, 2000 (the "Expiration Date"), 1,250,000 (subject to adjustment as set forth
herein) fully paid and non-assessable shares (the "Shares") of the Company's
Common Stock, $0.01 par value per share (the "Common Stock"), at a price equal
to the exercise price per share, initially $10.00 (subject to adjustment as set
forth herein) per share (the "Exercise Price").

          1.   Exercise of Warrant; Company Office.  This Warrant may be 
               -----------------------------------       
exercised at any time or from time to time prior to the Expiration Date as to
the entire number or any lesser number of whole shares of Common Stock, by the
surrender of this Warrant to the Company at its office at 2835 Holmes Road
Houston, Texas 77051, or such other place as is designated in writing by the
Company pursuant to this Section 1, together with (a) a duly executed election
in substantially the form of Exhibit A attached hereto and made a part hereof 
                             ---------                    
for all purposes, and (b) a wire transfer or a certified or bank cashier's check
payable to the order of the Company in an amount equal to the Exercise Price
multiplied by the number of shares of Common Stock covered by such election.
Notwithstanding the foregoing sentence, at any time that the Current Market
Price (as hereinafter defined) is greater than the Exercise Price, the Holder
may, at its option, exercise this Warrant at any time or from time to time prior
to the Expiration Date as to the entire number or any lesser number of whole
shares of Common Stock, by the surrender of this Warrant to the Company at the
location designated in the foregoing sentence together with a duly executed 
election in substantially the form of Exhibit A attached hereto and made a part 
                                      ---------                
hereof for all purposes and, in return therefor, the Company shall deliver to
the Holder that certain number of shares of Common Stock that is determined by
dividing (aa) the product of (1) the number of shares of Common Stock covered by
such election and (2) the difference between the Current Market Price at the
date of such exercise and the Exercise Price in effect on the date of such
exercise by (bb) the Current Market Price at the date of such exercise. For so
long as this Warrant is outstanding, the Company shall continue to maintain an
office in the State of Texas where notices, presentations and demands in respect
of this Warrant may be made
<PAGE>
 
upon it and shall notify the Holder in writing at least 15 days before changing
the location of any such office.

          2.  Stock Ownership; Stock Certificates; Partial Exercise.  
              -----------------------------------------------------   
Upon each exercise of this Warrant, the Holder shall be deemed to be the holder
of record of the shares of Common Stock issuable upon such exercise as of the
close of business on the day this Warrant is exercised, notwithstanding that the
stock transfer books of the Company shall then be closed or certificates
representing such shares shall not then have been actually delivered to the
Holder. As soon as possible after each such exercise of this Warrant, the
Company shall issue and deliver to the Holder a certificate or certificates for
the shares issuable upon such exercise issued in such denominations as may be
specified by Holder and registered in the name of the Holder or, subject to
Section 9, such other name or names as shall be designated in the Holder's
election to exercise. If this Warrant should be exercised in part only, the
Company shall, upon surrender of this Warrant for cancellation, execute and
deliver a new Warrant evidencing the right of the Holder to purchase the balance
of the shares subject to purchase hereunder on the terms and conditions set
forth herein (including all changes and adjustments that have occurred
hereunder). The Company will, at the time of each exercise of this Warrant, upon
the request of the Holder hereof, acknowledge in writing its continuing
obligation to afford to such Holder all rights to which such Holder shall
continue to be entitled after such exercise in accordance with the terms
of this Warrant; provided, however, that if the Holder of this Warrant shall
                 --------                                                   
fail to make any such request, such failure shall not affect the continuing
obligation of the Company to afford such rights to such Holder.

          3.  Company Records; Transfer or Assignment of Warrant; Exchange 
              ------------------------------------------------------------
of Warrant.  Any warrants issued in connection herewith or in substitution 
----------                                                   
herefor, upon complete or partial transfer, assignment or exercise (the
"Warrants") shall be numbered and shall be registered in the warrant register of
the Company (the "Warrant Register") as they are issued. The Company shall treat
the registered holder of any Warrant on the Warrant Register as the owner in
fact thereof for all purposes, except that if the Warrant is properly
transferred or assigned and notice of such transfer or assignment is given to
the Company, the Company shall treat the transferee or assignee as the owner
thereof for all purposes (or, if such transfer or assignment is properly made in
blank, the Company shall treat the bearer of this Warrant as the owner thereof
for all purposes). The Warrant shall be transferred by the Company upon delivery
thereof duly endorsed by the Holder or by his duly authorized attorney or
representative, or accompanied by proper evidence of succession, assignment or
authority to transfer. In case of transfer by executors, administrators,
guardians or other legal representatives, duly authenticated evidence of their
authority shall be produced if requested by the Company in its reasonable
discretion. The Company shall immediately register all assignments and transfers
in the Warrant Register and, upon any registration of assignment or transfer,
the Company shall deliver a new Warrant or Warrants to the person or entity
entitled thereto on the terms and conditions set forth herein (including all
changes and adjustments that have occurred hereunder). A Warrant, if properly
transferred or assigned, may be exercised by a subsequent Holder without having
a new Warrant issued. The Warrants may be exchanged at the option of the Holder
thereof for another Warrant, or

                                       2
<PAGE>
 
other Warrants, of different denominations and representing in the aggregate the
right to purchase the same number of shares of Common Stock on the terms and
conditions set forth herein (including all changes and adjustments that have
occurred hereunder) upon surrender to the Company or its duly authorized agent.
All provisions of this Section 3 shall be subject to Section 9.

          4.  Reserved Stock.  The Company shall reserve
              --------------                            
and keep available at all times solely for the purpose of providing for the
exercise of this Warrant the maximum number of shares of Common Stock as to
which this Warrant may then be exercised.  All such shares shall be duly
authorized and free of preemptive rights and, when issued upon such exercise,
shall be validly issued, fully paid and non-assessable.

          5.  Certain Adjustments.
              ------------------- 

          (a) Number of Shares; Exercise Price.  The number of shares of Common
              --------------------------------                                 
Stock which the Holder of this Warrant shall be entitled to receive upon each
exercise hereof shall be determined by multiplying the number of shares of
Common Stock which would otherwise (but for the provisions of this Section 5) be
issuable upon such exercise, as designated by the Holder hereof, by a fraction
of which (a) the numerator is $10.00 and (b) the denominator is the Exercise
Price in effect on the date of such exercise.  The Exercise Price shall be
adjusted and readjusted from time to time as provided in this Section 5 and, as
so adjusted or readjusted, shall remain in effect until a further adjustment or
readjustment thereof is required by this Section 5.

          (b) Issuance of Additional Shares of Common Stock or Certain
              --------------------------------------------------------
Convertible Securities.  If after the date hereof the Company shall issue any
----------------------                                                       
Common Stock other than Excluded Stock (as hereinafter defined) without
consideration or for a consideration per share less than the Current Market
Price in effect immediately prior to such issuance, the Exercise Price in effect
immediately prior to each such issuance shall immediately (except as otherwise
expressly provided below) be reduced to the price determined by dividing (1) an
amount equal to the sum of (A) the number of shares of Common Stock outstanding
immediately prior to such issuance multiplied by the Current Market Price in
effect immediately prior to such issuance and (B) the consideration, if any,
received by the Company upon such issuance, by (2) the total number of shares of
Common Stock outstanding immediately after such issuance.

          For the purposes of any adjustment of the Exercise Price pursuant to
this Section 5(b), the following provisions shall be applicable:

          (A) Cash.  In the case of the issuance of Common Stock for cash, the
              ----                                                            
amount of the consideration received by the Company shall be deemed to be the
amount of the cash proceeds received by the Company for such Common Stock before
deducting therefrom any discounts, commissions, taxes or other expenses allowed,
paid or incurred by the Company for any underwriting or otherwise in connection
with the issuance and sale thereof.

                                       3
<PAGE>
 
          (B) Consideration Other Than Cash.  In the case of the issuance of
              -----------------------------                                 
Common Stock (otherwise than upon the conversion of shares of capital stock or
other securities of the Company) for a consideration in whole or in part other
than cash, including securities acquired in exchange therefor (other than
securities of the Company that by their terms are exchangeable for such Common
Stock), the consideration other than cash shall be deemed to be the fair value
thereof as determined in good faith by the Board of Directors of the Company and
irrespective of any accounting treatment; provided, that such fair value as
                                          --------                         
determined by the Board of Directors shall not exceed the aggregate Current
Market Price of the shares of Common Stock being issued as of the date on which
the Board of Directors authorizes the issuance of such shares.

          (C) Options and Convertible Securities.  In the case of the issuance
              ----------------------------------                              
of (i) options, warrants or other rights to purchase or acquire Common Stock
(whether or not at the time exercisable), (ii) securities by their terms
convertible into or exchangeable for Common Stock (whether or not at the time so
convertible or exchangeable) or (iii) options, warrants or rights to purchase
such convertible or exchangeable securities (whether or not at the time
exercisable), other than in each case Excluded Stock:


          (1) the aggregate maximum number of shares of Common Stock deliverable
upon exercise of such options, warrants or other rights to purchase or acquire
Common Stock shall be deemed to have been issued at the time such options,
warrants or rights were issued and for a consideration equal to the
consideration (determined in the manner provided in subclauses (A) and (B)
above), if any, received by the Company upon the issuance of such options,
warrants or rights plus the minimum purchase price provided in such options,
warrants or rights for the Common Stock covered thereby;

          (2) the aggregate maximum number of shares of Common Stock deliverable
upon conversion of or in exchange for any such convertible or exchangeable
securities, or upon the exercise of options, warrants or other rights to
purchase or acquire such convertible or exchangeable securities and the
subsequent conversion or exchange thereof, shall be deemed to have been issued
at the time such securities were issued or such options, warrants, or rights
were issued and for a consideration equal to the consideration, if any, received
by the Company for any such securities and related options, warrants or rights
(excluding any cash received on account of accrued interest or accrued
dividends), plus the additional consideration (determined in the manner provided
in subclauses (A) and (B) above), if any, to be received by the Company upon the
conversion or exchange of such securities, or upon the exercise of any related
options,

                                       4
<PAGE>
 
warrants or rights to purchase or acquire such convertible or exchangeable
securities and the subsequent conversion or exchange thereof;

          (3) on any change in the number of shares of Common Stock deliverable
upon exercise of any such options, warrants or rights or conversion or exchange
of such convertible or exchangeable securities or any change in the
consideration to be received by the Company upon such exercise, conversion or
exchange, including, but not limited to, a change resulting from the anti-
dilution provisions thereof, the Exercise Price as then in effect shall
forthwith be readjusted to such Exercise Price as would have been obtained had
an adjustment been made upon the issuance of such options, warrants or rights
not exercised prior to such change, or of such convertible or exchangeable
securities not converted or exchanged prior to such change, upon the basis of
such change;

          (4) on the expiration or cancellation of any such options, warrants or
rights or the termination of the right to convert or exchange such convertible
or exchangeable securities, if the Exercise Price shall have been adjusted upon
the issuance thereof, the Exercise Price shall forthwith be readjusted to such
Exercise Price as would have been obtained had an adjustment been made upon the
issuance of such options, warrants, rights or such convertible or exchangeable
securities on the basis of the issuance of only the number of shares of Common
Stock actually issued upon the exercise of such options, warrants or rights, or
upon the conversion or exchange of such convertible or exchangeable securities;
and

          (5) if the Exercise Price shall have been adjusted upon the issuance
of any such options, warrants, rights or convertible or exchangeable securities,
no further adjustment of the Exercise Price shall be made for the actual
issuance of Common Stock upon the exercise, conversion or exchange thereof.

          (D) Excluded Stock.  "Excluded Stock" shall mean (1) shares of Common
              --------------                                                   
Stock issued by the Company as a stock dividend payable in shares of Common
Stock, or upon any subdivision or split-up of the outstanding shares of Common
Stock for which an adjustment to the Exercise Price is made pursuant to Section
5(c), (2) options to acquire Common Stock and shares of Common Stock issued or
to be issued from time to time to directors, officers, employees, consultants,
advisors, independent contractors and agents of the Company pursuant to stock
option plans or other employee benefit plans approved of by the Board of
Directors, or an authorized committee thereof, of

                                       5
<PAGE>
 
the Company, (3) the shares of Common Stock issued or issuable upon exercise of
the Warrants or any other warrants to purchase shares of Common Stock issued and
outstanding as of the date hereof and (4) shares of Common Stock issued by the
Company pursuant to an underwritten public offering of Common Stock or pursuant
to a public tender or exchange offer.

          (c) Stock Dividends, Subdivisions, Reclassifications or Combinations.
              ----------------------------------------------------------------  
If the Company shall (i) declare a dividend or make a distribution on its Common
Stock in shares of its Common Stock, (ii) subdivide or reclassify the
outstanding shares of Common Stock into a greater number of shares, or (iii)
combine or reclassify the outstanding Common Stock into a smaller number of
shares, the Exercise Price in effect at the time of the record date for such
dividend or distribution or the effective date of such subdivision, combination
or reclassification shall be proportionately adjusted so that the Holder of this
Warrant who exercises this Warrant after such date shall be entitled to receive
the number of shares of Common Stock which he would have owned or been entitled
to receive had this Warrant been exercised immediately prior to such date.
Successive adjustments in the Exercise Price shall be made whenever any event
specified above shall occur.

          (d) Other Distributions.  In case the Company shall fix a record date
              -------------------                                              
for the making of a distribution to all holders of shares of its Common Stock
(i) of shares of any class other than its Common Stock or (ii) of evidences of
indebtedness of the Company or any subsidiary or (iii) of other assets,
including cash, (excluding dividends or distributions referred to in Section
5(c) above and excluding any cash dividend or cash distribution if the per share
amount when combined with the per share amount of all cash dividends and
distributions paid by the Company on Common Stock during the 365-day period
ending on such record date (as adjusted to appropriately reflect any of the
events referred to in Section 5(c) or in this Section 5(d) and excluding cash
dividends or distributions for which an adjustment to the Exercise Price was
previously made pursuant to this Section 5(d)), does not exceed 10% of the
Current Market Price on such record date) or (iv) of rights or warrants
(excluding those referred to in Section 5(b) above), in each case the Exercise
Price in effect immediately prior thereto shall be reduced immediately
thereafter to the price determined by dividing (1) an amount equal to the
difference resulting from (x) the number of shares of Common Stock outstanding
on such record date multiplied by the Current Market Price on such record date,
less (y) the fair market value (as determined in good faith by the Board of
Directors) of said shares or evidences of indebtedness or assets or rights or
warrants to be so distributed, by (2) the number of shares of Common Stock
outstanding on such record date.  Such adjustment shall be made successively
whenever such a record date is fixed.  In the event that such distribution is
not so made, the Exercise Price then in effect shall be readjusted, effective as
of the date when the Board of Directors determines not to distribute such
shares, evidence of indebtedness, assets, rights or warrants, as the case may
be, to the Exercise Price which would then be in effect if such record date had
not been fixed.

          (e) Other Dilutive Events.  In case any event shall occur as to which
              ---------------------                                            
the provisions of this Section 5 are not strictly applicable but the failure to
make any adjustment relating thereto would not fairly protect the purchase
rights represented by this Warrant in accordance with the essential intent and
principles of this Section 5, then, in each such case, the Company shall
immediately make all adjustments necessary to preserve, without dilution,

                                       6
<PAGE>
 
the purchase rights represented by this Warrant on a basis consistent with the
intent and principles established in this Section 5 and shall also immediately
appoint a firm of independent certified public accountants of recognized
national standing (which may be the regular auditors of the Company if they
satisfy such standard), which shall give their opinion that such adjustment, if
any, preserves, without dilution, the purchase rights represented by this
Warrant on a basis consistent with the intent and principles established in this
Section 5.  Upon receipt of such opinion, the Company will immediately deliver a
copy thereof to the Holder of this Warrant.  The Company shall not, by amendment
of its certificate of incorporation or through any consolidation, merger,
reorganization, transfer of assets, dissolution, issue or sale of securities or
any other voluntary action, avoid or seek to avoid the observance or performance
of any of the terms of this Warrant, and will at all times in good faith assist
in carrying out all of such terms and in the taking of all such actions as may
be necessary or appropriate in order to protect the rights of the Holder of this
Warrant against dilution or other impairment. Without limiting the generality of
the foregoing, the Company (i) will not permit the par value of any shares of
stock receivable upon the exercise of this Warrant to exceed the amount payable
therefor upon such exercise, (ii) will take all such action as may be necessary
or appropriate in order that the Company may validly and legally issue fully
paid and nonassessable shares of stock on the exercise of the Warrants from time
to time outstanding, and (iii) will not take any action which results in any
adjustment of the Exercise Price if the total number of shares of Common Stock
issuable after such action upon the exercise of all of the Warrants would exceed
the total number of shares of Common Stock then authorized by the Company's
certificate of incorporation and available for the purpose of issuance upon such
exercise.

          (f) Size of Adjustment; Rounding.  No adjustment in the Exercise Price
              ----------------------------                                      
shall be required unless such adjustment would require an increase or decrease
of at least one cent ($.01) in such price; provided, however, that any
                                           --------                   
adjustment which is thereby not required to be made shall be carried forward and
taken into account in any subsequent adjustment.  All calculations under this
Section 5 shall be made to the nearest cent or to the nearest one-hundredth of a
Share, as the case may be.

          (g) Notice.  Whenever there shall be an adjustment as provided in this
              ------                                                            
Section 5, the Company shall promptly cause written notice thereof to be sent to
the Holder, which notice shall be accompanied by an officer's certificate
setting forth the Exercise Price after such adjustment and setting forth a brief
statement of the facts requiring such adjustment and the computation thereof.
However, the failure by the Company to satisfy its obligations under this
Section 5(g) shall not in any manner affect or alter the rights of the Holder
under this Warrant.

          (h) Fractional Shares.  The Company shall not be required to issue
              -----------------                                             
fractions of shares of Common Stock or other capital stock of the Company upon
the exercise of Warrants.  If any fraction of a share would be issuable upon the
exercise of any Warrant (or specified portions thereof), the Company shall
purchase such fraction for an amount in cash equal to the same fraction of the
Current Market Price of such share of Common Stock on the date of exercise of
the Warrant.

                                       7
<PAGE>
 
          (i) Current Market Price.  The Current Market Price at any date shall
              --------------------                                             
mean, in the event the Common Stock is publicly traded, the average of the daily
closing prices per share of Common Stock for 30 consecutive trading days ending
3 trading days before such date (as adjusted for any stock dividend, other
dividend for which an adjustment to the Exercise Price would be required
pursuant to Section 5(d), split, combination or reclassification that took
effect during such 30 trading day period).  The closing price for each day shall
be the last reported sale price regular way or, in case no such reported sale
takes place on such day, the average of the last closing bid and asked prices
regular way, in either case on the principal national securities exchange on
which the Common Stock is listed or admitted to trading, or if not listed or
admitted to trading on any national securities exchange, the closing sale price
for such day reported by NASDAQ, if the Common Stock is traded over-the-counter
and quoted in the National Market System, or if the Common Stock is so traded,
but not so quoted, the average of the closing reported bid and asked prices of
the Common Stock as reported by NASDAQ or any comparable system or, if the
Common Stock is not listed on NASDAQ or any comparable system, the average of
the closing bid and asked prices as furnished by two members of the National
Association of Securities Dealers, Inc. selected from time to time by the
Company for that purpose.  If the Common Stock is not traded in such manner that
the quotations referred to above are available for the period required
hereunder, the Current Market Price per share of Common Stock shall be deemed to
be the fair value per share of Common Stock as determined by the Board of
Directors of the Company in good faith and irrespective of any accounting
treatment.

          (j) Treasury Stock.  For the purposes of this Section 5, the sale or
              --------------                                                  
other disposition of any Common Stock theretofore held in the Company's treasury
shall be deemed to be an issue thereof.

          (k) Valid Issuance.  All shares of Common Stock which may be issued
              --------------                                                 
upon the exercise of this Warrant will upon issuance by the Company be duly and
validly issued, fully paid and nonassessable and free from all taxes, liens and
charges with respect to the issuance thereof, and the Company shall take no
action which will cause a contrary result (including, without limitation, any
action which would cause the Exercise Price to be less than the par value, if
any, of the Common Stock).

          6.  Certain Corporate Events or Actions.
              -----------------------------------

          (a) Consolidation, Merger, Etc.  In case of any consolidation with or
              ---------------------------                                      
merger of the Company with or into another corporation or other entity (except
for a merger or consolidation in which the Company is the continuing corporation
other than as a subsidiary of another corporation or other entity), or in case
of any sale, lease or conveyance to another corporation or other entity of the
assets of the Company as an entirety or substantially as an entirety, such
successor, purchasing, leasing or receiving corporation or other entity, as the
case may be, shall, prior to and as a condition to the occurrence of such event,
(i) execute with the Holder an agreement providing that the Holder shall have
the right thereafter to receive upon exercise of this Warrant the kind and
amount of shares of stock and other securities, property, cash or any
combination thereof receivable upon such consolidation, merger, sale, lease or
conveyance by a holder of the number of shares of Common Stock for

                                       8
<PAGE>
 
which this Warrant might have been exercised immediately prior to such
consolidation, merger, sale, lease or conveyance (provided that, if the holders
of shares have the right to make an election with respect to the kind or amount
of securities, cash or other property receivable upon consummation of such
event, then the kind and amount of securities, cash or other consideration
receivable to the Holder upon  consummation of such event shall be deemed to be
the kind and amount so receivable per share by a plurality of the shares held by
holders of such shares making such an election) and (ii) make effective
provision in its certificate of incorporation or otherwise, if needed, in order
to effect such agreement.  Such agreement shall provide for adjustments which
shall be equivalent to the adjustments in Section 5 and shall contain provisions
equivalent to this Section 6.

          (b) Reclassification, Etc.  In case of any reclassification or change
              ----------------------                                           
of the shares of Common Stock issuable upon exercise of this Warrant or in case
of any consolidation or merger of another corporation or other entity with or
into the Company in which the Company is the continuing corporation (other than
as a subsidiary of another corporation or other entity) and in which there is a
reclassification or change (including a change to the right to receive cash or
other property) of the shares of Common Stock, the Holder shall have the right
thereafter to receive upon exercise of this Warrant the kind and amount of
shares of stock and other securities, property, cash or any combination thereof
receivable upon such reclassification, change, consolidation or merger by a
holder of the number of shares of Common Stock into which this Warrant would
have been exercisable immediately prior to such reclassification, change,
consolidation or merger (provided that, if the holders of shares have the right
to make an election with respect to the kind or amount of securities, cash or
other property receivable upon consummation of such event, then the kind and
amount of securities, cash or other consideration receivable to the Holder upon
consummation of such event shall be deemed to be the kind and amount so
receivable per share by a plurality of the shares held by holders of such shares
making such an election).  Thereafter, appropriate provision (as determined by
the Board of Directors of the Company in good faith) shall be made for
adjustments which shall be equivalent to the adjustments in Section 5.  This
Section 6(b) shall be applicable to successive reclassifications, changes,
consolidations or mergers.

          7.  Certain Notices. In case at any time the Company shall propose 
              ---------------  
or have knowledge of any proposal:

          (a) to pay any dividend or make any distribution on shares of Common
Stock or to fix a record date for the making of any such dividend or
distribution to holders of Common Stock; or

          (b) to take, or fix a record date for, any action that would result in
any adjustment to the Exercise Price pursuant to Section 5; or

          (c) to effect any reclassification or change of outstanding shares of
Common Stock, or consolidation or merger, or sale, lease or conveyance of
property, of the type addressed in Section 6; or

                                       9
<PAGE>
 
          (d) to effect any voluntary or involuntary liquidation, dissolution or
winding-up of the Company;

then, and in any one or more of such cases, the Company shall give written
notice thereof to the Holder at least 30 days prior to the date on which (i) the
books of the Company shall close, or a record date shall be set, for any such
action described in Section 7(a) or (b) or (ii) such reclassification, change,
consolidation, merger, sale, lease, conveyance, liquidation, dissolution or
winding-up shall be effective, as the case may be.

          8.  Expenses.  The Company shall pay all costs, fees, taxes (other
              --------                                                      
than any federal or state income or stock transfer taxes) and expenses payable
in connection with the preparation, issuance and delivery from time to time of
Warrants and of shares of Common Stock or other securities issued upon the
exercise of Warrants.

          9.  Restrictions on Transfer.  The Holder, by its acceptance hereof,
              ------------------------                                        
represents and warrants that it is acquiring the Warrants and any Common Stock
issued upon the exercise of this Warrant for investment purposes, for its own
account, and not with an intent to sell or distribute the Warrants or any such
Common Stock except in compliance with applicable United States federal and
state securities law.  Neither this Warrant nor any of the Common Stock issued
upon the exercise of this Warrant, nor any interest in either, may be sold,
assigned, pledged, hypothecated, encumbered or in any other manner transferred
or disposed of, in whole or in part, except in compliance with applicable United
States federal and state securities laws and the terms and conditions hereof.
The provisions of this Section 9 shall be binding upon all subsequent holders of
this Warrant, if any.  This Warrant and the shares of Common Stock or other
securities issued upon exercise of this Warrant shall be subject to a stop-
transfer order and the certificate or certificates evidencing any such shares or
securities shall bear the following legend:

"THE SHARES (OR OTHER SECURITIES) REPRESENTED BY THIS CERTIFICATE HAVE BEEN
ACQUIRED FOR INVESTMENT AND HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF
1933, AS AMENDED, OR THE SECURITIES LAWS OF ANY STATE OR OTHER JURISDICTION.
SUCH SECURITIES MAY NOT BE SOLD, ASSIGNED OR OTHERWISE TRANSFERRED EXCEPT UPON
SUCH REGISTRATION OR UPON DELIVERY TO THE CORPORATION OF AN OPINION OF COUNSEL
REASONABLY SATISFACTORY TO THE CORPORATION STATING THAT SUCH SALE, ASSIGNMENT OR
TRANSFER IS EXEMPT FROM REGISTRATION UNDER SUCH ACT AND LAWS."

          10.  Registration of Common Stock; Listing.  If any shares of Common
               -------------------------------------                          
Stock required to be reserved for purposes of exercise of this Warrant require
registration with or approval of any governmental authority under any federal or
state law before such shares may be issued upon exercise, the Company will, at
its expense and as expeditiously as possible, cause such shares to be duly
registered or approved, as the case may be.  At any such time as Common Stock is
listed for trading, the Company will, at its expense, obtain promptly and
maintain the approval of all securities exchanges (including, for this purpose,

                                       10
<PAGE>
 
NASDAQ) on which the Common Stock is listed for trading for an additional
listing, upon official notice of issuance, of the shares of Common Stock
issuable upon exercise of the then outstanding Warrants and maintain the listing
of such shares after their issuance.

          11.  Availability of Information.  The Company will comply with the
               ---------------------------                                   
reporting requirements of Sections 13 and 15(d) of the Securities Exchange Act
of 1934, as amended (the "Exchange Act") (or, if the Company is not required to
so comply pursuant to the Exchange Act, it will make publicly available the
information specified by Rule 144(c)(2) under the Securities Act) and will
comply with all other public information reporting requirements of the
Securities and Exchange Commission (the "Commission") (including Rule 144
promulgated by the Commission under the Securities Act) from time to time in
effect and relating to the availability of an exemption from the Securities Act
for the sale of any restricted securities (as defined in the Securities Act) or
the sale of securities by affiliates (as defined in the Securities Act).  The
Company will also cooperate with each holder of any restricted securities in
supplying such information as may be necessary for such holder to complete and
file any information reporting forms presently or hereafter required by the
Commission as a condition to the availability of an exemption from the
Securities Act for the sale of any restricted securities or the sale of
securities by affiliates.  The Company will furnish to each Holder of a Warrant,
promptly upon their becoming available, copies of all financial statements,
reports, notices and proxy statements sent or made available generally by the
Company to its stockholders, and copies of all regular and periodic reports and
all registration statements and prospectuses filed by the Company with any
securities exchange or with the Commission.

          12.  Loss, Theft, Etc.  Upon receipt of evidence satisfactory to the
               -----------------                                              
Company of the loss, theft, destruction or mutilation of any Warrant and upon
surrender and cancellation of any Warrant if mutilated, the Company shall
execute and deliver to the Holder thereof a new Warrant in the form and
substance of the lost, stolen, destroyed or mutilated Warrant (including all
changes and adjustments that have occurred hereunder).  In the event a bond for
security therefor is required, the cost of such bond shall be paid by the
Holder.

          13.  No Rights or Liabilities as a Stockholder.  Nothing contained in
               -----------------------------------------                       
this Warrant shall be construed as conferring upon the Holder hereof any rights
as a stockholder of the Company or as imposing any obligation upon such Holder
to purchase any securities or as imposing any liability upon such Holder as a
stockholder of the Company, whether such obligation or liability is asserted by
the Company or by creditors of the Company at law or in equity.

          14.  Governing Law.  This Warrant shall be governed by and construed
               -------------                                                  
in accordance with the internal laws of the State of Delaware.

          15.  Remedies.  The Company stipulates that the remedies at law of the
               --------                                                         
Holder of this Warrant in the event of any default or threatened default by the
Company in the performance of or compliance with any of the terms of this
Warrant are not and will not be adequate, and that, to the extent permitted by
applicable law, such terms may be specifically enforced by a decree for the
specific performance of any agreement contained herein or by an injunction
against a violation of any of the terms hereof or otherwise.

                                       11
<PAGE>
 
          16.  Notices.  All notices and other communications provided for
               -------                                                    
herein shall be delivered or mailed by registered or certified mail, return
receipt requested, postage prepaid, addressed (a) if to any Holder of any
Warrant, to the address of such Holder as set forth in the Warrant Register or
to such other address as such Holder has notified the Company of in writing or
(b) if to the Company, to the address set forth in Section 1 or to such other
address as the Company has notified such Holder of pursuant to Section 1 and
this Section 16; provided, however, that the exercise of any Warrant shall be
effective in the manner provided in Section 1.  All notices given pursuant to
this Warrant shall be deemed to be effective upon receipt thereof by the party
to whom such notice is addressed.

          17.  Miscellaneous.  This Warrant and any term hereof may be changed,
               -------------                                                   
waived, discharged or terminated only by an instrument in writing signed by the
party against which enforcement of such change, waiver, discharge or termination
is sought.  Any provision of this Warrant which shall be prohibited or
unenforceable in any jurisdiction shall, as to such jurisdiction, be ineffective
to the extent of such prohibition or unenforceability without invalidating the
remaining provisions hereof, and any such prohibition or unenforceability in any
jurisdiction shall not invalidate or render unenforceable such provision in any
other jurisdiction. To the extent permitted by applicable law, the Company
waives any provision of law which shall render any provision hereof prohibited
or unenforceable in any respect.  The section and paragraph headings used in
this Warrant are inserted for convenience only and shall not be used for any
interpretive purpose.

          IN WITNESS WHEREOF, the Company has caused this Warrant to be duly
executed and its corporate seal to be impressed hereon and attested by its
Secretary or an Assistant Secretary.

Dated: _________________, 1996    TUBOSCOPE VETCO INTERNATIONAL
                                    CORPORATION


[Corporate Seal]                   By:
                                       -------------------------------------
Attest:



Secretary

                                       12
<PAGE>
 
                                                            EXHIBIT A TO WARRANT
                                                            --------------------


To:  TUBOSCOPE VETCO INTERNATIONAL CORPORATION
 
 


                              ELECTION TO EXERCISE

          The undersigned hereby exercises his or its rights to subscribe for
__________ shares of Common Stock covered by the within Warrant [and tenders
payment herewith in the amount of $____________] [and tenders no payment
herewith with respect to such shares of Common Stock covered by the within
Warrant and thus requests ____ shares of Common Stock (the quotient of (i) ___
shares covered by this exercise multiplied by $____) (the Current Market Price
at the date of this exercise minus the Exercise Price), divided by $_____ (the
Current Market Price at the date of this exercise)] in accordance with the terms
thereof, and requests that certificates for such shares in the following
denominations be issued in the name of, and delivered to, the person[s] at the
following address[es]:


                              Denominations:

 
 
 
              (Print Address[es] and Social Security Number[s] or
                Employer Identification Number[s] as applicable)

and, if said number of shares shall not be all the shares covered by the within
Warrant, that a new Warrant for the balance remaining of the shares covered by
the within Warrant be registered in the name of, and delivered to, the
undersigned at the address stated below:

Date:  __________, ____      Name:  ______________________________________
                                                    (Print)


 
                                                  (Signature)

                              Address:  __________________________________