HALLIBURTON CO
8-B12B, 1996-12-12
HEAVY CONSTRUCTION OTHER THAN BLDG CONST - CONTRACTORS
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<PAGE>
 
                                    FORM 8-B

                       SECURITIES AND EXCHANGE COMMISSION

                            WASHINGTON, D. C. 20549

            REGISTRATION OF SECURITIES OF CERTAIN SUCCESSOR ISSUERS

 FILED PURSUANT TO SECTION 12(b) OR (g) OF THE SECURITIES EXCHANGE ACT OF 1934



                              HALLIBURTON COMPANY
             (EXACT NAME OF REGISTRANT AS SPECIFIED IN ITS CHARTER)

         DELAWARE                                          96-75-2677995
(STATE OR OTHER JURISDICTION OF                          (I.R.S. Employer
 INCORPORATION OR ORGANIZATION)                          Identification Number)

                               3600 Lincoln Plaza
                                  500 N. Akard
                            Dallas, Texas 75201-3391
                                 (214) 978-2600
         (Address, including zip code, and telephone number,  including
            area code, of registrant's principal executive offices)



     Securities to be registered pursuant to Section 12 (b) of the Act:

         Title of each class                 Name of each exchange on which
         to be so registered                  each class is to be registered
 
    Common Stock, par value $2.50            New York Stock Exchange, Inc.
 
    Preferred Stock Purchase Rights          New York Stock Exchange, Inc.

    Securities to be registered pursuant to Section 12(g) of the Act:  None.
<PAGE>
 
ITEM 1.  GENERAL INFORMATION.

     (a) The Registrant was organized as a corporation under the laws of the
State of Delaware on  November 7, 1996.

     (b) The Registrant's fiscal year ends on December 31.

ITEM 2.  TRANSACTION OF SUCCESSION.

     (a) The Registrant is the successor to Halliburton Company, a corporation
organized under the laws of the State of Delaware (the "Predecessor"), which,
until the transaction described in subsection (b) of this item, had its Common
Stock, par value $2.50, registered pursuant to Section 12(b) of the Act.

     (b) The Predecessor has reorganized (the "Reorganization") its operations
into a holding company structure pursuant to which the Predecessor became an
indirect wholly-owned subsidiary of the Registrant. To effect the
Reorganization, the Predecessor caused the Registrant to be incorporated as a
wholly-owned subsidiary of the Predecessor, Halliburton Delaware, Inc. ("Newco")
to be incorporated as a wholly-owned subsidiary of Registrant and Halliburton
Merge Co. ("Merger Sub") to be incorporated as a wholly-owned subsidiary of
Newco. Prior to the Reorganization, each of Registrant, Newco and Merger Sub had
a nominal amount of stock outstanding and no business or properties of its own.

     Under the terms of an Agreement and Plan of Reorganization dated as of
December 11, 1996 among the Predecessor, Registrant and Merger Sub (the "Merger
Agreement"), Merger Sub, pursuant to Section 251(g) of the DGCL, merged (the
"Merger") with and into the Predecessor on the date of this Registration
Statement. The Predecessor is the corporation that survived the Merger, and the
separate corporate existence of Merger Sub ceased. Pursuant to the terms of the
Merger Agreement:

          (i)   each share of Common Stock of the Predecessor (the "Predecessor
     Common Stock") issued and outstanding immediately prior to the Merger was
     converted into a share of Common Stock of the Registrant (the "Registrant
     Common Stock") having the same designations, rights, powers and
     preferences, and qualifications, limitations and restrictions thereof, as
     the shares of Predecessor Common Stock so converted;

          (ii)  each share of Predecessor Common Stock that was issued and
     previously held in the treasury of the Predecessor, having been contributed
     to the capital of Registrant immediately prior to the Merger, was also
     converted into a share of Registrant Common Stock, where it is held as
     treasury stock;

          (iii) each share of capital stock of Merger Sub issued and outstanding
     immediately prior to the Merger was converted into a share of common stock
     of the Predecessor; and

          (iv)  each share of issued and outstanding capital stock of Registrant
     was contributed by the 
<PAGE>
 
     Predecessor to the Registrant at the Effective Time (as hereinafter
     defined) of the Merger, where it is held as treasury stock.

In connection with the Merger, the certificate of incorporation of the
Predecessor was amended to change the name of the Predecessor to "Halliburton
Energy Services, Inc." and, immediately thereafter, the certificate of
incorporation of Registrant was amended by a separate filing to change the
corporate name of Registrant to "Halliburton Company". Given that, immediately
after the Merger, the name of Registrant and the designations, rights, powers
and privileges, and qualifications, limitations and restrictions thereof, of the
capital stock of Registrant were, in each case, identical with those of the
Predecessor immediately prior to the Merger, no post-Merger exchange of stock
certificates will be made (the outstanding Predecessor Common Stock certificates
will subsequent to the Merger evidence shares of Registrant Common Stock).

 
In addition, prior to the effective time (the "Effective Time") of the Merger,
the Registrant adopted a Rights Agreement (the "Registrant Rights Agreement")
that is in all substantive matters identical to the Rights Agreement of the
Predecessor (the "Predecessor Rights Agreement") except that Registrant is the
party thereto, rather than the Predecessor. Prior to the Effective Time, the
Board of Directors of Registrant caused the Registrant to distribute immediately
prior to the Effective Time preferred stock purchase rights (the "Registrant
Purchase Rights") to the Predecessor, as the holder of all the then outstanding
Registrant Common Stock, to purchase shares of Registrant Series A Junior
Participating Preferred Stock (the "Registrant Series A Preferred Stock"), the
designation, rights, powers and preferences of which, and the qualifications,
limitations and restrictions thereof, are identical to those of the Predecessor
Series A Preferred Stock subject to the Predecessor Rights Plan. The expiration
date of Registrant Purchase Rights is identical with that of the Predecessor
Purchase Rights. Under the terms of the Registrant Rights Agreement, the
Registrant is obligated (pursuant to a provision identical to one that formerly
obligated the Predecessor) to issue one Registrant Purchase Right at the time of
each issuance thereafter of one share of Registrant Common Stock. As a result of
these transactions, each share of Registrant Common Stock issued pursuant to the
Merger was accompanied by a Registrant Purchase Right and all previously
outstanding Predecessor Purchase Rights were canceled.
 
     The Merger was effected by action of the Board of Directors of the
Predecessor without a vote of its stockholders pursuant to Section 251(g) of the
DGCL. In a reorganization pursuant to Section 251(g), appraisal rights are not
available to any of the stockholders of any constituent corporation.

     Except for certain amendments to the certificate of incorporation of the
Predecessor effected in accordance with Section 251(g) of the DGCL in
conjunction with the Merger, the provisions of the certificate of incorporation
of Registrant, including its authorized capital stock and the designations,
rights, powers and preferences of such capital stock, and the qualifications,
limitations and restrictions thereof, are, following the Merger, identical to
those of the Predecessor immediately prior to the Merger.  As a result, the
Predecessor's stockholders received securities of the same class evidencing the
same proportional interests in the Registrant and having the same designations,
rights, powers and preferences, and qualifications, limitations and restrictions
thereof, as those previously held in the Predecessor.

     The provisions of the by-laws of the Registrant, following the Merger, are
identical with the provisions of the bylaws of the Predecessor in effect
immediately prior to the Merger. The directors of the Registrant immediately
after the Merger are the same individuals as were directors of the 
<PAGE>
 
Predecessor immediately prior thereto. Finally, the management of the Registrant
following the Merger is the same as the management of the Predecessor
immediately prior to the Merger.
 
     In connection with the consummation of the Merger, the Predecessor received
(i) an opinion of its counsel, Vinson & Elkins L.L.P., to the effect that the
Merger qualified as a reorganization under section 368(a) of the Internal
Revenue Code of 1986, as amended (the "Code"), and, as a result, the
stockholders of the Predecessor would not recognize gain or loss for United
States federal income tax purposes.

     The Merger conformed in all respects with the required provisions of
Section 251(g) of the DGCL.

ITEM 4.  DESCRIPTION OF REGISTRANT'S SECURITIES TO BE REGISTERED.

DESCRIPTION OF CAPITAL STOCK

     General. The following descriptions of certain of the provisions of the
Certificate of Incorporation of the Registrant and of the Registrant Rights
Agreement (as defined below) are necessarily general and do not purport to be
complete and are qualified in their entirety by reference to such documents,
which are included as exhibits to the Registration Statement of which this
Prospectus is a part.

     Common Stock. The Registrant is authorized to issue 200,000,000 shares of
Common Stock, par value $2.50. As of November 30,1996, there were 125,258,208
shares of Predecessor Common Stock issued and outstanding, all of which was, at
the Effective Time, converted into Registrant Common Stock on a share for share
basis, and approximately 15,050 holders of record of Predecessor Common Stock.
The holders of Registrant Common Stock are entitled to one vote for each share
on all matters submitted to a vote of stockholders. The holders of Registrant
Common Stock do not have cumulative voting rights in the election of directors.
Subject to the rights of the holders of Registrant Preferred Stock (as defined
below), the holders of Registrant Common Stock are entitled to receive ratably
such dividends, if any, as may be declared by the Board of Directors of the
Registrant out of legally available funds. In the event of liquidation,
dissolution or winding up of the Registrant, the holders of Registrant Common
Stock are entitled to share ratably in all assets of the Registrant remaining
after the full amounts, if any, to which the holders of outstanding Registrant
Preferred Stock are entitled. The holders of Registrant Common Stock have no
preemptive, subscription, redemptive or conversion rights. The outstanding
shares are fully paid and nonassessable.

     Preferred Stock. The Registrant is authorized to issue 5,000,000 shares of
Preferred Stock, without par value (the "Registrant Preferred Stock"). No shares
of Registrant Preferred Stock are outstanding. The Board of Directors of the
Registrant has authority, without stockholder approval (subject to a limited
exception), to issue shares of Registrant Stock in one or more series and to
determine the number of shares, designations, dividend rights, conversion
rights, voting power, redemption rights, liquidation preferences and other terms
of such series. The issuance of Registrant Preferred Stock, while providing
desired flexibility in connection with possible acquisitions and other corporate
purposes, could adversely affect the voting power of holders of Registrant
Common Stock 
<PAGE>
 
and the likelihood that such holders will receive dividend payments and payments
upon liquidation and could have the effect of delaying, deferring or preventing
a change in control of the Registrant. The Registrant has no present plans to
issue any Registrant Preferred Stock.

     Series A Preferred Stock. The Board of Directors of the Registrant has, in
conjunction with its adoption of the Rights Agreement described below,
designated 2,000,000 shares of Registrant Preferred Stock as the Series A Junior
Participating Preferred Stock. The terms of the Registrant Series A Preferred
Stock are designed so that the value of each one-hundredth of a share
purchasable upon exercise of a Right will approximate the value of one share of
Registrant Common Stock. The Registrant Series A Preferred Stock is
nonredeemable and will rank junior to all other series of Registrant Preferred
Stock. Each whole share of Registrant Series A Preferred Stock is entitled to
receive a cumulative quarterly preferential dividend in an amount per share
equal to the greater of (i) $1.00 in cash or (ii), in the aggregate, 100 times
the dividend declared on the Registrant Common Stock. In the event of
liquidation, the holders of the Registrant Series A Preferred Stock are entitled
to receive a preferential liquidation payment equal to the greater of (i)
$100.00 per share or (ii), in the aggregate, 100 times the payment made on the
Registrant Common Stock, plus, in either case, the accrued and unpaid dividends
and distributions thereon. In the event of any merger, consolidation or other
transaction in which the Registrant Common Stock is exchanged for or changed
into other stock or securities, cash or property, each whole share of Registrant
Series A Preferred Stock is entitled to receive 100 times the amount received
per share of Registrant Common Stock. Each whole share of Registrant Series A
Preferred Stock is entitled to 100 votes on all matters submitted to a vote of
the stockholders of the Registrant, and holders of Registrant Series A Preferred
Stock will generally vote together as one class with the holders of Registrant
Common Stock and any other capital stock on all matters submitted to a vote of
stockholders of the Registrant.

DESCRIPTION OF PREFERRED STOCK PURCHASE RIGHTS

     General.  On December 11, 1996, the Board of Directors of the Registrant
declared a dividend of one preferred share purchase right (a "Right") for each
outstanding share of Registrant Common Stock held of record on that date and
approved the further issuance of Rights with respect to all shares of Registrant
Common Stock that are subsequently issued, including without limitation the
shares of Registrant Common Stock issued pursuant to the Merger. The Rights were
issued subject to a Rights Agreement dated as of December 1, 1996 between the
Registrant and ChaseMellon Shareholder Services, L.L.C., as Rights Agent. Each
Right now entitles the registered holder to purchase from the Registrant one-
hundredth of a share of Series A Preferred Stock at a price of $150.00 in cash
(the "Purchase Price"), subject to adjustment. Until the occurrence of certain
events described below, the Rights are not exercisable, will be evidenced by the
certificates for Registrant Common Stock and will not be transferable apart from
the Registrant Common Stock.

     Detachment of Rights; Exercise.  The Rights are currently attached to all
certificates representing outstanding shares of Registrant Common Stock and no
separate Right certificates have been distributed. The Rights will separate from
the Registrant Common Stock and a distribution date ("Distribution Date") will
occur upon the earlier of (i) ten business days following the public
<PAGE>
 
announcement that a person or group of affiliated or associated persons (an
"Acquiring Person") has acquired beneficial ownership of 15% or more of the
outstanding Voting Shares (as defined in the Registrant Rights Agreement) of the
Registrant or (ii) ten business days following the commencement or announcement
of an intention to commence a tender offer or exchange offer, the consummation
of which would result in the beneficial ownership by a person or group of 15% or
more of such outstanding Voting Shares.

     The Rights are not exercisable until the Distribution Date.  As soon as
practicable following the Distribution Date, separate certificates evidencing
the Rights will be mailed to holders of record of Registrant Common Stock as of
the close of business on the Distribution Date and such separate certificates
alone will thereafter evidence the Rights.

     If a person or group were to acquire 15% or more of the Voting Shares of
the Registrant, each Right then outstanding (other than Rights beneficially
owned by the Acquiring Person which would become null and void) would become a
right to buy that number of shares of Registrant Common Stock (or, under certain
circumstances, the equivalent number of one-hundredths of a share of Series A
Preferred Stock) that at the time of such acquisition would have a market value
of two times the Purchase Price of the Right.

     If the Registrant were acquired in a merger or other business combination
transaction or more than 50% of its consolidated assets or earning power were
sold, proper provision would be made so that each holder of a Right would
thereafter have the right to receive, upon the exercise thereof at the then
current Purchase Price of the Right, that number of shares of common stock of
the acquiring company which at the time of such transaction would have a market
value of two times the Purchase Price of the Right.

     Additional and Other Adjustments. The number of shares (or fractions
thereof) of Series A Preferred Stock or other securities or property issuable
upon exercise of the Rights, and the Purchase Price payable, are subject to
customary adjustments from time to time to prevent dilution. The number of
outstanding Rights and the number of shares (or fractions thereof) of Series A
Preferred Stock issuable upon exercise of each Right are also subject to
adjustment in the event of a stock split of the Registrant Common Stock or a
stock dividend on the Registrant Common Stock payable in Registrant Common Stock
or any subdivision, consolidation or combination of the Registrant Common Stock
occurring, in any such case, prior to the Distribution Date.

     Exchange Option.  At any time after the acquisition by a person or group of
affiliated or associated persons of beneficial ownership of 15% or more of the
outstanding Voting Shares of the Registrant and before the acquisition by a
person or group of 50% or more of the outstanding Voting Shares of the
Registrant, the Board of Directors may, at its option, issue Registrant Common
Stock in mandatory redemption of, and in exchange for, all or part of the then
outstanding and exercisable Rights (other than Rights owned by such person or
group which would become null and void) at an exchange ratio of one share of
Registrant Common Stock (or one-hundredth of a share of Series A Preferred
Stock) for each two shares of Registrant Common Stock for which each Right is
then exercisable, subject to adjustment.
<PAGE>
 
     Redemption of Rights.  At any time prior to the first public announcement
that a person or group has become the beneficial owner of 15% or more of the
outstanding Voting Shares, the Board of Directors of the Registrant may redeem
all but not less than all the then outstanding rights at a price of $.01 per
Right (the "Redemption Price").  The redemption of the Rights may be made
effective at such time, on such basis and with such conditions as the Board of
Directors of the Registrant in its sole discretion may establish.  Immediately
upon the action of the Board of Directors ordering redemption of the Rights, the
right to exercise the Rights will terminate and the only right of the holders of
Rights will be to receive the Redemption Price.

     Expiration; Amendment of Rights.  The Rights will expire on December 15,
2005, unless earlier extended, redeemed or exchanged.  The terms of the Rights
may be amended by the Board of Directors without the consent of the holders of
the Rights, including an amendment to extend the expiration date of the Rights,
and, provided a Distribution Date has not occurred, to extend the period during
which the Rights may be redeemed, except that after the first public
announcement that a person or group has become the beneficial owner of 15% or
more of the outstanding Voting Shares, no such amendment may materially and
adversely affect the interests of holders of the Rights.

     The Rights have certain anti-takeover effects.  The Rights will cause
substantial dilution to a person or group that attempts to acquire the
Registrant without the approval of the Board of Directors. The Rights should
not, however, interfere with any merger or other business combination that is
approved by the Board of Directors of the Registrant.

     The foregoing description of the Rights does not purport to be complete and
is qualified in its entirety by reference to the Rights Agreement, a copy of
which is filed as an exhibit to the Registration Statement and is available free
of charge from the Registrant.

ITEM 5.  FINANCIAL STATEMENTS AND EXHIBITS.

     (a)  No financial statements are filed herewith because the capital
structure and consolidated balance sheet of the Registrant immediately after the
succession were substantially the same as those of the Predecessor.

     (b)  Exhibits.

     1.1  ---Agreement and Plan of Reorganization dated as of December 11, 1996
          among Halliburton Company, Halliburton Hold Co. and Halliburton Merge
          Co.

     3.1  ---Certificate of Incorporation of the Registrant, as amended.

     3.2  ---By-laws of the Registrant, as amended.

     4.1  ---Senior Indenture dated as of January 2, 1991 between the
          Predecessor and Texas Commerce Bank National Association, as Trustee
          (incorporated by reference to Exhibit 4(b) to the Predecessor's
          Registration Statement on Form S-3 (File No. 33-38394) originally
          filed with the Securities and Exchange Commission on December 
<PAGE>
 
          21, 1990), as supplemented and amended by the First Supplemental
          Indenture dated as of December 12, 1996 among the Predecessor, the
          Registrant and the Trustee.

     4.2  ---Second Senior Indenture dated as of December 1, 1996 between the
          Predecessor and Texas Commerce Bank National Association, as Trustee
          (incorporated by reference to Exhibit 4.4 to the Predecessor's
          Registration Statement on Form S-3 (File No. 33-65772) originally
          filed with the Securities and Exchange Commission on July 9, 1993 and
          as post effectively amended on December 5, 1996), as supplemented and
          amended by the First Supplemental Indenture dated as of December 5,
          1996 between the Predecessor and the Trustee and the Second
          Supplemental Indenture dated as of December 5, 1996 among the
          Predecessor, the Registrant and the Trustee.

     4.3  ---Subordinated Indenture dated as of January 2, 1991 between the
          Predecessor and Texas Commerce Bank National Association, as Trustee
          (incorporated by reference to Exhibit 4(c) to the Predecessor's
          Registration Statement on Form S-3 (File No. 33-38394) originally
          filed with the Securities and Exchange Commission on December 21,
          1990), as supplemented and amended by the First Supplemental Indenture
          dated as of December 12, 1996 among the Predecessor, the Registrant
          and the Trustee.

     4.4  ---Rights Agreement dated as of December 1, 1996 between the
          Registrant and ChaseMellon Shareholder Services, L.L.C.

     8.1  ---Opinion of Vinson & Elkins L.L.P. as to certain tax matters.

    11.1  ---Statement re computation of per share earnings (incorporated by
          reference to Exhibit 11 to the Predecessor's Annual Report on Form 10-
          K for the year ended December 31, 1995 (File No. 1-3492), filed with
          the Securities and Exchange Commission on March 11, 1996).

    12.1  ---Computation of Ratio of Earnings to Fixed Charges (incorporated by
          reference to Exhibit 12.1 to the Predecessor's Registration Statement
          on Form S-3 (File No. 33-65772) originally filed with the Securities
          and Exchange Commission on July 9, 1993 and as post effectively
          amended on December 5, 1996).

    21.1  ---Subsidiaries of the Registrant.
<PAGE>
 
                                   SIGNATURE

     Pursuant to the requirements of Section 12 of the Securities Exchange Act
of 1934, as amended, the Registrant has duly caused this Registration Statement
to be signed on its behalf by the undersigned, thereunto duly authorized.

                              HALLIBURTON COMPANY



Date:  December 12, 1996      By: /s/ Susan S. Keith  
                                 ________________________________
                              Name: Susan S. Keith
                              Title: Vice President and Secretary

<PAGE>
 
                                                                     EXHIBIT 1.1





                             AGREEMENT AND PLAN OF

                                 REORGANIZATION

                           among Halliburton Company,

                Halliburton Hold Co. and Halliburton Merge Co.

                         dated as of December 11, 1996
<PAGE>
 
                               TABLE OF CONTENTS


<TABLE>
<S>                                                                     <C>
ARTICLE I
     THE MERGER

     Section 1.1  The Merger.........................................    2
     Section 1.2  Effective Time.....................................    2
     Section 1.3  Certificate of Incorporation.......................    3
     Section 1.4  By-laws............................................    4
     Section 1.5  Directors..........................................    4
     Section 1.6  Officers...........................................    4
     Section 1.7  Additional Actions.................................    4
     Section 1.8  Conversion of Securities...........................    4
     Section 1.9  Preferred Share Purchase Rights....................    5
     Section 1.10 No Surrender of Certificates; Stock Transfer Books.    6

ARTICLE II
     ACTIONS TO BE TAKEN IN
     CONNECTION WITH THE MERGER

     Section 2.1  Company Indebtedness...............................    6
     Section 2.2  Assumption of Benefit Plans........................    7
     Section 2.3  Reservation of Shares..............................    7

ARTICLE III
     CONDITIONS OF MERGER

     Section 3.1  Conditions Precedent...............................    7

ARTICLE IV
     COVENANTS

     Section 4.1  Election of Directors..............................    9
     Section 4.2  Listing of Holding Company Common Stock............    9
     Section 4.3  Employee Benefit Plans.............................    9
</TABLE> 
<PAGE>
 
<TABLE>
<S>                                                                     <C>
     Section 4.4  Change in Capitalization...........................    9
     Section 4.5  Change of Name of Holdco...........................    9
     Section 4.6  Contribution of Treasury Stock.....................    9
     Section 4.7  Contribution of Outstanding Holdco Stock...........   10
     Section 4.8  Contribution of Alphabet Stock.....................   10
     Section 4.9  InterCompany Stock Distributions...................   10

ARTICLE V
     TERMINATION AND AMENDMENT

     Section 5.1  Termination........................................   10
     Section 5.2  Amendment..........................................   10

ARTICLE VI
     MISCELLANEOUS PROVISIONS

     Section 6.1  Governing Law......................................   10
     Section 6.2  Counterparts.......................................   11
     Section 6.3  Entire Agreement...................................   11
</TABLE>
<PAGE>
 
                      AGREEMENT AND PLAN OF REORGANIZATION

     THIS AGREEMENT AND PLAN OF REORGANIZATION ("Agreement"), dated as of
December 11, 1996, is among Halliburton Company, a Delaware corporation (the
"Company"), Halliburton Hold Co., a Delaware corporation ("Holdco") and a
direct, wholly owned subsidiary of the Company, and Halliburton Merge Co., a
Delaware corporation ("Mergeco") and a direct, wholly owned subsidiary of
Halliburton Delaware, Inc.,  a Delaware corporation ("Newco") that is itself a
direct, wholly owned subsidiary of Holdco.

                                    RECITALS

     A.   The Company's authorized capital stock consists of (i) 200,000,000
shares of common stock, par value $2.50 per share ("Company Common Stock"), of
which 125,258,208 shares were issued and outstanding as of November 30, 1996 and
4,012,502 shares were held in treasury on such date, and (ii) 5,000,000 shares
of preferred stock, without par value, none of which is currently outstanding
but of which 2,000,000 shares have been designated as the Halliburton Company
Series A Junior Participating Preferred Stock ("Company Series A Preferred
Stock").

     B.   As of the date hereof, Holdco's authorized capital stock consists of
(i) 200,000,000 shares of common stock, par value $2.50 per share ("Holdco
Common Stock"), of which 1,000 shares are issued and outstanding and no shares
are held in treasury, and (ii) 5,000,000 shares of preferred stock, without par
value, none of which is currently outstanding but of which 2,000,000 shares have
been designated as the Halliburton Hold Co. Series A Junior Participating
Preferred Stock ("Holdco Series A Preferred Stock").

     C.   The designations, rights and preferences, and the qualifications,
limitations and restrictions thereof, of the Holdco Series A Preferred Stock and
the Holdco Common Stock are the same as those of the Company Series A Preferred
Stock and the Company Common Stock.

     D.     The Certificate of Incorporation and the By-laws of Holdco
immediately after the Effective Time (as hereinafter defined) will contain
provisions identical to the Certificate of Incorporation and By-laws of the
Company immediately before the Effective Time (other than with respect to
matters excepted by Section 251(g) of the General Corporation Law of the State
of Delaware (the "DGCL")).
<PAGE>
 
     E.   The directors of the Company immediately prior to the Merger (as
hereinafter defined) will be the directors of Holdco as of the Effective Time.
 
     F.   Holdco, Newco and Mergeco are newly formed corporations organized for
the purpose of participating in the transactions herein contemplated.

     G.   The Company desires to create a new holding company structure by
merging Mergeco with and into the Company with the Company being the surviving
corporation, and converting each outstanding share of Company Common Stock into
a like number of shares of Holdco Common Stock, all in accordance with the terms
of this Agreement.

     H.   The Boards of Directors of Holdco, Mergeco and the Company have
approved this Agreement and the merger of Mergeco with and into the Company upon
the terms and subject to the conditions set forth in this Agreement (the
"Merger").

     I.   Pursuant to authority granted by the Board of Directors of the
Company, the Company will, immediately prior to the Effective Time of the
Merger, contribute to the capital of Holdco all of the shares of Company Common
Stock then held by the Company in its treasury.

     NOW, THEREFORE, in consideration of the premises and the covenants and
agreements contained in this Agreement, and intending to be legally bound
hereby, the Company, Holdco and Mergeco hereby agree as follows:

                                   ARTICLE I
                                  THE MERGER

      Section 1.1   The Merger.  In accordance with Section 251(g) of the DGCL
and subject to and upon the terms and conditions of this Agreement, Mergeco
shall, at the Effective Time, be merged with and into the Company, the separate
corporate existence of Mergeco shall cease and the Company shall continue as the
surviving corporation.  The Company as the surviving corporation after the
Merger is hereinafter sometimes referred to as the "Surviving Corporation."  At
the Effective Time, the effect of the Merger shall be as provided in Section 259
of the DGCL.

      Section 1.2   Effective Time.  The Merger shall become effective upon the
filing, after the date hereof and on or before December 31, 1996, of a copy of
this Agreement with the Secretary of State of the State of Delaware (the time of
such filing being referred to herein as the "Effective Time").


                              HALLIBURTON COMPANY
                     AGREEMENT AND PLAN OF REORGANIZATION

                                       2
<PAGE>
 
      Section 1.3   Certificate of Incorporation.  From and after the Effective
Time the Composite Certificate of Incorporation of the Company, as in effect
immediately prior to the Effective Time, shall be the certificate of
incorporation of the Surviving Corporation until thereafter amended as provided
by law; provided, however, that, from and after the Effective Time:

     (a)  Article One thereof shall be amended so as to read in its entirety as
follows:

          "First:  The name of this Corporation is Halliburton Energy Services,
     Inc."

     (b)  Article Fourth thereof shall be amended so as to read in its entirety
as follows:

          "Fourth:  The aggregate number of shares which the Corporation shall
     have authority to issue shall be one thousand (1,000), consisting of one
     thousand (1,000) shares of Common Stock, par value $1.00 per share. No
     shares of the previously designated Series A Junior Participating Preferred
     Stock having been issued, such series is hereby terminated and all matters
     set forth in this certificate of incorporation with respect to such series
     are hereby eliminated from this certificate of incorporation."

     (c)  A new Article Seventeenth shall be added thereto which shall be and
read in its entirety as follows:

          "Seventeenth:  Any act or transaction by or involving the Corporation
     that requires for its adoption under the General Corporation Law of the
     State of Delaware or its certificate of incorporation the approval of the
     stockholders of the Corporation shall, by virtue of this reference to
     Section 251(g) of the General Corporation Law of the State of Delaware,
     require, in addition, the approval of the stockholders of Halliburton
     Company, a Delaware corporation (formerly Halliburton Hold Co.), or any
     successor thereto by merger, so long as such corporation or its successor
     is the ultimate parent, directly or indirectly, of this Corporation, by the
     same vote that is required by the General Corporation Law of the State of
     Delaware and/or the certificate of incorporation of this Corporation.  For
     the purposes of this Article Seventeenth, the term "parent" shall mean a
     corporation that owns, directly or indirectly, at least a majority of the
     outstanding capital stock of this Corporation entitled to vote in the
     election of directors of this Corporation without regard to the occurrence
     of any contingency."

      Section 1.4   By-laws.  From and after the Effective Time, the By-laws of
Mergeco, as in effect immediately prior to the Effective Time, shall be the By-
laws of the Surviving Corporation until thereafter amended as provided therein
or by applicable law.


                              HALLIBURTON COMPANY
                     AGREEMENT AND PLAN OF REORGANIZATION

                                       3
<PAGE>
 
      Section 1.5   Directors.  The directors of Mergeco immediately prior to
the Effective Time shall be the initial directors of the Surviving Corporation
and will hold office from the Effective Time until their successors are duly
elected or appointed and qualified in the manner provided in the Certificate of
Incorporation and the By-laws of the Surviving Corporation or as otherwise
provided by law.

      Section 1.6   Officers.  The officers of Mergeco immediately prior to the
Effective Time shall be the initial officers of the Surviving Corporation and
will hold office from the Effective Time until their successors are duly elected
or appointed and qualified in the manner provided in the Certificate of
Incorporation and the By-laws of the Surviving Corporation or as otherwise
provided by law.

      Section 1.7   Additional Actions.  Subject to the terms of this Agreement,
the parties hereto shall take all such reasonable and lawful action as may be
necessary or appropriate in order to effectuate the Merger.  If, at any time
after the Effective Time, the Surviving Corporation shall consider or be advised
that any deeds, bills of sale, assignments, assurances or any other actions or
things are necessary or desirable to vest, perfect or confirm, of record or
otherwise, in the Surviving Corporation its right, title or interest in, to or
under any of the rights, properties or assets of either of Mergeco or the
Company acquired or to be acquired by the Surviving Corporation as a result of,
or in connection with, the Merger or otherwise to carry out this Agreement, the
officers and directors of the Surviving Corporation shall be authorized to
execute and deliver, in the name and on behalf of each of Mergeco and the
Company, all such deeds, bills of sale, assignments and assurances and to take
and do, in the name and on behalf of each of Mergeco and the Company or
otherwise, all such other actions and things as may be necessary or desirable to
vest, perfect or confirm any and all right, title and interest in, to and under
such rights, properties or assets in the Surviving Corporation or otherwise to
carry out this Agreement.

      Section 1.8   Conversion of Securities.  At the Effective Time, by virtue
of the Merger and without any action on the part of Holdco, Mergeco, the Company
or the holder of any of the following securities:

          (a)  Each share of Company Common Stock issued and outstanding
     immediately prior to the Effective Time shall be converted into and
     thereafter represent one duly issued, fully paid and nonassessable share of
     Holdco Common Stock.

          (b)  Each share of Company Common Stock issued but held by Holdco in
     its treasury immediately prior to the Effective Time shall be converted
     into and thereafter 


                              HALLIBURTON COMPANY
                     AGREEMENT AND PLAN OF REORGANIZATION

                                       4
<PAGE>
 
     represent one duly issued, fully paid and nonassessable share of Holdco
     Common Stock held by Holdco in its treasury immediately after the Effective
     Time of the Merger.

          (c)  Each share of common stock, par value $1.00 per share, of Mergeco
     issued and outstanding immediately prior to the Effective Time shall be
     converted into and thereafter represent one duly issued, fully paid and
     nonassessable share of common stock, par value $1.00 per share, of the
     Surviving Corporation.

          (d)  From and after the Effective Time, holders of certificates
     formerly evidencing Company Common Stock shall cease to have any rights as
     stockholders of the Company, except as provided by law; provided, however,
     that such holders shall have the rights set forth in Section 1.10 herein.

      Section 1.9   Preferred Share Purchase Rights.

          (a)  In accordance with Section 36 of that certain Second Amended and
     Restated Rights Agreement dated as of December 15, 1995, as thereafter
     amended, between the Company and ChaseMellon Shareholder Services, L.L.C.,
     as Rights Agent (the "Company Rights Plan"), each outstanding preferred
     share purchase right of the Company ("Company Purchase Right") shall
     terminate as of the Effective Time.

          (b)  Holdco shall, prior to the Effective Time, adopt a preferred
     share purchase rights plan (the "Holdco Rights Plan") substantially similar
     in form and substance to the Company Rights Plan and, in accordance
     therewith, Holdco shall, at the Effective Time but without duplication of
     Holdco's obligations under the Holdco Rights Plan, issue to each holder of
     Holdco Common Stock issued pursuant hereto one preferred share purchase
     right ("Holdco Purchase Right") for each share of Holdco Common Stock
     issued by it pursuant to Section 1.8(a) herein.

      Section 1.10  No Surrender of Certificates; Stock Transfer Books.  As a
result of the provisions of Section 1.3 herein, in conjunction with the
provisions of a certificate of amendment of certificate of incorporation of
Holdco to be filed with the Secretary of State of the State of Delaware and to
become effective at immediately after the Effective Time, the corporate name of
Holdco immediately following the Effective Time will be "Halliburton Company",
the same name as the corporate name of the Company immediately prior to the
Effective Time.  Accordingly, until thereafter surrendered for transfer or
exchange in the ordinary course, each outstanding certificate that, immediately
prior to the Effective Time, evidenced Company Common Stock shall be deemed and
treated for all corporate purposes to evidence the ownership of the number of
shares of Holdco 


                              HALLIBURTON COMPANY
                     AGREEMENT AND PLAN OF REORGANIZATION

                                       5
<PAGE>
 
Common Stock into which such shares of Company Common Stock were converted
pursuant to the provisions of Sections 1.8 (a) and (b) herein. In addition,
immediately after the Effective Time, each such certificate shall also evidence
a number of Holdco Purchase Rights equal to the number of Company Purchase
Rights evidenced thereby immediately prior to the Effective Time of the Merger.

                                   ARTICLE II
                             ACTIONS TO BE TAKEN IN
                           CONNECTION WITH THE MERGER

      Section 2.1   Company Indebtedness.  As of the date of this Agreement, the
Company is a party to the following indentures (individually, an "Indenture"
and, collectively, the "Indentures"):
 
          (1)  Senior Indenture (the "First Senior Indenture") dated as of
     January 2, 1991 between the Company and Texas Commerce Bank National
     Association, as trustee, pursuant to which the Company has heretofore
     issued $200 million in aggregate principal amount of a series of 8.75%
     Debentures due February 15, 2021 (the "Debentures"), all of which currently
     remain outstanding; and

          (2)  Second Senior Indenture (the "Second Senior Indenture") dated as
     of December 1, 1996 between the Company and Texas Commerce Bank National
     Association, as trustee, pursuant to which no debt securities are currently
     outstanding; and

          (3)  Subordinated Indenture (the "Subordinated Indenture") dated as of
     December 1, 1996 between the Company and Texas Commerce Bank National
     Association, as trustee, pursuant to which no debt securities are currently
     outstanding.

     As of the Effective Time, Holdco and the Company shall, with respect to
each such Indenture and, in the case of the First Senior Indenture, with respect
to the Debentures outstanding thereunder, together with the trustee under each
Indenture, execute, acknowledge and deliver indentures supplemental (each, a
"Supplemental Indenture") to each of such Indentures pursuant to which Holdco
shall assume and agree to perform all obligations of the Company thereunder
without, subject to certain exceptions set forth in such Supplemental
Indentures, releasing the Company from such obligations and Holdco will agree to
pay, perform and discharge all obligations of the Company under the Debentures.
 
      Section 2.2   Assumption of Benefit Plans. Holdco and the Company hereby
agree that they will, at the Effective Time, execute, acknowledge and deliver an
assumption agreement pursuant to which Holdco will, from and after the Effective
Time, assume and agree to perform all

                              HALLIBURTON COMPANY
                     AGREEMENT AND PLAN OF REORGANIZATION

                                       6
<PAGE>
 
obligations of the Company pursuant to the Halliburton Company Career Executive
Incentive Stock Plan, the 1993 Stock and Long-Term Incentive Plan, the Landmark
Graphics Corporation 1984 Incentive Stock Option Plan, the Landmark Graphics
Corporation 1985 Incentive Stock Option Plan, the Landmark Graphics Corporation
1987 Nonqualified Stock Option Plan, the Landmark Graphics Corporation 1989
Flexible Stock Option Plan, the Landmark Graphics Corporation Directors' Stock
Option Plan, the Landmark Graphics Corporation Consultants' Stock Option Plan,
the Landmark Graphics Corporation 1990 Employee Stock Option Plan and the
Landmark Graphics Corporation 1994 Flexible Incentive Plan (the "Benefit
Plans").

      Section 2.3   Reservation of Shares.  On or prior to the Effective Time,
Holdco will reserve sufficient shares of Holdco Common Stock to provide for the
issuance of Holdco Common Stock upon exercise of options outstanding under the
Benefit Plans and will reserve a number of shares of Holdco Series A Preferred
Stock sufficient to provide for the issuance thereof upon exercise of Holdco
Purchase Rights.

                                  ARTICLE III
                             CONDITIONS OF MERGER

      Section 3.1   Conditions Precedent.  The obligations of the parties to
this Agreement to consummate the Merger and the transactions contemplated by
this Agreement shall be subject to fulfillment or waiver by the parties hereto
of each of the following conditions:
 
          (a)  Prior to the Effective Time, the Holdco Common Stock to be issued
     pursuant to the Merger shall have been approved for listing, upon official
     notice of issuance, by the New York Stock Exchange.

          (b)  Holdco shall have adopted the Holdco Rights Plan and distributed
     Holdco Purchase Rights as a dividend on the then issued and outstanding
     shares of Holdco Common Stock, and, prior to the Effective Time, the Holdco
     Purchase Rights to be issued in conjunction with the issuance of Holdco
     Common Stock pursuant to the Merger shall have been approved for listing,
     upon official notice of issuance, by the New York Stock Exchange.

          (c)  The Company, Holdco and the Trustee shall have executed and
     delivered the Supplemental Indentures contemplated by Article II herein
     subject only to the occurrence of the Effective Time of the Merger.

          (d)  Prior to the Effective Time, the Company shall have received
     certain revenue rulings from the Internal Revenue Service requested by it
     pursuant to a letter dated August 


                              HALLIBURTON COMPANY
                     AGREEMENT AND PLAN OF REORGANIZATION

                                       7
<PAGE>
 
     30, 1996, to the Internal Revenue Service from Vinson & Elkins L.L.P.,
     counsel to the Company.

          (e)  Prior to the Effective Time, Vinson & Elkins L.L.P., counsel to
     the Company, shall have received an interpretive or no-action letter from
     the Securities and Exchange Commission, in form and substance satisfactory
     to the Company, in response to that certain request therefor dated December
     6, 1996 from such firm.

          (f)  Prior to the Effective Time, Vinson & Elkins L.L.P., counsel to
     the Company, shall have rendered an opinion to the Board of Directors of
     the Company, in form and substance satisfactory to the Company, to the
     effect that the Merger will constitute a tax-free reorganization under
     Section 368(a) of the Code and that no gain or loss will be recognized by
     the stockholders of the Company upon receipt of the Holdco Common Stock
     in exchange for their shares of Company Common Stock pursuant to the
     Merger.
 
          (g)  Prior to the Effective Time, no order, statute, rule, regulation,
     executive order, injunction, stay, decree, judgment or restraining order
     shall have been enacted, entered, promulgated or enforced by any court or
     governmental or regulatory authority or instrumentality which prohibits or
     makes illegal the consummation of the Merger or the transactions
     contemplated hereby.

 
                                  ARTICLE IV
                                   COVENANTS

      Section 4.1   Election of Directors.  Effective as of  the Effective Time,
the Company, in its capacity as the sole stockholder of Holdco, will remove each
of the then directors of Holdco, will cause the board of directors of Holdco to
effect such amendments to the bylaws of Holdco as are necessary to increase the
number of directors of Holdco to equal the number of directors of the Company
and will elect each person who is then a member of the board of directors of the
Company as a director of Holdco, each of whom shall serve until the next annual
meeting of shareholders of Holdco and until his successor shall have been
elected and qualified.
 
      Section 4.2   Listing of Holding Company Common Stock.  Holdco will use
its best efforts to obtain, at or before the Effective Time, authorization to
list, upon official notice of issuance, on the New York Stock Exchange Holdco
Common Stock issuable pursuant to the Merger and Holdco Purchase Rights issuable
in conjunction therewith.


                              HALLIBURTON COMPANY
                     AGREEMENT AND PLAN OF REORGANIZATION

                                       8
<PAGE>
 
      Section 4.3   Employee Benefit Plans.  The Company and Holdco will take or
cause to be taken all actions necessary or desirable in order for Holdco to
assume the Benefit Plans and to assume (or become a participating employer in)
each other existing employee benefit plan and agreement of the Company, with or
without amendments, or to adopt comparable plans, all to the extent deemed
appropriate by the Company and Holdco and permitted under applicable law.

      Section 4.4   Change in Capitalization.  Prior to the Effective Time,
Holdco and the Company agree to take all action necessary or desirable under the
DGCL to designate 2,000,000 shares of Preferred Stock of Holdco as Series A
Junior Participating Preferred Stock having terms and provisions substantially
similar to those of the Company's Series A Junior Participating Preferred Stock.

      Section 4.5   Change of Name of Holdco.  Holdco and the Company will take
or cause to be taken all such actions as may be necessary or desirable to effect
an amendment to the Certificate of Incorporation of Holdco immediately after the
Effective Time changing the name of Holdco to "Halliburton Company".

      Section 4.6   Contribution of Treasury Stock.  Immediately prior to the
Effective Time, the Company will contribute to the capital of Holdco all the
Company Common Stock then held in the treasury of the Company.

      Section 4.7   Contribution of Outstanding Holdco Stock.  At the Effective
Time, the Company will contribute to the capital of Holdco all shares of Holdco
Common Stock and all Holdco Purchase Rights outstanding immediately prior to the
Merger and owned of record and beneficially by the Company.

      Section 4.8   Contribution of Alphabet Stock. Prior to the Merger, the
Company shall cause Brown & Root Holdings, Inc., a Delaware corporation
("BRHI"), to contribute all the outstanding capital stock designated Series B
issued by Halliburton Holdings, Inc. ("HHI") and owned by BRHI to Brown & Root,
Inc., a Texas corporation.

      Section 4.9   InterCompany Stock Distributions. Promptly after the
Effective Time, the Surviving Corporation shall contribute the stock of certain
controlled foreign corporations to its direct, wholly owned subsidiary
Halliburton Affiliates Corporation, a Delaware corporation ("HAC") and the stock
of HHI owned by the Surviving Corporation to Halliburton International, Inc.
("HII"); promptly thereafter the Surviving Corporations shall distribute to
Newco all of the outstanding stock of BRHI, HII, Landmark Graphics Corporation
and HAC.


                              HALLIBURTON COMPANY
                     AGREEMENT AND PLAN OF REORGANIZATION

                                       9
<PAGE>
 
                                   ARTICLE V
                           TERMINATION AND AMENDMENT

      Section 5.1   Termination.  This Agreement may be terminated and the
Merger contemplated hereby may be abandoned at any time prior to the Effective
Time by action of the Board of Directors of the Company, Holdco or Mergeco if it
should determine that for any reason the completion of the transactions provided
for herein would be inadvisable or not in the best interest of such corporation
or its stockholders.  In the event of such termination and abandonment, this
Agreement shall become void and neither the Company, Holdco or Mergeco nor their
respective stockholders, directors or officers shall have any liability with
respect to such termination and abandonment.

      Section 5.2   Amendment.  This Agreement may be supplemented, amended or
modified by the mutual consent of the Boards of Directors of the parties to this
Agreement.

                                  ARTICLE VI
                           MISCELLANEOUS PROVISIONS

      Section 6.1   Governing Law.  Except with respect to matters contained
herein governed by the DGCL, this Agreement has been executed and delivered in
the State of Texas and shall be governed by and construed and enforced under the
laws of the State of Texas, regardless of the laws that might otherwise govern
under applicable Texas principles of conflicts of law.

      Section 6.2   Counterparts.  This Agreement may be executed in one or more
counterparts, each of which when executed shall be deemed to be an original but
all of which shall constitute one and the same agreement.

      Section 6.3   Entire Agreement.  This Agreement, including the documents
and instruments referred to herein, constitutes the entire agreement and
supersedes all other prior agreements and undertakings, both written and oral,
among the parties, or any of them, with respect to the subject matter hereof.

     In Witness Whereof, Holdco, Mergeco and the Company have caused this
Agreement to be executed as of the date first written above by their respective
officers thereunto duly authorized.

                                        HALLIBURTON COMPANY
 



                              HALLIBURTON COMPANY
                     AGREEMENT AND PLAN OF REORGANIZATION

                                       10
<PAGE>
 
                              By: /s/ Lester L. Coleman 
                                 _____________________________________
                              Name:      Lester L. Coleman
                              Title:     Executive Vice President and
                                         General Counsel

                              HALLIBURTON HOLD CO.


                              By: /s/ Robert M. Kennedy 
                                 _____________________________________
                              Name:      Robert M. Kennedy
                              Title:     Vice President

                              HALLIBURTON MERGE CO.


                              By: /s/ Robert M. Kennedy 
                                 _____________________________________
                              Name:      Robert M. Kennedy 
                              Title:     Vice President

 
     I, Susan S. Keith, Vice President and Secretary of Halliburton Company do
hereby certify that the Board of Directors of Halliburton Company has approved
and adopted this Agreement by duly authorized written consent dated December 5,
1996.


                                     /s/ Susan S. Keith
                                 ______________________________________
                                             Susan S. Keith
                                      Vice President and Secretary

          I, Susan S. Keith, Vice President and Secretary of Halliburton Hold
Co. do hereby certify that the Board of Directors of Halliburton Hold Co. has
approved and adopted this Agreement by duly authorized written consent dated
December 5, 1996.

                  
                                    /s/ Susan S. Keith
                                 ______________________________________
                                             Susan S. Keith
                                      Vice President and Secretary



                              HALLIBURTON COMPANY
                     AGREEMENT AND PLAN OF REORGANIZATION

                                       11
<PAGE>
 
          I, Susan S. Keith, Vice President and Secretary of Halliburton Merge
Co. do hereby certify that the Board of Directors of Halliburton Merge Co. has
approved and adopted this Agreement by duly authorized written consent dated
December 5, 1996.



                                    /s/ Susan S. Keith
                                 ______________________________________
                                             Susan S. Keith
                                      Vice President and Secretary



                              HALLIBURTON COMPANY
                     AGREEMENT AND PLAN OF REORGANIZATION

                                       12

<PAGE>
 
                                                                     EXHIBIT 3.1

                         CERTIFICATE OF INCORPORATION
                                      OF
                             HALLIBURTON HOLD CO.



     FIRST: The name of this Corporation is HALLIBURTON HOLD CO.

     SECOND: The location of its principal office in the State of Delaware is
1209 Orange Street in the City of Wilmington, County of New Castle.  The name of
the agent therein and in charge of thereof is THE CORPORATION TRUST COMPANY,
1209 Orange Street, Wilmington, Delaware.

     THIRD: The nature of the business, or objects, or purposes to be
transacted, promoted or carried on are:

     (a) To acquire, own and hold United States and Foreign Letters patent; and
Licenses thereunder, relating to the cementing and finishing of oil wells, gas
wells and water wells, including processes and machines for mixing cement and
other substances in an efficient manner and forcing same into such wells; and
measuring devices used in the process of cementing wells; and under such patents
and licenses and to conduct the business of cementing and finishing oil wells,
gas and water wells, and to purchase, own and use all necessary and convenient
tools, implements and appliances, including trucks, for the conduct of such
business; also such real and personal property as may be needful in its
operations.  To transact any of its business in any part of the world.

     (b) To manufacture, sell, lease, use or service any and all kinds of
supplies, tools, appliances, accessories, specialties, machinery and equipment
relating to or useful in connection with the cementing, testing, drilling,
completing, cleaning, repairing or operating oil wells, gas wells and water
wells.
<PAGE>
 
                                      -2-

     (c) To acquire, own and operate such machinery, apparatus, appliances and
equipment as may be necessary, proper or incidental to the cementing, testing,
completing, repairing, cleaning and operating of oil wells, gas wells and water
wells, or for any of the purposes for which this Corporation is organized.

     (d) To apply for, purchase or in any manner to acquire, hold, use, sell,
assign, lease, grant licenses in respect of, mortgage, or otherwise dispose of
letters patent of the United States or any foreign country, patent rights,
licenses and privileges, inventions, improvements, and processes, copyrights,
trademarks, and trade names relating to or useful in connection with any
business of this Corporation, and to work, operate or develop the same, and to
carry on any business, manufacturing or otherwise, which may directly or
indirectly effectuate these objects or any of them.

     (e)  In general, upon approval of the Board of Directors of the
Corporation, to carry on any other business, including selling, leasing,
manufacturing and servicing, even though unrelated to the objects and purposes
enumerated in paragraphs (a), (b), (c) and (d) hereof, and to have and exercise
all the powers conferred by the laws of Delaware upon corporations, and to have
one or more offices out of the State of Delaware, and to hold, purchase,
mortgage and convey real and personal property out of the State of Delaware, and
to do any or all of the things hereinbefore set forth to the same extent as
natural persons might or could do.

     (f)  The objects and purposes specified in the foregoing clauses shall,
except where otherwise expressed, be in no wise limited or restricted by
reference to, or inference from, the terms of any other clause in this
Certificate of Incorporation, but the objects and purposes specified in each of
the foregoing clauses of this article shall be regarded as independent objects
and purposes.
<PAGE>
 
                                      -3-

     FOURTH: The aggregate number of shares which the Corporation shall have
authority to issue shall be two hundred five million (205,000,000), consisting
of two hundred million (200,000,000) shares of Common Stock of the par value of
Two & 50/100 Dollars ($2.50) per share and five million (5,000,000) shares of
Preferred Stock without par value.  The relative rights, preferences and
limitations of the shares of each class are as follows:

                           (A) PREFERRED STOCK

     (1) Shares of the Preferred Stock may be issued in one or more series at
such time or times and for such consideration or considerations as the Board of
Directors may determine and authority is vested in the Board of Directors, by
resolution or resolutions from time to time to establish and designate series,
to issue shares of any such series and to fix the relative, participating,
optional, or other rights, powers, privileges, preferences, and the
qualifications, limitations or restrictions thereof, including, but not limited
to, the following:

     (a) The distinctive designation and number of shares comprising any series,
which number may (except where otherwise provided by the Board of Directors in
creating such series) be increased or decreased (but not below the number of
shares thereof then outstanding) from time to time by like action of the Board
of Directors;

     (b) The dividend rate or rates on the shares of any series and the
preference or preferences, if any, over any other series (or of any other series
over such series) with respect to dividends, the terms and conditions upon which
such dividends shall be payable, and whether and upon what conditions dividends
on the shares of any series shall be cumulative, and on such shares of any
series having cumulative dividend rights, the date or dates from which dividends
on the shares of such series shall be cumulative;
<PAGE>
 
                                      -4-

     (c) The terms, if any, upon which the shares of any series shall be
convertible into, or exchangeable for, shares of a different series of Preferred
Stock or for Common Stock including but not limited to the price or prices or
rate of exchange, and conditions of any adjustments thereof, which price or rate
may, but need not, vary according to the time or circumstances of the conversion
or exchange;

     (d)  Whether or not the shares of any series shall be subject to purchase
or redemption, the time or times when, and the price or prices at which such
shares shall be redeemable as well as the manner for selecting shares to be
redeemed, if less than all of a series is to be redeemed at any given time, and
other terms and conditions of such purchase or redemption;

     (e) The obligation, if any, of the Corporation to purchase or redeem shares
of any series pursuant to a sinking or other fund and the price or prices which,
the period or periods within which and the terms and conditions upon which the
shares of the series shall be redeemed in whole or in part pursuant to such
fund;

     (f) The rights to which the holders of shares of any series shall be
entitled upon liquidation, dissolution of, or winding up of the Corporation,
whether the same be a voluntary or involuntary liquidation, dissolution or
winding up of the Corporation.

     (g) The voting powers, full or limited, if  any, to which the shares of any
series shall be entitled in addition to those required by law, including without
limitation the vote or votes per share and the transaction of any business or of
any specified item of business in connection with which the shares of any series
shall vote as a class;

     (h) Any other preferences, privileges and powers and relative,
participating, optional or other rights and qualifications, limitations or
restrictions thereof, of any series not inconsistent herewith or with applicable
law.
<PAGE>
 
                                      -5-

     (2) The shares of each series of Preferred Stock shall entitle the holders
thereof to receive, when, as and if declared by the Board of Directors out of
funds legally available for dividends, cash dividends at the rate, under the
conditions and for the periods fixed by resolution or resolutions of the Board
of Directors pursuant to authority granted in this Article for each series, and
no more, and so long as any Preferred Stock or any series thereof shall remain
outstanding, no dividends shall be declared or paid upon any shares of the
Common Stock, other than dividends payable in shares of any series or class
subordinate to the Preferred Stock, unless dividends on all outstanding
Preferred Stock of all series fixed by the Board of Directors in accordance with
and pursuant to the authority granted in this Article for each series shall be
paid or set apart for payment.

     (3) In the event of any voluntary or involuntary liquidation, dissolution
or winding up of the Corporation, the holders of the Preferred Stock of each
series then outstanding shall be entitled to receive payment out of the net
assets of the Corporation whether from capital or surplus or both of the
liquidation price fixed for such series by the Board of Directors by resolution,
if any is so fixed, at the time and under the circumstances applicable before
any payment shall be made to the holders of shares of any series of lesser rank
to such series or to holders of shares of Common Stock of the Corporation. If
the stated amounts payable in such event on the Preferred Stock of all series
are not paid in full, the shares of all series of equal rank shall share ratably
in any distribution of assets in accordance with the sums which would be payable
on such distribution if all sums payable were discharged in full. Neither the
merger or the consolidation of the Corporation nor the voluntary sale or
conveyance of the Corporation property as an entirety or any part thereof shall
be deemed to be a liquidation, dissolution or winding up of the Corporation for
the purposes of this paragraph.
<PAGE>
 
                                      -6-

     (4) Except as is otherwise required by law or as otherwise provided in a
resolution or resolutions by the Board of Directors in accordance with the
provisions of this Article, the holders of any series of Preferred Stock shall
not be entitled to vote at any meeting of the stockholders for the election of
Directors or for any other purpose or otherwise to participate in any action
taken by the Corporation or the stockholders thereof, or to receive notice of
any meeting of stockholders.  If the holders of any series of Preferred Stock
should become entitled to vote at any meeting of the stockholders for the
election of Directors, no such holder shall have the right of cumulative voting.

     (5) Each share of a series of Preferred Stock shall be equal in every
respect to every other share of the same series.

     (6) Shares of Preferred Stock which have been purchased or redeemed,
whether through the operation of a sinking fund or otherwise, or which, if
convertible or exchangeable, have been converted into or exchanged for shares of
stock of any other class or series shall have the status of authorized and
unissued shares of Preferred Stock of the same series and may be reissued as a
part of the series of which they were originally a part or may be reclassified
and reissued as part of a new series of Preferred Stock to be created by
resolution or resolutions of the Board of Directors or as part of any other
series of Preferred Stock, unless otherwise provided with respect to any series
in the resolution or resolutions adopted by the Board of Directors providing for
the issuance of any series of Preferred Stock.

                            (B) COMMON STOCK

     (1) Subject to the rights of the outstanding Preferred Stock with respect
to the payment of preferential dividends, if any, and after the Corporation
shall have complied with the requirements, if any, with respect to setting aside
sinking or analogous funds as to any series of
<PAGE>
 
                                      -7-

Preferred Stock, holders of the Common Stock shall be entitled to receive such
dividends as may be declared from time to time by the Board of Directors out of
any funds of the Corporation legally available therefor.

     (2) Upon any liquidation, dissolution or winding up of the Corporation,
whether voluntary or involuntary, and after the full amounts, if any, to which
the holders of outstanding Preferred Stock of each series are respectively
preferentially entitled have been distributed or set apart for distribution, all
the remaining assets of the Corporation available for distribution shall be
distributed pro rata to the holders of Common Stock.

     (3) Except as may be otherwise required by law or provided by this
Certificate of Incorporation, each holder of Common Stock shall have one vote in
respect of each share of stock held by him on all matters voted upon by the
stockholders.

     FIFTH:  The name and mailing address of the Incorporator are as follows:

     NAME                                MAILING ADDRESS
     ----                                ---------------

     Robert M. Kennedy                   Halliburton Company
                                         3600 Lincoln Plaza
                                         500 North Akard
                                         Dallas, Texas   75201-3391

     SIXTH:  The Corporation is to have perpetual existence.

     SEVENTH:  The private property of the stockholders shall not be subject to
the payment of corporate debts to any extent whatever.

     EIGHTH:  Cumulative voting shall not be allowed.  Each Stockholder
shall be entitled, at all elections of Directors of this Corporation, to as many
votes as shall equal the number of shares of stock held and owned by him and
entitled to vote at such meeting under this Certificate of Incorporation for as
many Directors as there are to be elected, unless such right to vote in such
manner is limited or denied by other provisions of this Certificate of
Incorporation.
<PAGE>
 
                                      -8-

     Vacancies caused by the death or resignation of any Director and newly
created directorships resulting from any increase in the authorized number of
Directors may be filled by a vote of at least a majority of the Directors then
in office, though less than a quorum, and the Director so chosen shall hold
office until the next annual meeting of the Stockholders.

     NINTH: The By-laws may be altered or repealed at any regular meeting of the
Stockholders, or at any special meeting of the Stockholders at which a quorum is
present or represented, provided notice of the proposed alteration or repeal be
contained in the notice of such special meeting, by the affirmative vote of the
majority of the Stockholders entitled to vote at such meeting and present or
represented thereat, or by the affirmative vote of the majority of the Board of
Directors at any regular meeting of the Board, or at any special meeting of the
Board, if notice of the proposed alteration or repeal be contained in the notice
of such special meeting; provided, however, that no change of the time or place
of the meeting for the election of Directors shall be made within sixty (60)
days next before the day on which such meeting is to be held, and that in case
of any change of time or place, notice thereof shall be given to each
Stockholder in person or by letter mailed to his last known post office address
at least twenty (20) days before the meeting is held.

     Voting for Directors need not be by ballot except upon the demand, at or
before the election, of the holders of ten percent (10%) or more of the shares
in person or by proxy and entitled to vote at such election.

     TENTH:  The Corporation is hereby authorized to, and shall, indemnify
directors, officers and employees of the Corporation and such other parties as
are set forth below in accordance with the following provisions:

     (a) The Corporation shall indemnify any person who was or is a party or is
threatened to be made a party to any threatened, pending or completed action,
suit or proceeding, whether
<PAGE>
 
                                      -9-

civil, criminal, administrative or investigative (other than an action by or in
the right of the Corporation)  by reason of the fact that he  is or was a
director, officer, employee or agent of the Corporation, or is or was serving at
the request of the Corporation as a director, officer, employee or agent of
another corporation, partnership, joint venture, trust or other enterprise,
against expenses, including attorneys' fees, judgments, fines and amounts paid
in settlement actually and reasonably incurred by him in connection with such
action, suit or proceeding if he acted in good faith and in a manner he
reasonably believed to be in or not opposed to the best interests of the
Corporation, and, with respect to any criminal action or proceeding had no
reasonable cause to believe his conduct was unlawful.  The termination of any
action, suit, or proceeding by judgment, order, settlement, conviction, or upon
a plea of nolo contendere or its equivalent, shall not, of itself, create a
presumption that the person did not act in good faith and in a manner which he
reasonably believed to be in or not opposed to the best interests of the
Corporation, and, with respect to any criminal action or proceeding, had
reasonable cause to believe that his conduct was unlawful.

     (b) The Corporation shall indemnify any person who was or is a party or is
threatened to be made a party to any threatened, pending or completed action or
suit by or in the right of the Corporation to procure a judgment in its favor by
reason of the fact that he is or was a director, officer, employee or agent of
the Corporation, or is or was serving at the request of the Corporation as a
director, officer, employee or agent of another corporation, partnership, joint
venture, trust or other enterprise against expenses, including attorneys' fees
actually and reasonably incurred by him in connection with the defense or
settlement of such action or suit if he acted in good faith and in a manner he
reasonably believed to be in or not opposed to the best interests of the
Corporation and except that no indemnification shall be made in respect of any
claim, issue or matter as to which such person shall have been adjudged to be
liable for
<PAGE>
 
                                     -10-

negligence or misconduct in the performance of his duty to the Corporation
unless and only to the extent that the Court of Chancery or the court in which
such action or suit was brought shall determine upon application that, despite
the adjudication of liability but in view of all the circumstances of the case,
such person is fairly and reasonably entitled to indemnity for such expenses
which the Court of Chancery or such other court shall deem proper.

     (c) To the extent that any such person referred to hereinabove has been
successful on the merits or otherwise in defense of any action, suit or
proceeding referred to in subsections (a) and (b), or in the defense of any
claim, issue or matter therein, he shall be indemnified against expenses,
including attorneys' fees, actually and reasonably incurred by him in connection
therewith.

     (d) Except in those instances where the provisions of subsection (c) of
this Article are applicable, or unless ordered by a court, any indemnification
under subsections (a) and (b) hereof shall be made by the Corporation only as
authorized in the specific case upon a determination that indemnification of
such person referred to hereinabove is proper in the circumstances because he
has met the applicable standard of conduct set forth in subsections (a) and (b)
of this Article.  Such determination shall be made (1) by the Board of Directors
by a majority vote of a quorum consisting of directors who were not parties to
such action, suit or proceeding, or (2) if such a quorum is not obtainable, or,
even if obtainable, if a quorum of disinterested directors so directs, by
independent legal counsel in a written opinion, or (3) by the Stockholders.

     (e) Expenses incurred in defending a civil or criminal action, suit or
proceeding may be paid by the Corporation in advance of the final disposition of
such action, suit or proceeding as authorized by the Board of Directors in the
specific case upon receipt of an undertaking by
<PAGE>
 
                                     -11-

or on behalf of the director, officer, employee or agent to repay such amount
unless it shall ultimately be determined that he is entitled to be indemnified
by the Corporation as authorized in this Article.

     (f) The indemnification provided by this Article shall not be deemed
exclusive of any other rights to which any person referred to hereinabove may be
entitled under any By-law, agreement, vote of the Stockholders or disinterested
directors or otherwise, both as to action in his official capacity and as to
action in another capacity while holding such office, and shall continue as to a
person who has ceased to act in any capacity hereinabove named in this Article
and shall inure to the benefit of the heirs, executors and administrators of
such a person.

     (g) The indemnification provided by this Article shall not be deemed
exclusive of any other power to indemnify or right to indemnification which the
Corporation or any person referred to hereinabove may have or acquire under the
laws of the State of Delaware including without limitation the General
Corporation Law of Delaware or any amendment thereto or substitute therefor.

     (h) The provisions of this Article shall be applicable to claims, actions,
suits or other proceedings referred to in subsections (a) and (b) of this
Article made or commenced after the adoption hereof, whether arising from
conduct or act or omission occurring before or after the adoption hereof.

     ELEVENTH: Both Stockholders and Directors shall have power, if the By-laws
so provide, to hold their meeting either within or without the State of Delaware
and to keep the books of this Corporation (subject to the provisions of the
Statutes) outside of the State of Delaware at such places as may be from time to
time designated in the By-laws.
<PAGE>
 
                                     -12-

     TWELFTH: In furtherance and not in limitation of the power conferred by
statute, the Board of Directors of this Corporation are expressly authorized to
fix the amount to be reserved as working capital, to authorize and cause to be
executed mortgages and liens upon the real and personal property belonging to
it.

     THIRTEENTH: This Corporation reserves the right to amend, alter, change or
repeal any provision contained in this Certificate of Incorporation in the
manner now or hereafter prescribed by statute and all rights conferred on
Stockholders herein are granted subject to this reservation.

     FOURTEENTH: No holder of any class of stock of this Corporation shall have
any preemptive or preferential right of subscription or purchase with reference
to the issuance or sale of any class of stock of the Corporation whether now or
hereafter authorized, or of any securities or obligations convertible into or
carrying or evidencing any right to purchase any class of stock of the
Corporation whether now or hereafter authorized.

     FIFTEENTH: No director shall be personally liable to the Corporation or any
stockholder for monetary damages for breach of fiduciary duty by such director
as a director; except for any matter in respect of which such director shall be
liable under Section 174 of the Delaware General Corporation Law or any
amendment thereto or successor provision thereof or shall be liable by reason
that, in addition to any and all other requirements for such liability, such
director (i) shall have breached the duty of loyalty to the Corporation or its
stockholders, (ii) in acting or failing to act, shall not have acted in good
faith or shall have acted in a manner involving intentional misconduct or a
knowing violation of law or (iii) shall have derived an improper personal
benefit.  Neither the amendment nor repeal of this Article FIFTEENTH shall
eliminate or reduce the effect of this Article FIFTEENTH in respect of any
matter occurring, or any cause
<PAGE>
 
                                     -13-

of action, suit or claim that, but for this Article FIFTEENTH, would accrue or
arise, prior to such amendment or repeal.  If the Delaware General Corporation
Law is amended after approval by the stockholders of this Article FIFTEENTH to
authorize corporate action further eliminating or limiting the personal
liability of directors, then the liability of a director of the Corporation
shall be eliminated or limited to the fullest extent permitted by the Delaware
General Corporation Law, as so amended from time to time.

     THE UNDERSIGNED, being the incorporator hereinbefore named, for the purpose
of forming a corporation pursuant to the General Corporation Law of the State of
Delaware, does make this certificate, hereby declaring and certifying that this
is his act and deed and the facts herein stated are true, and accordingly has
hereunto set his hand this 6th day of November, 1996.


                                    /s/ ROBERT M. KENNEDY
                                    -----------------------------
                                    Robert M. Kennedy
<PAGE>
 
                          CERTIFICATE OF DESIGNATION,

                            RIGHTS AND PREFERENCES


                                      OF

                    SERIES A JUNIOR PARTICIPATING PREFERRED
                           STOCK, WITHOUT PAR VALUE

                                      of

                             HALLIBURTON HOLD CO.



     Halliburton Hold Co., a corporation organized and existing under and by
virtue of the General Corporation Law of the State of Delaware, DOES HEREBY
CERTIFY:

     That at a meeting of the Board of Directors of Halliburton Hold Co. ("Hold
Co.") the following resolution, creating a series of two (2) million shares of
Preferred Stock, designated as Series A Junior Participating Preferred Stock was
duly adopted pursuant to the authority granted to and vested in the Board of
Directors of this corporation in accordance with the provisions of its
Certificate of Incorporation:

          RESOLVED, that, pursuant to the authority granted to and vested in the
     Board of Directors of Hold Co. in accordance with the provisions of the
     Certificate of Incorporation of Hold Co., a series of 2,000,000 shares of
     Series A Junior Participating Preferred Stock, without par value, of Hold
     Co. (the "Preferred Shares") be, and hereby is, created, and that the
     designation and amount thereof and the relative rights, preferences and
     limitations thereof (in addition to the provisions set forth in the
     Certificate of Incorporation of Hold Co. which are applicable to the
     Preferred Stock of all series) are as follows:

     I.   Designation and Amount. The shares of such series shall be designated
          -----------------------                                              
as the "Series A Junior Participating Preferred Stock" (the "Junior Preferred
Stock") and the number of shares constituting such series shall be two (2)
million.  Such number of shares may be increased or decreased by resolution of
the Board of Directors; provided, that no decrease shall reduce the number of
                        --------                                             
shares of Junior Preferred Stock to a number less than that of the shares then
outstanding plus the number of shares issuable upon exercise of outstanding
rights, options or warrants or upon conversion of outstanding securities issued
by the corporation.
<PAGE>
 
     II.  Dividends and Distributions.
          ----------------------------

          (A)  Subject to the prior and superior rights of the holders of any
     shares of any series of Preferred Stock ranking prior and superior to the
     shares of Junior Preferred Stock with respect to dividends, the holders of
     shares of Junior Preferred Stock, in preference to the holders of common
     stock, $2.50 par value, of the corporation (the "Common Stock") and of any
     other stock ranking junior (as to dividends) to Junior Preferred Stock,
     shall be entitled to receive, when, as and if declared by the Board of
     Directors out of funds legally available for the purpose, cumulative
     quarterly dividends payable in cash or in kind, as hereinafter provided, on
     the last day of March, June, September and December in each year (each such
     date being referred to herein as a "Quarterly Dividend Payment Date"),
     commencing on the first Quarterly Dividend Payment Date after the first
     issuance of a share or fraction of a share of Junior Preferred Stock, in an
     amount per share (rounded to the nearest cent) equal to the greater of (a)
     $1.00 (payable in cash) or (b) subject to the provision for adjustment
     hereinafter set forth, 100 times the aggregate per share amount (payable in
     cash) of all cash dividends, and 100 times the aggregate per share amount
     (payable in kind) of all non-cash dividends or other distributions, other
     than a dividend payable in shares of Common Stock (by reclassification or
     otherwise), declared on the Common Stock since the immediately preceding
     Quarterly Dividend Payment Date or, with respect to the first Quarterly
     Dividend Payment Date, since the first issuance of any share or fraction of
     a share of Junior Preferred Stock.  If the corporation shall at any time
     declare or pay any dividend on Common Stock payable in shares of Common
     Stock or effect a subdivision or combination of the outstanding shares of
     Common Stock (by reclassification or otherwise), into a greater or lesser
     number of shares of Common Stock, then in each such case the amount to
     which holders of shares of Junior Preferred Stock were entitled immediately
     prior to such event under clause (b) of the preceding sentence shall be
     adjusted by multiplying such amount by a fraction the numerator of which is
     the number of shares of Common Stock outstanding immediately after such
     event and the denominator of which is the number of shares of Common Stock
     that was outstanding immediately prior to such event.

          (B)  The corporation shall declare a dividend or distribution on the
     Junior Preferred Stock as provided in paragraph (A) of this Section
     immediately after it declares a dividend or distribution on the Common
     Stock (other than a dividend payable in shares of Common Stock); provided
     that, if no dividend or distribution shall have been declared on the Common
     Stock during the period between any Quarterly Dividend Payment Date and the
     next subsequent Quarterly Dividend Payment Date, a dividend of $1.00 per
     share on the Junior Preferred Stock shall nevertheless accrue and be
     cumulative on the outstanding shares of Junior Preferred Stock as provided
     in paragraph (C) of this Section.

          (C)  Dividends shall begin to accrue and be cumulative on outstanding
     shares of Junior Preferred Stock from the Quarterly Dividend Payment Date
     next preceding the date of issue of such shares of Junior Preferred Stock,
     unless the date of issue of such 

                                       2
<PAGE>
 
     shares is prior to the record date for the first Quarterly Dividend Payment
     Date, in which case dividends on such shares shall begin to accrue from the
     date of issue of such shares, or unless the date of issue is a Quarterly
     Dividend Payment Date or is a date after the record date for the
     determination of holders of shares of Junior Preferred Stock entitled to
     receive a quarterly dividend and before such Quarterly Dividend Payment
     Date, in either of which events such dividends shall begin to accrue and be
     cumulative from such Quarterly Dividend Payment Date. Accrued but unpaid
     dividends shall not bear interest. Dividends paid on the shares of Junior
     Preferred Stock in an amount less than the total amount of such dividends
     at the time accrued and payable on such shares shall be allocated pro rata
     on a share by share basis among all such shares at the time outstanding.
     The Board of Directors may fix a record date for the determination of
     holders of shares of Junior Preferred Stock entitled to receive payment of
     a dividend or distribution declared thereon, which record date shall be not
     more than 60 days prior to the date fixed for the payment thereof.

     III. Voting Rights.  The holders of shares of Junior Preferred Stock
          --------------                                                 
shall have the following voting rights:

          (A)  Subject to the provision for adjustment hereinafter set forth,
     each share of Junior Preferred Stock shall entitle the holder thereof to
     100 votes on all matters submitted to a vote of the shareholders of the
     corporation.  If the corporation shall at any time declare or pay any
     dividend on Common Stock payable in shares of Common Stock, or effect a
     subdivision or combination of the outstanding shares of Common Stock (by
     reclassification or otherwise) into a greater or lesser number of shares of
     Common Stock, then in each such case the number of votes per share to which
     holders of shares of Junior Preferred Stock were entitled immediately prior
     to such event shall be adjusted by multiplying such number by a fraction
     the numerator of which is the number of shares of Common Stock outstanding
     immediately after such event and the denominator of which is the number of
     shares of Common Stock that were outstanding immediately prior to such
     event.

          (B)  Except as otherwise provided in the Certificate of Incorporation
     or by law, the holders of shares of Junior Preferred Stock and the holders
     of shares of Common Stock shall vote together as one class on all matters
     submitted to a vote of shareholders of the corporation.

     IV.  Certain Restrictions.
          ---------------------

          (A)  Whenever quarterly dividends or other dividends or distributions
     payable on the Junior Preferred Stock as provided in Section II are in
     arrears, thereafter and until all accrued and unpaid dividends and
     distributions, whether or not declared, on shares of Junior Preferred Stock
     outstanding shall have been paid in full, the corporation shall not:

                                       3
<PAGE>
 
          (i)    declare or pay dividends on, make any other distributions on,
                 or redeem or purchase or otherwise acquire for consideration
                 any shares of stock ranking junior (as to dividends) to the
                 Junior Preferred Stock;

          (ii)   declare or pay dividends on or make any other distributions on
                 any shares of stock ranking on a parity (as to dividends) with
                 the Junior Preferred Stock, except dividends paid ratably on
                 the Junior Preferred Stock and all such parity stock on which
                 dividends are payable or in arrears in proportion to the total
                 amounts to which the holders of all such shares are then
                 entitled; or

          (iii)  purchase or otherwise acquire for consideration any shares of
                 Junior Preferred Stock, or any shares of stock ranking on a
                 parity (as to dividends) with the Junior Preferred Stock,
                 except in accordance with a purchase offer made in writing or
                 by publication (as determined by the Board of Directors) to all
                 holders of such shares upon such terms as the Board of
                 Directors, after consideration of the respective annual
                 dividend rates and other relative rights and preferences of the
                 respective series and classes, shall determine in good faith
                 will result in fair and equitable treatment among the
                 respective series or classes.

          (B)  The corporation shall not permit any subsidiary of the
     corporation to purchase or otherwise acquire for consideration any shares
     of stock of the corporation unless the corporation could, under paragraph
     (A) of this Section IV, purchase or otherwise acquire such shares at such
     time and in such manner.

     V.   Reacquired Shares.  Any shares of Junior Preferred Stock purchased or
          ------------------                                                   
otherwise acquired by the corporation in any manner whatsoever shall be retired
and cancelled promptly after the acquisition thereof.  All such shares shall
upon their cancellation become authorized but unissued shares of Preferred Stock
and may be reissued as part of a series of Preferred Stock to be created by
resolution or resolutions of the Board of Directors, subject to the conditions
and restrictions on issuance set forth herein.

     VI.  Liquidation, Dissolution or Winding Up.  Upon any liquidation,
          ---------------------------------------                       
dissolution or winding up of the corporation, no distribution shall be made (1)
to the holders of shares of stock ranking junior (as to amounts payable upon
liquidation, dissolution or winding up) to the Junior Preferred Stock unless,
prior thereto, the holders of Junior Preferred Stock shall have received an
amount per share (rounded to the nearest cent) equal to the greater of (a)
$100.00 per share, or (b) an amount per share, subject to the provision for
adjustment hereinafter set forth, equal to 100 times the aggregate amount to be
distributed per share to holders of Common Stock, plus, in either case, an
amount equal to accrued and unpaid dividends and distributions thereon, whether
or not declared, to the date of such payment, or (2) to the holders of stock
ranking on a parity (as to amounts payable or upon liquidation, dissolution or
winding up) with the Junior Preferred Stock, except distributions made ratably
on the 

                                       4
<PAGE>
 
Junior Preferred Stock and all other such parity stock in proportion to
the total amounts to which the holders of all such shares are entitled upon such
liquidation, dissolution or winding up.  If the corporation shall at any time
declare or pay any dividend on Common Stock payable in shares of Common Stock,
or effect a subdivision or combination of the outstanding shares of Common Stock
(by reclassification or otherwise) into a greater or lesser number of shares of
Common Stock, then in each such case the aggregate amount to which holders of
shares of Junior Preferred Stock were entitled immediately prior to such event
under the provision in clause (1) (b) of the preceding sentence shall be
adjusted by multiplying such amount by a fraction the numerator of which is the
number of shares of Common Stock outstanding immediately after such event and
the denominator of which is the number of shares of Common Stock that were
outstanding immediately prior to such event.

     VII.    Consolidation, Merger, etc.  If the corporation shall enter
             ---------------------------                                
into any consolidation, merger, combination or other transaction in which the
shares of Common Stock are exchanged for or changed into other stock or
securities, cash or any other property, or any combination thereof, then in any
such case the shares of Junior Preferred Stock shall at the same time be
similarly exchanged or changed in an amount per share (subject to the provision
for adjustment hereinafter set forth) equal to 100 times the aggregate amount of
stock, securities, cash or any other property, or any combination thereof, into
which or for which each share of Common Stock is changed or exchanged.  If the
corporation shall at any time declare or pay any dividend on Common Stock
payable in shares of Common Stock, or effect a subdivision or combination of the
outstanding shares of Common Stock (by reclassification or otherwise) into a
greater or lesser number of shares of Common Stock, then in each such case the
amount set forth in the preceding sentence with respect to the exchange or
change of shares of Junior Preferred Stock shall be adjusted by multiplying such
amount by a fraction the numerator of which is the number of shares of Common
Stock outstanding immediately after such event and the denominator of which is
the number of shares of Common Stock that were outstanding immediately prior to
such event.

     VIII.   No Redemption.  The shares of Junior Preferred Stock shall not
             --------------                                                
be redeemable.  So long as any shares of Junior Preferred Stock remain
outstanding, the corporation shall not purchase or otherwise acquire for
consideration any shares of stock ranking junior (either as to dividends or upon
liquidation, dissolution or winding up) to the Junior Preferred Stock unless the
corporation shall substantially concurrently also purchase or acquire for
consideration a proportionate number of shares of Junior Preferred Stock.

     IX.     Rank.  Except as otherwise provided in its Certificate of
             -----                                                    
Incorporation, the corporation may authorize or create any series of Preferred
Stock ranking prior to or on a parity with the Junior Preferred Stock as to
dividends or as to distribution of assets upon liquidation, dissolution or
winding up.

     X.      Amendment.  The Certificate of Incorporation of the corporation 
             ---------
shall not be amended in any manner which would materially alter or change the
powers, preferences or special rights of the Junior Preferred Stock so as to
affect them adversely without the affirmative vote of the holders of a majority
of the outstanding shares of Junior Preferred Stock, voting together as a single
class.

                                       5
<PAGE>
 
     The foregoing resolution was adopted by the Board of Directors of the
corporation, pursuant to the authority vested in it by the Certificate of
Incorporation of the corporation, at a meeting of the Board of Directors duly
held on the 5th day of December, 1996.

     IN WITNESS WHEREOF, this Certificate has been executed on behalf of the
Corporation by its Vice-President this 9th day of December, 1996.

                               HALLIBURTON HOLD CO.



                                By: /s/ Robert M. Kennedy
                                   ________________________
                                    Robert M. Kennedy
                                    Vice-President


                                       6
<PAGE>
 
                          CERTIFICATE OF AMENDMENT OF
                        CERTIFICATE OF INCORPORATION OF
                             HALLIBURTON HOLD CO.

     Halliburton Hold Co., a corporation organized and existing under and by
virtue of the General Corporation Law of the State of Delaware,

     DOES HEREBY CERTIFY:

     FIRST:  That at a meeting of the Board of Directors of Halliburton Hold
Co., resolutions were duly adopted setting forth a proposed amendment of the
Certificate of Incorporation of said corporation, declaring said amendment to be
advisable and calling a meeting of the stockholders of said corporation for
consideration thereof.  The resolution setting forth the proposed amendment is
as follows:

          RESOLVED, that, subject to the approval thereof by the stockholder of
     this corporation as required by law, the Certificate of Incorporation of
     this corporation shall be amended by changing the Article thereof numbered
     "First" so that as amended said Article shall be and read in its entirety
     as follows:

          "FIRST:  The name of this Corporation is HALLIBURTON COMPANY."

     SECOND:  That thereafter, pursuant to resolution of its Board of
Directors, a special meeting of the stockholders of said corporation was duly
called and held, and by Stockholder's Consent in Lieu of Meeting the necessary
number of shares as required by statute were voted in favor of the amendment.

     THIRD:  That said amendment was duly adopted in accordance with the
provisions of Section 242 of the General Corporation Law of the State of
Delaware.

     FOURTH:  That said amendment shall be effective at 11:31 a.m. Eastern 
Standard Time on December 12, 1996.

     IN WITNESS WHEREOF, this Certificate has been executed on behalf of the
Corporation by its Vice President this 11th day of December, 1996.

                               HALLIBURTON HOLD CO.


                                By: /s/ Susan S. Keith
                                   ------------------------
                                   Susan S. Keith
                                   Vice President

<PAGE>
 
                                                                     EXHIBIT 3.2

                              HALLIBURTON COMPANY
                                    BY-LAWS
                                   AS AMENDED

                                    Offices
                                    -------
     1.  The principal office shall be in the City of Wilmington, County of New
Castle, State of Delaware, and the name of the agent in charge thereof shall be
The Corporation Trust Company of America, and the Corporation shall also have
offices in the Cities of Dallas and Houston, State of Texas, in the City of
Duncan, State of Oklahoma, and at such other places as the Board of Directors
may, from time to time, appoint.

                                      Seal
                                      ----
     2.  The corporate seal shall have inscribed thereon around the margin the
words "Halliburton Company" and "Delaware" and across the center thereof the
words "Corporate Seal".

                             Stockholders' Meetings
                             ----------------------

     3.  All meetings of the stockholders for the election of Directors shall be
held in the City of Dallas, State of Texas, at such place as may be fixed from
time to time by the Board of Directors or at such other place either within or
without the State of Delaware as shall be designated from time to time by the
Board of Directors and stated in the notice of the meeting.  Meetings of
stockholders for any other purpose may be held at such time and place within or
without the State of Delaware, as shall be stated in the notice of the meeting.

     4.  Annual meetings of the stockholders shall be held on the third Tuesday
in the month of May each year if not a legal holiday, and if a legal holiday,
then on the next succeeding business day, at 9:00 a.m., or at such other date
and time as shall be designated, from time to time, by the Board of Directors
and stated in the notice of meeting, at which time they shall elect

                                       1
<PAGE>
 
by a plurality vote a Board of Directors, in the manner provided for in the
Certificate of Incorporation, and transact such other business as may be brought
before the meeting.

     5.  At an annual meeting of the stockholders, only such business shall be
conducted as shall have been properly brought before the meeting.  To be
properly brought before an annual meeting, business must be (i) specified in the
notice of meeting (or any supplement thereto) given by  or at the direction of
the Board, (ii) otherwise properly brought before the meeting by or at the
direction of the Board, or (iii) otherwise properly brought before the meeting
by a stockholder.  In addition to any other applicable requirements, for
business to be properly brought before an annual meeting by a stockholder, the
stockholder must have given timely notice thereof in writing to the Secretary.
To be timely, a stockholder's notice must be delivered to or mailed and received
at the principal executive offices of the Corporation, not less than ninety (90)
days prior to the first anniversary date of the immediately preceding annual
meeting of stockholders of the Corporation.  A stockholder's notice to the
Secretary shall set forth as to each matter the stockholder proposes to bring
before the annual meeting (a) a brief description of the business desired to be
brought before the annual meeting and the reasons for conducting such business
at the annual meeting, (b) the name and address, as they appear on the
Corporation's books, of the stockholder proposing such business, (c) the class
and number of shares of the Corporation which are beneficially owned by the
stockholder, (d) a representation that the stockholder or a qualified
representative of the stockholder intends to appear in person at the meeting to
bring the proposed business before the annual meeting, and (e) any material
interest of the stockholder in such business.

                                       2
<PAGE>
 
     Notwithstanding anything in the By-laws to the contrary, no business shall
be conducted at the annual meeting except in accordance with the procedures set
forth in this Section 5; provided, however, that nothing in this Section 5 shall
be deemed to preclude discussion by any stockholder of any business properly
brought before the annual meeting in accordance with said procedure.

     The Chairman of an annual meeting shall, if the facts warrant, determine
and declare to the meeting that business was not properly brought before the
meeting in accordance with the provisions of this Section 5, and if he should so
determine, he shall so declare to the meeting and any such business not properly
brought before the meeting shall not be transacted.

     Notwithstanding the foregoing provisions of this Section 5, a stockholder
shall also comply with all applicable requirements of the Securities and
Exchange Act of 1934, as amended, and the rules and regulations promulgated
thereunder with respect to the matters set forth in this Section 5.

     6.  Only persons who are nominated in accordance with the following
procedures shall be eligible for election as Directors.  Nominations of persons
for election to the Board of Directors of the Corporation may be made at a
meeting of stockholders (i) by or at the direction of the Board of Directors by
any nominating committee or person appointed by the Board or (ii) by any
stockholder of the Corporation entitled to vote for the election of Directors at
the meeting and who complies with the notice procedures set forth in this
Section 6.  Such nominations, other than those made by or at the direction of
the Board, shall be made pursuant to timely notice in writing to the Secretary.
To be timely, a stockholder's notice shall be delivered to or mailed and
received at the principal executive offices of the Corporation (a) with respect
to an election to

                                       3
<PAGE>
 
be held at the annual meeting of stockholders, not less than ninety (90) days
prior to the first anniversary date of the immediately preceding annual meeting
of stockholders of the Corporation and (b) with respect to an election to be
held at a special meeting of stockholders, not later than the close of business
on the tenth (10th) day following the day on which notice of the date of the
special meeting was mailed to stockholders or public disclosure of the date of
the special meeting was made, whichever first occurs.  Such stockholder's notice
to the Secretary shall set forth (x) as to each person whom the stockholder
proposes to nominate for election or re-election as a Director, (i) the name,
age, business address and residence address of the person, (ii) the principal
occupation or employment of the person, (iii) the class and number of shares of
capital stock of the Corporation which are beneficially owned by the person, and
(iv) all other information relating to the person that is required to be
disclosed in solicitations for proxies for election of Directors, or is
otherwise required, pursuant to Regulation 14A under the Securities Exchange Act
of 1934 as amended (including such person's written consent to being named in
the proxy statement as a nominee and to serve as a Director, if elected; and (y)
as to the stockholder giving the notice (i) the name and address, as they appear
on the Corporation's books, of such stockholder and (ii) the class and number of
shares of capital stock of the Corporation which are beneficially owned by the
stockholder.  The Corporation may require any proposed nominee to furnish such
other information as may reasonably be required by the Corporation to determine
the eligibility of such proposed nominee to serve as Director of the
Corporation.  Other than Directors chosen pursuant to the provisions of Section
13, no person shall be eligible for election as a Director of the Corporation
unless nominated in accordance with the procedures set forth herein.

                                       4
<PAGE>
 
     The Chairman of the meeting shall, if the facts warrant, determine and
declare to the meeting that a nomination was not made in accordance with the
foregoing procedure, and if he should so determine, he shall so declare to the
meeting and the defective nomination shall be disregarded.

     Notwithstanding the foregoing provisions of this Section 6, a stockholder
shall also comply with all applicable requirements of the Securities Exchange
Act of 1934, as amended, and the rules and regulations thereunder with respect
to the matters set forth in this Section 6.

     7.  The holders of a majority of the voting stock issued and outstanding,
present in person, or represented by proxy shall constitute a quorum at all
meetings of the stockholders for the transaction of business.

     8.  At each meeting, every stockholder shall be entitled to vote in person
or by proxy and shall have one (1) vote for each share of voting stock
registered in his name on the stock books except as provided in Section 13
hereof.

     9.  Written notices of the annual meeting shall be mailed not less than ten
(10) nor more than sixty (60) days before the date of the meeting to each
stockholder entitled to vote at such meeting directed to his address as it
appears on the records of the Corporation.

     10.  A complete list of the stockholders entitled to vote at each meeting
of the stockholders, arranged in alphabetical order, and showing the address of
each stockholder and the number of shares registered in the name of each
stockholder shall be prepared and shall be open to the examination of any
stockholder, for any purpose germane to the meeting during ordinary business
hours, for a period of at least ten (10) days prior to the meeting, either at a
place within the city where the meeting is to be held, which place shall be
specified in the notice of meeting,

                                       5
<PAGE>
 
or, if not so specified, at the place where the meeting is to be held.  The list
shall also be produced and kept at the time and place of the meeting during the
whole time thereof, and may be inspected by any stockholder who is present.

     11.  Special meetings of the stockholders may be called by the Chairman of
the Board (if any), by the President, by the Board of Directors, or by
stockholders owning a majority in the amount of the entire stock of the
Corporation with voting privileges issued and outstanding.     

     12. Written notice of a special meeting of stockholders shall be mailed not
less than ten (10) nor more than fifty (50) days before the date of the meeting
to each stockholder entitled to vote at such meeting directed to his address as
it appears on the records of the Corporation.

     13.  Cumulative voting shall not be allowed.  Each stockholder shall be
entitled, at all elections of Directors of the Corporation, to as many votes as
shall equal the number of shares of stock held and owned by him and entitled to
vote at such meeting under Article NINTH of the Certificate of Incorporation, as
amended, for as many Directors as there are to be elected, unless such right to
vote in such manner is limited or denied by other provisions of the Certificate
of Incorporation.

     Vacancies caused by the death or resignation of any Director and newly
created directorships resulting from any increase in the authorized number of
Directors may be filled by a vote of at least a majority of the Directors then
in office, though less than a quorum, and the Directors so chosen shall hold
office until the next annual meeting of the stockholders.

                                   Directors
                                   ---------

     14.  The property and business of the Corporation shall be managed by its
Board of Directors.  The number of Directors which shall constitute the whole
Board shall not be less than

                                       6
<PAGE>
 
eight (8) nor more than twenty (20).  Within the limits above specified, the
number of Directors shall be determined by resolution of the Board of Directors
or by the stockholders at the annual meeting.  Each Director shall be elected to
serve for the term of one (1) year and until his successor shall be elected and
shall qualify.

     15.  The Directors shall hold their meetings in Dallas, Texas, and at such
other places as they may designate, and may keep the books of the Corporation
outside of Delaware, in the City of Duncan, Oklahoma, in the City of Dallas,
Texas, or at such other places as they may, from time to time, determine.

     16.  In addition to the powers and authorities by these By-laws expressly
conferred upon them, the Board may exercise all such powers of the Corporation
and do all such lawful acts and things as are permitted by the Certificate of
Incorporation and not by statute required to be exercised or done by the
stockholders.

     17.  Each member of the Board shall be paid such fee as the Board of
Directors may, from time to time, by resolution determine.

                             Meetings of the Board
                             ---------------------

     18.  Immediately after each annual stockholders' meeting, the newly elected
Board shall meet and for the ensuing year elect such officers with such titles
and duties as may be necessary to enable the Corporation to sign instruments and
stock certificates which comply with Sections 103(a)(2) and 158 of Chapter 1,
General Corporation Laws of the State of Delaware, and may elect such other
officers as may be specified in these By-laws or as may be determined by the
Board and shall attend to such other business as may come before the Board.

                                       7
<PAGE>
 
     19.  Regular meetings of the Board may be held without notice at such time
and place as shall be determined by the Board.

     20.  At all meetings of the Board, a majority of Directors shall be
necessary to constitute a quorum.

     21.  Special meetings of the Board may be called by the Chairman of the
Board (if any) or the President upon one (1) day's notice to each Director
either personally or in the manner permitted by Section 34 hereof.  Special
meetings shall be called by the Chairman of the Board (if any), the President or
Secretary in like manner and on like notice on the written request of two (2)
Directors.

                                    Officers
                                    --------

     22.  The officers of the Corporation shall be a President, one or more Vice
Presidents (any one or more of whom may be designated Executive Vice President
or Senior Vice President), a Secretary, a Treasurer, a Controller, one or more
Assistant Secretaries and, if the Board of Directors so elects, a Chairman of
the Board.  Such officers shall be elected or appointed by the Board of
Directors. All officers as between themselves and the Corporation, shall have
such authority and perform such duties in the management of the Corporation as
may be provided in these By-laws, or, to the extent not provided, as may be
prescribed by the Board of Directors or by the President acting under authority
delegated to him by the Board.

     23.  The Chairman of the Board (if any) and the President shall be members
of the Board.  The other officers need not be members of the Board.  Any two (2)
or more offices may be held by the same person.

                                       8
<PAGE>
 
     24.  The Board may elect or appoint such other officers and agents as it
may deem necessary, who shall have such authority and shall perform such duties
as shall be prescribed by the Board.

     25.  The officers of the Corporation shall hold office for one (1) year
from date of their election and until their successors are chosen and qualify.
Any officer elected or appointed by the Board may be removed at any time by the
affirmative vote of a majority of the whole Board.

                                   Vacancies
                                   ---------

     26.  If any office of the Corporation is vacant for any reason, the Board
of Directors may choose a successor, who shall hold office for the unexpired
term, or the powers or duties of any such office may be delegated as the Board
may determine.

                      Duties of Officers May Be Delegated
                      -----------------------------------

     27.  In case of the absence, inability or refusal to act of any officer,
the Board may delegate the powers or duties of such officer to any other
officer, for the time being.

                              Certificate of Stock
                              --------------------

     28.  The Board of Directors may make such rules and regulations as it
may deem expedient for the issuance, transfer and registration of certificates
for shares of stock of the Corporation, including the appointment of transfer
agents and registrars.

          Such certificates shall be numbered and entered on the books of the
Corporation as they are issued, and shall set forth the holder's name and number
of shares and shall be impressed with the corporate seal or bear a facsimile
thereof, and shall be signed by the Chairman of the Board (if any), the
President or any Vice President and the Secretary or Assistant Secretary of the
Corporation and countersigned by an independent transfer agent and registered by
an

                                       9
<PAGE>
 
independent registrar.  Any or all of the signatures may be facsimiles unless
the regulations of the New York Stock Exchange then in effect shall require to
the contrary.  In case any officer, transfer agent or registrar who has signed
or whose facsimile signature has been placed upon a certificate shall cease to
be such officer, transfer agent or registrar before such certificate is issued,
it may be issued by the Corporation with the same effect as if he were such
officer, transfer agent or registrar at the date of issue.

                               Transfer of Stock
                               -----------------

     29.  Transfer of stock shall be made on the books of the Corporation
only upon written order of the person named in the certificate or his attorney,
lawfully constituted in writing and upon surrender of such certificate.

     30.  In order that the Corporation may determine the stockholders
entitled to notice of or to vote at any meeting of stockholders or any
adjournment thereof, or to express consent to corporate action in writing
without a meeting, or entitled to receive payment of any dividend or other
distribution or allotment of any rights, or entitled to exercise any rights in
respect of any change, conversion or exchange of stock or for the purpose of any
other lawful action, the Board may fix, in advance, a record date, which shall
not be more than sixty (60) nor less than ten (10) days before the date of such
meeting, nor more than sixty (60) days prior to any other action.  A
determination of stockholders of record entitled to notice of or to vote at a
meeting of stockholders shall apply to any adjournment of the meeting; provided,
however, that the Board may fix a new record date for the adjourned meeting.

     31.  All checks, unless otherwise directed by the Board, shall be
signed by the Treasurer or Assistant Treasurer and countersigned by the Chairman
of the Board (if any),

                                       10
<PAGE>
 
President, any Vice President or the Controller.  The Treasurer or Assistant
Treasurer, Chairman of the Board (if any), President, any Vice President, the
Controller, or any one of them, may appoint such officers or employees of the
Corporation as the one or ones so making the appointment shall deem advisable to
audit and approve Corporation vouchers and checks and to sign such checks with
an approved mechanical check-signer.  Any officer or employee so designated to
audit, approve or sign checks shall execute a bond to the Corporation in such
amount as the Directors, from time to time, may designate, and with sureties
satisfactory to the Directors.  All notes, debentures and bonds, unless
otherwise directed by the Board, or unless otherwise required by law, shall be
signed by the Treasurer or Assistant Treasurer and countersigned by the Chairman
of the Board (if any), President or any Vice President.

                                   Dividends
                                   ---------

     32.  Dividends upon the capital stock, when earned, may be declared by
the Board at any regular or special meeting.

     33.  Before payment of any dividend, there shall be set aside out of
the surplus or net profits of the Corporation such sum or sums as the Directors,
from time to time, think proper as a reserve fund to meet contingencies, or for
such other purposes as the Directors shall think conducive to the interest of
the Corporation.

     34.  Whenever, under the provisions of these By-laws, notice is
required to be given it shall not be construed to mean personal notice, but such
notice may be given in writing by mail, addressed to such stockholder, officer
or Director, at such address as appears on the records of the Corporation, with
postage thereon prepaid, and such notice shall be deemed to be given at the time
when the same shall be deposited in the United States mail.  Notice may also be
given

                                       11
<PAGE>
 
by prepaid telegram, telex or facsimile transmission, which notice shall be
deemed to have been given when sent or transmitted.

     35.  Any stockholder, Director or officer may waive any notice required to
be given under these By-laws.

     36.  These By-laws may be altered or repealed at any regular meeting
of the stockholders, or at any special meeting of the stockholders at which a
quorum is present or represented, provided notice of the proposed alteration or
repeal be contained in the notice of such special meeting, by the affirmative
vote of the majority of the stockholders entitled to vote at such meeting and
present or represented thereat, or by the affirmative vote of the majority of
the Board of Directors at any regular meeting of the Board, or at any special
meeting of the Board, if notice of the proposed alteration or repeal be
contained in the notice of such special meeting; provided, however, that no
change in these By-laws setting the time or place of the meeting for the
election of Directors shall be made within sixty (60) days next before the day
on which such meeting is to be held, and that in case of any change in such time
or place, notice thereof shall be given to each stockholder in person or by
letter mailed to his last known post office address at least twenty (20) days
before the meeting is held.

                      Provisions for National Emergencies
                      -----------------------------------

     37.  During periods of emergency resulting from an attack on the
United States or on a locality in which the Corporation conducts its business or
customarily holds meetings of its Board of Directors or its stockholders, or
during any nuclear or atomic disaster, or during the existence of any
catastrophe, or other similar emergency condition, the following provisions
shall apply notwithstanding any different provisions elsewhere contained in
these By-laws:

                                       12
<PAGE>
 
          (a) Whenever, during such emergency and as a result thereof, a quorum
of the Board of Directors or a standing committee thereof cannot readily be
convened for action, a meeting of such Board or committee thereof may be called
by any officer or Director by a notice of the time and place given only to such
of the Directors as it may be feasible to reach at the time and by such means as
may be feasible at the time, including publications or radio.  The Director or
Directors in attendance at the meeting shall constitute a quorum; provided,
however, that the officers or other persons present who have been designated on
a list approved by the Board before the emergency, all in such order of priority
and subject to such conditions and for such period of time as may be provided in
the resolution approving such list, or in the absence of such a resolution, the
officers of the Corporation who are present, in order of rank, and within the
same rank in order of seniority, shall to the extent required to provide a
quorum be deemed Directors for such meeting.

          (b) The Board, either before or during any such emergency, may
provide, and from time to time modify, lines of succession in the event that
during such emergency any or all officers or agents of the Corporation shall for
any reason be rendered incapable of discharging their duties.

          (c) The Board either before or during any such emergency, may,
effective in the emergency, change the head office or designate several
alternative head offices or regional offices, or authorize the officers so to
do.

          (d) No officer, Director or employee acting in accordance with this
article shall be liable except for willful misconduct.

                                       13
<PAGE>
 
          (e) To the extent not inconsistent with this article, all other
articles of these By-laws shall remain in effect during any emergency described
in this article and upon its termination the provisions of this article covering
the duration of such emergency shall cease to be operative.

                       Divisions and Divisional Officers
                       ---------------------------------

                           Groups and Group Officers
                           -------------------------

     38.  (a)  Divisions of the Corporation may be formed, and existing
divisions dissolved, by resolution of the Board of Directors of the Corporation
or through designation in writing by the President.

          The President of the Corporation, or his delegate, shall supervise the
management and operations of its divisions and shall have the authority to
appoint the officers thereof and the power to remove them and to fill any
vacancies.

          To the extent not inconsistent with these By-laws or a resolution of
the Board of Directors of the Corporation, the officers of each division shall
perform such duties and have such authority with respect to the business and
affairs of that division as may be granted, from time to time, by the President
of the Corporation, or his delegate.  With respect to the affairs of such
division and in the regular course of business of such division, officers of
each division may sign contracts and other documents in the name of the
division, where so authorized; provided, however, subject to the provisions of
the next succeeding sentence of this Paragraph, that an officer of one division
shall not have authority to bind any other division of the Corporation, nor to
bind the Corporation, except as to the normal and usual business and affairs of
the division of which he is an officer.  Notwithstanding the provisions of the
preceding sentence, if a division

                                       14
<PAGE>
 
of the Corporation is formed to provide shared services for the Corporation
and/or its operating units, officers, to the extent that and with respect to
matters to which they have been delegated such authority in writing by the
President or his delegate, may execute contracts in the name of and bind the
Corporation or any of its divisions; provided, however, that no officer of a
division formed to perform shared services shall contract in the name of or
otherwise bind a subsidiary or other legal entity in which the Corporation owns
an interest with respect to shared services matters unless such officer of such
division taking such action (i) is an officer of such subsidiary or such other
legal entity and is duly authorized to take such action in the name of and on
behalf of such subsidiary or other legal entity or (ii) takes such action on
behalf of such subsidiary or other legal entity pursuant to the grant of a duly
authorized power of attorney.  A divisional officer, unless specifically elected
to one of the designated offices of the Corporation, shall not be construed as
an officer of the Corporation.

          (b) To facilitate the attainment of certain goals and objectives by
various divisions and subsidiaries of the Corporation engaged in common pursuits
or in activities within the same or similar areas of business activity, a group
or groups of such subsidiaries and divisions may be formed by resolution of the
Board of Directors of the Corporation or through designation in writing by the
President of the Corporation, or his delegate.

          The activities of any such group shall be administered and coordinated
by the officers of the group and, if desired by the President of the
Corporation, or his delegate, by an operating committee.  In such event, the
number of members of such operating committee shall be determined by the
President of the Corporation, or his delegate, who shall appoint the members
thereof and have the power to remove them and substitute other members.  The
duties

                                       15
<PAGE>
 
of any such operating committee shall be to aid in the administration and
coordination of group activities and to consult with and advise the officers of
the group in achieving goals and objectives of such group.

          Officers of a group established pursuant to the provisions hereof may
include a chairman, a president, one or more vice presidents, a treasurer, a
secretary and such other officers as may facilitate operations of the group.
The President, or his delegate, shall have the authority to appoint the officers
of a group and the power to remove them and to fill any vacancies.  To the
extent not inconsistent with these By-laws or a resolution of the Board of
Directors of the Corporation, the officers of each group shall have such duties
and authority with respect to the activities and affairs of the group as may be
granted, from time to time, by the President of the Corporation, or his
delegate.

          Contracts may not be entered into in the name of any group, but any
officer of the group, where so authorized, may execute contracts and other
documents in the name of the Corporation on behalf of the members of the group
or any division of the Corporation that is a member of the group; provided,
however, that in no case shall an officer of the group have authority to bind
the Corporation except as to the normal and usual business and affairs of the
group of which he or she is an officer; and provided further that a group
officer may not execute contracts for any subsidiary who is a member of the
group unless (i) he or she executes the same under a duly authorized power of
attorney or (ii) he or she is also an officer of such subsidiary and executes
the contract in such capacity.

                                Indemnification
                                ---------------

     39.  (a)  Each person who was or is made a party or is threatened to
be made a party to or is involved in any action, suit or proceeding, whether
civil, criminal, administrative or

                                       16
<PAGE>
 
investigative (hereinafter a "proceeding"), by reason of the fact that he or she
is or was or has agreed to become a director or officer of the Corporation or is
or was serving or has agreed to serve at the request of the Corporation as a
director or officer of another corporation or of a partnership, joint venture,
trust or other enterprise, including service with respect to employee benefit
plans, whether the basis of such proceeding is alleged action in an official
capacity as a director or officer or in any other capacity while serving or
having agreed to serve as a director or officer shall be indemnified and held
harmless by the Corporation to the fullest extent authorized by the Delaware
General Corporation Law, as the same exists or may hereafter be amended, (but,
in the case of any such amendment, only to the extent that such amendment
permits the Corporation to provide broader indemnification rights than said law
permitted the Corporation to provide prior to such amendment) against all
expense, liability and loss (including attorneys' fees, judgments, fines, ERISA
excise taxes or penalties and amounts paid or to be paid in settlement)
reasonably incurred or suffered by such person in connection therewith and such
indemnification shall continue as to a person who has ceased to serve in the
capacity which initially entitled such person to indemnity hereunder and shall
inure to the benefit of his or her heirs, executors and administrators;
provided, however, that the Corporation shall indemnify any such person seeking
- --------  -------                                                              
indemnification in connection with a proceeding (or part thereof) initiated by
such person only if such proceeding (or part thereof) was authorized by the
Board of Directors of the Corporation.  The right to indemnification conferred
in this Section 39 shall be a contract right and shall include the right to be
paid by the Corporation the expenses incurred in defending any such proceeding
in advance of its final disposition; provided, however, that, if the Delaware
                                     --------  -------                       
General Corporation Law requires, the payment of such expenses incurred by a
director or officer in his or her capacity as a director or officer (and not in
any other capacity in which service was

                                       17
<PAGE>
 
or is rendered by such person while a director or officer, including, without
limitation, service to an employee benefit plan) in advance of the final
disposition of a proceeding, shall be made only upon delivery to the Corporation
of an undertaking, by or on behalf of such director or officer, to repay all
amounts so advanced if it shall ultimately be determined that such director or
officer is not entitled to be indemnified under this Section or otherwise.

          (b) If a claim under Paragraph (a) of this Section 39 is not paid in
full by the Corporation within ninety days after a written claim has been
received by the Corporation, the claimant may at any time thereafter bring suit
against the Corporation to recover the unpaid amount of the claim and, if
successful in whole or in part, the claimant shall be entitled to be paid also
the expense of prosecuting such claim.  It shall be a defense to any such action
(other than an action brought to enforce a claim for expenses incurred in
defending any proceeding in advance of its final disposition where the required
undertaking, if any is required, has been tendered to the Corporation) that the
claimant has not met the standards of conduct which make it permissible under
the Delaware General Corporation Law for the Corporation to indemnify the
claimant for the amount claimed, but the burden of proving such defense shall be
on the Corporation.  Neither the failure of the Corporation (including its Board
of Directors, independent legal counsel, or its stockholders) to have made a
determination prior to the commencement of such action that indemnification of
the claimant is proper in the circumstances because he or she has met the
applicable standard of conduct set forth in the Delaware General Corporation
Law, nor an actual determination by the Corporation (including its Board of
Directors, independent legal counsel, or its stockholders) that the claimant has
not met such applicable standard of conduct, shall be a defense to the action or
create a presumption that the claimant has not met the applicable standard of
conduct.

                                       18
<PAGE>
 
          (c) The right to indemnification and the advancement and payment of
expenses conferred in this Section 39 shall not be exclusive of any other right
which any person may have or hereafter acquire under any law (common or
statutory), provision of the Certificate of Incorporation of the Corporation,
By-law, agreement, vote of stockholders or disinterested directors or otherwise.

          (d) The Corporation may maintain insurance, at its expense, to protect
itself and any person who is or was serving as a director or officer of the
Corporation or is or was serving at the request of the Corporation as a director
or officer of another corporation, partnership, joint venture, trust or other
enterprise against any expense, liability or loss, whether or not the
Corporation would have the power to indemnify such person against such expense,
liability or loss under the Delaware General Corporation Law.

          (e) If this Section 39 or any portion hereof shall be invalidated on
any ground by any court of competent jurisdiction, then the Corporation shall
nevertheless indemnify and hold harmless each director or officer of the
Corporation as to costs, charges and expenses (including attorneys' fees),
judgments, fines and amounts paid in settlement with respect to any action, suit
or proceeding, whether civil, criminal, administrative or investigative to the
full extent permitted by any applicable portion of this Section 39 that shall
not have been invalidated and to the full extent permitted by applicable law.

REVISED DECEMBER 5, 1996

                                       19

<PAGE>
 
                                                                     EXHIBIT 4.1


                         FIRST SUPPLEMENTAL INDENTURE

                         DATED AS OF DECEMBER 12, 1996

                                     AMONG

                             HALLIBURTON COMPANY,

                             HALLIBURTON HOLD CO.

                                      and

                   TEXAS COMMERCE BANK NATIONAL ASSOCIATION

                                  as Trustee



(First Senior Indenture)
<PAGE>
 
     This First Supplemental Indenture dated as of December 12, 1996 is among
Halliburton Company, a Delaware corporation (the "Issuer"), Halliburton Hold
Co., a Delaware corporation ("Holding Company"), and Texas Commerce Bank
National Association, a national banking association, as Trustee, and
supplements, amends and modifies that certain Senior Indenture dated as of
January 2, 1991 between the Issuer and the Trustee (the "First Senior
Indenture"):

                                   RECITALS:

     The Issuer, the Holding Company and Halliburton Merge Co., a Delaware
corporation and an indirect, wholly owned subsidiary of the Issuer ("Mergeco"),
have executed and delivered an Agreement and Plan of Reorganization dated as of
December 11, 1996 pursuant to which Mergeco will be merged with and into the
Issuer (the "Merger"), which will be the corporation surviving the Merger, and
the outstanding capital stock of the Issuer will be converted into capital stock
of the Holding Company.

     To effect the Reorganization, the Issuer has incorporated the Holding
Company as a new first-tier subsidiary corporation, which in turn has
incorporated Halliburton Delaware, Inc., a Delaware corporation ("Newco"), as a
new second-tier subsidiary, which in turn has incorporated Mergeco as a new
third-tier subsidiary corporation.

     As a result of effectuation of the Merger, the Holding Company will become
a holding company and the Issuer will become an indirect wholly-owned subsidiary
of the Holding Company.

     The Merger will be effected pursuant to Section 251(g) of the General
Corporation Law of the State of Delaware ("DGCL"), which permits effectuation of
such a merger without a vote of stockholders of either constituent corporation.

     Pursuant to the Merger, the corporate name of the Issuer will be
changed to "Halliburton Energy Services, Inc." and, immediately thereafter, the
corporate name of the Holding Company will be changed to "Halliburton
Company".

     The Issuer has outstanding certain indebtedness issued pursuant to the
First Senior Indenture and the Holding Company and the Issuer intend that the
Holding Company will, as a primary obligor, assume the obligations of the Issuer
with respect to such indebtedness and with respect to the First Senior Indenture
and that the Issuer will remain obligated as a primary obligor with respect to
such indebtedness and, except as hereinafter set forth, with respect to the
First Senior Indenture to the extent that it relates to such indebtedness.

     NOW, THEREFORE, in consideration of the premises, the covenants herein
contained  and other good and valuable consideration, the receipt and
sufficiency of which are hereby acknowledged by the parties hereto, the parties
hereto covenant and agree as follows:
<PAGE>
 
                                   ARTICLE I

     Section 1.1    Definitions.  Capitalized terms used but not defined herein
are defined in the First Senior Indenture and are used herein with the meanings
ascribed to them therein.

     Section 1.2    Debentures.  The Holding Company shall, effective as of the
effective time of the Merger under the DGCL (the "Effective Time"), assume, and
shall thereafter timely pay, perform and discharge, each and every obligation of
the Issuer under and with respect to those certain 8.75% Debentures due February
15, 2021 (the "Debentures") issued by the Issuer in an aggregate principal
amount of $200,000,000 pursuant to the First Senior Indenture.  Notwithstanding
such assumption, the Issuer will remain obligated as a primary obligor with
respect to the payment, performance and discharge of such Debentures.

     Section 1.3    First Senior Indenture. The Holding Company shall, effective
as of the Effective Time, assume, and shall thereafter timely pay, perform and
discharge, each and every obligation of the Issuer under and with respect to the
First Senior Indenture, including without limitation those certain covenants
contained in Sections 3.6, 3.7 and 3.8 of the First Senior Indenture (the
"Special Covenants"). In this regard, the Special Covenants shall be
interpreted, from and after the Effective Time, (i) to apply to the Holding
Company, as the "Issuer" thereunder, and to the Issuer, as a "Restricted
Subsidiary" thereunder, and (ii) not to apply to the Issuer, as the "Issuer"
thereunder. From and after the Effective Time, the Issuer shall have no
obligation to pay, perform or discharge any indebtedness thereafter issued under
the First Senior Indenture, all such obligations being solely those of the
Holding Company.

                                  ARTICLE II

     Section 2.1    Effectiveness.  Although this First Supplemental Indenture
may be executed and delivered by the parties hereto prior thereto, the
provisions hereof shall not become effective unless and until the Merger becomes
effective under the DGCL and, under such circumstances, shall become effective
concurrently with the Effective Time of such Merger.  From and after the
Effective Time, the First Senior Indenture, as hereby supplemented, amended and
modified, shall remain in full force and effect.

     Section 2.2    References.  Each reference in the First Senior Indenture or
this First Supplemental Indenture to any article, section, term or provision of
the First Senior Indenture shall mean and be deemed to refer to such article,
section, term or provision of the First Senior Indenture, as modified by this
First Supplemental Indenture, except where the context otherwise indicates.

     Section 2.3    Benefit. All the covenants, provisions, stipulations and
agreements contained in this First Supplemental Indenture are and shall be for
the sole and exclusive benefit of the parties hereto, their successors and
assigns, and of the holders and registered owners from time to time of the
Debentures and any other Securities issued and outstanding from time to time
under the First Senior Indenture, as hereby amended and supplemented.
<PAGE>
 
     Section 2.4    Counterparts. This First Supplemental Indenture may be
executed in any number of counterparts, each of which shall be deemed an
original and all of which taken together shall be deemed to be a single
instrument.

     Section 2.5    Governing Law.  This First Supplemental Indenture shall be
deemed to be a contract under the laws of the State of New York, and for all
purposes shall be construed in accordance with the laws of such state without
regard to principles of conflicts of laws, except as may otherwise required by
mandatory provisions of law.

     Section 2.6    Headings.  The Article and Section headings herein are for
convenience only and shall not affect the construction hereof.

     IN WITNESS WHEREOF, the said Halliburton Company, Halliburton Hold Co. and
Texas Commerce Bank National Association have each caused this First
Supplemental Indenture to be executed in its corporate name by the officer whose
name is subscribed below, thereunto duly authorized, and its corporate seal to
be hereunto affixed and, in the cases of Halliburton Company and Halliburton
Hold Co., attested by its Secretary or Assistant Secretary, all as of the day
and year first above written.

                                    HALLIBURTON COMPANY


                                    By  /s/ Lester L. Coleman
Attest:                             Name:  Lester L. Coleman
                                    Title: Executive Vice President

By  /s/ Susan S. Keith
Name:  Susan S. Keith
Title: Vice President and
        Secretary

                                    HALLIBURTON HOLD CO.


                                    By  /s/ Robert M. Kennedy
Attest:                             Name:  Robert M. Kennedy
                                    Title: Vice President

By  /s/ Susan S. Keith
Name:  Susan S. Keith
Title: Secretary

                                    TEXAS COMMERCE BANK
                                         NATIONAL ASSOCIATION


                                    By  /s/ Terry L. Stewart
                                    Name:  Terry L. Stewart
                                    Title: Assistant Vice President

<PAGE>
 
                                                                     EXHIBIT 4.2


                         FIRST SUPPLEMENTAL INDENTURE

                         DATED AS OF DECEMBER 5, 1996

                                    BETWEEN

                              HALLIBURTON COMPANY

                                      AND

                   TEXAS COMMERCE BANK NATIONAL ASSOCIATION

                                  AS TRUSTEE
<PAGE>
 
                               TABLE OF CONTENTS
                                                                          Page
                                                                          ----
                                   ARTICLE I

                                  DEFINITIONS
<TABLE>
<S>                                                                        <C>
Section 1.1  Definitions.................................................  1
Section 1.2  Administrative Procedures...................................  1
Section 1.3  Business Day................................................  1
Section 1.4  Fixed Rate Notes............................................  1
Section 1.5  Floating Rate Notes.........................................  2
Section 1.6  Maturity Date...............................................  2
Section 1.7  Note Terms Certificate......................................  2
Section 1.8  Notes.......................................................  2
Section 1.9  Stated Maturity Date........................................  2
Section 1.10  Interest Rate Bases; Related Terms.........................  2
Section 1.11  Redemption/Repayment Terms.................................  4
Section 1.12  Record Date................................................  4

                                  ARTICLE II

                              GENERAL PROVISIONS

Section 2.1  Establishment of Series.....................................  4
Section 2.2  Authentication and Issuance.................................  5
Section 2.3  Maturities..................................................  6
Section 2.4  Currency....................................................  6
Section 2.5  Registration................................................  6
Section 2.6  Payments of Principal, Premium and Interest.................  6
Section 2.7  Interest in General.........................................  7
Section 2.8  Interest on Fixed Rate Notes................................  7
Section 2.9  Interest on Floating Rate Notes.............................  7
Section 2.10  Redemption at the Option of the Issuer.....................  9
Section 2.11  Repayment at the Option of the Holder......................  9

                                  ARTICLE III

                                 MISCELLANEOUS

Section 3.1 Counterparts.................................................  9
Section 3.2  Effect of Headings..........................................  9
Section 3.3  Provisions for the Sole Benefit of Parties and Holders......  9
</TABLE>

                                       i
<PAGE>
 
                         FIRST SUPPLEMENTAL INDENTURE

     This First Supplemental Indenture dated as of December 5, 1996 is between
Halliburton Company, a Delaware corporation (the "Issuer"), and Texas Commerce
Bank National Association, a national banking association, as Trustee, and
amends and supplements that certain Second Senior Indenture dated December 1,
1996 between the Issuer and the Trustee (the "Indenture").

                                   RECITALS:

     The Issuer proposes to offer, sell and issue from time to time, at an
aggregate initial offering price of up to $300,000,000, certain notes of its
series of medium-term notes due nine months or more from date of issue.

     For that purpose, the Issuer proposes, by means of this First Supplemental
Indenture, to establish such series of medium-term notes and certain terms and
provisions thereof that are different from, or in addition to, those provided in
the Indenture and to acknowledge that the remaining terms and provisions of such
medium-term notes will be established pursuant to the provisions of Section 2.3
of the Indenture.

     NOW, THEREFORE, in consideration of the premises, the covenants herein
contained and other good and valuable consideration, the receipt and sufficiency
of which are hereby acknowledged by the parties hereto, the parties hereto
covenant and agree as follows:

                                   ARTICLE I

                                  DEFINITIONS

      Section 1.1  Definitions.  Capitalized terms used but not defined herein
are defined in the Indenture and are used herein with the definitions ascribed
to them therein.

      Section 1.2  Administrative Procedures.  The term "Administrative
Procedures" shall have the meaning ascribed to such term in Section 2.2 of this
First Supplemental Indenture.

      Section 1.3  Business Day.  For purposes of the Notes only, the term
"Business Day" shall mean any day, other than a Saturday or Sunday, that is
neither a legal holiday nor a day on which banking institutions are authorized
or required by law, regulation or executive order to close in The City of New
York; provided, however, that, with respect to Notes as to which LIBOR is an
applicable Interest Rate Basis, such day is also a London Business Day which,
for this purpose shall mean a day on which dealings in United States dollars are
transacted in the London interbank market.

      Section 1.4  Fixed Rate Notes.  The term "Fixed Rate Notes" shall have the
meaning ascribed to such term in Section 2.2 of the First Supplemental
Indenture.

      Section 1.5  Floating Rate Notes.  The term "Floating Rate Notes" shall
have the meaning ascribed to such term in Section 2.2 of the First Supplemental
Indenture.
<PAGE>
 
      Section 1.6  Maturity Date.  The term "Maturity Date" shall have the
meaning ascribed to such term in Section 2.3 of this First Supplemental
Indenture.

      Section 1.7  Note Terms Certificate.  The term "Note Terms Certificate"
shall have the meaning ascribed to such term in Section 2.2 of this First
Supplemental Indenture.

      Section 1.8  Notes.  The term "Notes" shall have the meaning ascribed to
such term in Section 2.1 of this First Supplemental Indenture.

      Section 1.9  Stated Maturity Date.  The term "Stated Maturity Date" shall
have the meaning ascribed to such term in Section 2.2 of this First Supplemental
Indenture.

      Section 1.10  Interest Rate Bases; Related Terms.  The rate of interest of
a Floating Rate Note is determined by reference to one or more of the CD Rate,
the CMT Rate, the Commercial Paper Rate, the Eleventh District Cost of Funds
Rate, the Federal Funds Rate, LIBOR, the Prime Rate and the Treasury Rate or
such other interest rate basis as may be specified in the Note Terms Certificate
(each, an "Interest Rate Basis").  Each of the following terms is defined in
Exhibit A attached hereto and by this reference incorporated herein:  the "CD
Rate," the "CMT Rate," the "Commercial Paper Rate," the "Eleventh District Cost
of Funds Rate," the "Federal Funds Rate," "LIBOR," the "Prime Rate," and the
"Treasury Rate," as well as each of the defined terms used in such definitions.
In addition:

          (a) The term "Interest Payment Date" shall have the meanings ascribed
     to such term in Sections 2.8 and 2.9 of this First Supplemental Indenture.

          (b) The term "Spread" shall mean the number of basis points to be
     added to or subtracted from the related Interest Rate Basis or Bases
     applicable to a Floating Rate Note.

          (c) The term "Spread Multiplier" shall mean the percentage of the
     related Interest  Rate Basis or Bases applicable to a Floating Rate Note by
     which such Interest Rate Basis or Bases shall be multiplied to determine
     the applicable interest rate on such Floating Rate Note.

          (d) The term "Index Maturity" shall mean the period to maturity of the
     instrument or obligation with respect to which the related Interest Rate
     Basis or Bases will be calculated.

          (e) The term "Interest Period" shall have the meaning ascribed to such
     term in Section 2.7(b) of this First Supplemental Indenture.

          (f) The term "Interest Reset Date" shall mean the date or dates
     specified in the applicable Note Terms Certificate on which the rate of
     interest on a Floating Rate Note will be reset.

          (g) The term "Interest Reset Period" shall mean the period, whether
     daily, weekly, monthly, quarterly, semiannual or annual, between Interest
     Reset Dates relating to a Floating Rate Note, as specified in the
     applicable Note Terms Certificate.

                                       2
<PAGE>
 
          (h) The term "Interest Determination Date" shall mean, (i) with
     respect to the CD Rate, the CMT Rate, the Commercial Paper Rate, the
     Federal Funds Rate and the Prime Rate, the second Business Day immediately
     preceding the applicable Interest Reset Date; (ii) with respect to the
     Eleventh District Cost of Funds Rate, the last Business Day of the month
     immediately preceding the applicable Interest Reset Date on which the
     Federal Home Loan Bank of San Francisco publishes the Index; (iii) with
     respect to LIBOR, the second London Business Day immediately preceding the
     applicable Interest Reset Date; and (iv), with respect to the Treasury
     Rate, the day in the week in which the Interest Reset Date occurs on which
     Treasury Bill are normally auctioned (except that if the auction is held on
     the Friday of the immediately preceding week, the Interest Determination
     Date shall be that Friday). The Interest Determination Date pertaining to a
     Floating Rate Note the interest rate of which is determined by reference to
     two or more Interest Rate Bases shall be the second Business Day next
     preceding the Interest Reset Date for such Floating Rate Note on which each
     Interest Rate Basis in determinable; each Interest Rate Basis shall be
     determined as of such date, and the applicable interest rate shall take
     effect on the applicable Interest Reset Date.

          (i) The term "Maximum Interest Rate" shall have meaning ascribed to
     such term in Section 2.9 of this First Supplemental Indenture.

          (j) The term "Minimum Interest Rate" shall have meaning ascribed to
     such term in Section 2.9 of this First Supplemental Indenture.

          (k) The term "Calculation Agent" shall mean an agent appointed from
     time to time by the Issuer for the purpose of determining the rates of
     interest in effect from time to time with respect to one or more issues of
     Notes and calculating the amount of interest payable from time to time with
     respect thereto.  Unless otherwise specified in the Note Terms Certificate
     with respect to an issue of Notes, the Calculation Agent shall be the New
     York affiliate of the Trustee.

          (l) The term "Calculation Date", as it pertains to any Interest
     Determination Date, shall, unless otherwise specified in the applicable
     Note Terms Certificate, mean the earlier of (i) the tenth calendar day
     after such Interest Determination Date or, if such day is not a Business
     Day, the next succeeding Business Day or (ii) the Business Day immediately
     preceding the applicable Interest Payment Date or the Maturity Date, as the
     case may be.

     Section 1.11  Redemption/Repayment Terms.

          (a) The term "Initial Redemption Date" shall mean the date set forth
     on the face of a Note that is the first date on which a Note that is
     subject to redemption prior to its Stated Maturity Date at the option of
     the Issuer may be redeemed.

          (b) The term "Redemption Price" shall mean, with respect to a Note
     that is redeemable prior to its Stated Maturity Date at the option of the
     Issuer, an amount equal to the Initial Redemption Percentage specified in
     the applicable Note Terms Certificate, as adjusted by any applicable Annual
     Redemption Percentage Reduction, multiplied by the unpaid principal amount
     to be redeemed.

                                       3
<PAGE>
 
          (c) The term "Initial Redemption Percentage" shall mean, with respect
     to a Note that is redeemable prior to its Stated Maturity Date at the
     option of the Issuer, the percentage specified in the applicable Note Terms
     Certificate, which Initial Redemption Percentage shall decline at each
     anniversary of the Initial Redemption Date by an amount equal to the
     applicable Annual Redemption Percentage Reduction, if any, until the
     Redemption Price is equal to 100% of the unpaid principal amount to be
     redeemed.

          (d) The term "Annual Redemption Percentage Reduction" shall mean the
     percentage specified as such in the applicable Note Terms Certificate.

          (e) The term "Optional Repayment Date" shall mean the date set forth
     on the face of a Note that is the first date on which a Note that is
     subject to repayment prior to its Stated Maturity Date at the option of the
     Holder may be repaid.

      Section 1.12  Record Date.  The term "Record Date" shall, unless otherwise
specified in the applicable Note Terms Certificate, mean the fifteenth calendar
day (whether or not a Business Day) immediately preceding the related Interest
Payment Date with respect to any Note.

                                  ARTICLE II

                              GENERAL PROVISIONS

      Section 2.1  Establishment of Series.  Pursuant to the provisions of
Section 2.3 of the Indenture, there is hereby established a series of Securities
designated generally as the Medium-Term Notes Due Nine Months or More From Date
of Issue, Series A, that may be sold and issued from time to time, at an
aggregate initial offering price of up to U. S. $300,000,000 (the "Notes"),
subject to reduction by the aggregate initial offering price of any other
Securities that may be theretofore sold and issued by the Issuer pursuant to the
terms of the Indenture.  Forms of a Fixed Rate Note and a Floating Rate Note,
excluding in each case terms and provisions to be included therein pursuant to a
Note Terms Certificate, are attached hereto as Exhibits B-1 and B-2,
respectively, and by this reference incorporated herein.

      Section 2.2  Authentication and Issuance.  The Notes may be authenticated
and issued in one or more issues or tranches of Notes of like tenor and terms.
The entire series of Notes shall be deemed to be subject to a Periodic Offering;
the procedures for authentication and delivery of one or more issues or tranches
of Notes subject to such Periodic Offering to which reference is made in Section
2.4 of the Indenture are set forth in the Administrative Procedures (the
"Administrative Procedures") authorized and adopted by the Board of Directors of
the Issuer and attached hereto as Exhibit C; and the New York affiliate of the
Trustee (the "Issuing and Paying Agent"), upon compliance by the Issuer with the
requirements of Section 2.4 of the Indenture, shall authenticate and deliver
Notes in accordance with the Administrative Procedures. To the extent that the
terms of any such issue or tranche are not set forth in the Indenture, as
supplemented and amended by this First Supplemental Indenture, they shall be
established by means of an Officer's Certificate delivered to the Issuing and
Paying Agent pursuant to Section 2.3 of the Indenture (a "Note Terms
Certificate"). In accordance with the procedures set forth in the Indenture and
the Administrative Procedures, and to the extent the following terms and
provisions are set forth in a Note Terms Certificate:

                                       4
<PAGE>
 
          (a) Each Note shall be dated a date determined in accordance with the
     Administrative Procedures, which date may vary among the Notes;

          (b) each Note will mature on a day nine months or more from its date
     of issue (its "Stated Maturity Date") determined in accordance with the
     Administrative Procedures, which Stated Maturity Date may vary among the
     Notes;

          (c) each Note shall bear interest, if any, at a fixed rate (a "Fixed
     Rate Note") or at a floating rate (a "Floating Rate Note"), and the
     interest rate for a Fixed Rate Note or the Interest Rate Basis for
     determining the floating interest rate for a Floating Rate Note shall be
     established in accordance with the Administrative Procedures, which
     interest rate or Interest Rate Basis may vary among the Notes;

          (d) interest on each Fixed Rate Note and each Floating Rate Note shall
     accrue from its date of issue;

          (e) the floating interest rate on each Floating Rate Note shall be
     reset on such date or dates as shall be established in accordance with the
     Administrative Procedures, which date or dates may vary among the Notes;

          (f) interest on each Note shall be payable in arrears on the date or
     dates specified therein and determined in accordance with the
     Administrative Procedures, which date or dates may vary among the Notes;

          (g) each Note may be subject to redemption, in whole or in part, prior
     to its Stated Maturity Date at the option of the Issuer to the extent so
     provided in accordance with the Administrative Procedures; and

          (h) each Note may be subject to repayment, in whole or in part, prior
     to its Stated Maturity Date at the option of the Holder thereof to the
     extent so provided in accordance with the Administrative Procedures.

      Section 2.3  Maturities.  Each Note will mature on its Stated Maturity
Date, unless the principal thereof (or any installment of principal thereof)
becomes due and payable prior to such Stated Maturity Date, whether by the
declaration of acceleration of maturity, notice of redemption at the option of
the Issuer, notice of the Holder's option to elect repayment or otherwise (the
Stated Maturity Date or such prior date, as the case may be, being referred to
herein as the "Maturity Date" with respect to the principal of such Note
repayable on such date).

      Section 2.4  Currency.  The Notes will be denominated in, and payments of
principal, premium, if any, and interest, if any, in respect thereof will be
made in United States dollars or such other currency as is then lawful for the
settlement of public and private debts within the United States of America.

                                       5
<PAGE>
 
      Section 2.5  Registration.  Each Note shall be issued in book entry form
eligible for deposit in the book-entry system maintained by a Depositary (a
"Book-Entry Note") represented by one or more fully registered Global Securities
or in fully registered form (a "Certificated Note").

      Section 2.6  Payments of Principal, Premium and Interest.  In the case of
Book-Entry Notes, payments of principal thereof, and premium, if any, and
interest, if any, thereon shall be made by the Issuer through the Issuing and
Paying Agent to the Depositary.  In the case of Certificated Notes, payments of
principal and premium, if any, due on any Maturity Date shall be made in
immediately available funds upon presentation and surrender thereof (and, in the
case of any repayment on an Optional Repayment Date, as hereinafter defined,
upon submission of a duly completed election form in accordance with the
provisions hereinafter described) at the office or agency maintained by the
Issuer for such purpose in the Borough of Manhattan, The City of New York.
Payments of interest, if any, due on such Maturity Date of a Certificated Note
shall be made to the person to whom payment of the principal thereof and
premium, if any, thereon shall be made.  Payments of interest, if any, due on a
Certificated Note on any Interest Payment Date, other than any Maturity Date,
shall be made by check mailed to the address of the Holder entitled thereto as
such address shall appear in the Security Register of the Issuer.  A Holder of
$10,000,000 or more in aggregate principal amount of Certificated Notes (whether
having identical or different terms and provisions) will be entitled to receive
interest payments, if any, on any Interest Payment Date, other than any Maturity
Date, by wire transfer of immediately available funds if appropriate wire
transfer instructions have been received in writing by the Issuing and Paying
Agent or other paying agent not less than 15 days prior to such Interest Payment
Date.  Any such wire transfer instructions received by the Issuing and Paying
Agent or other paying agent shall remain in effect until revoked by such Holder.

      Section 2.7  Interest in General.  Unless otherwise specified in an
applicable Note Terms Certificate:

          (a) Each interest-bearing Note shall bear interest from the date of
     its issue at the rate per annum, in the case of a Fixed Rate Note, or
     pursuant to the interest rate formula, in the case of a Floating Rate Note,
     in each case as specified in the Note;

          (b) Interest payments in respect of Fixed Rate Notes and Floating Rate
     Notes shall be made in an amount equal to the interest accrued from and
     including the immediately preceding Interest Payment Date in respect of
     which interest has been paid or duly made available for payment (or from
     and including the date of issue, if no interest has been paid or duly made
     available for payment) to but excluding the applicable Interest Payment
     Date or the Maturity Date, as the case may be (each, an "Interest Period");
     and

          (c) The first payment of interest on any such Note originally issued
     between a Record Date and the related Interest Payment Date shall be made
     on the Interest Payment Date immediately following the next succeeding
     Record Date to the Holder on such next succeeding Record Date.

      Section 2.8  Interest on Fixed Rate Notes.  Interest on Fixed Rate Notes
will be payable on March 31 and September 30 of each year or on such other date
or dates specified in the applicable Note Terms Certificate (each, an "Interest
Payment Date" with respect to Fixed Rate Notes) and on 

                                       6
<PAGE>
 
the Maturity Date with respect to all or part of the principal thereof; unless
otherwise specified in the applicable Note Terms Certificate, interest on Fixed
Rate Notes shall be computed on the basis of a 360-day year of twelve 30-day
months;

      Section 2.9  Interest on Floating Rate Notes.  Interest on Floating Rate
Notes shall be payable on the date or dates specified in the applicable Note
Terms Certificate (each, an "Interest Payment Date" with respect to Floating
Rate Notes) and shall be determined as follows:

          (a) Any Floating Rate Note (a "Regular Floating Rate Note"), other
     than a Floating Rate/Fixed Rate Note, an Inverse Floating Rate Note or a
     Note that is subject to an Addendum or to "Other/Additional Provisions,"
     shall, except as otherwise provided in the applicable Note Terms
     Certificate, bear interest at the rate determined by reference to the
     applicable Interest Rate Basis or Bases (i) plus or minus the applicable
     Spread, if any, and (ii) multiplied by the applicable Spread Multiplier, if
     any.  Commencing on the initial Interest Reset Date for such Note (the
     "Initial Interest Reset Date"), the rate at which interest on such Regular
     Floating Rate Note shall be payable shall be reset as of each Interest
     Reset Date;

          (b) If a Note is designated as a Floating Rate/Fixed Rate Note, such
     Note shall, except as otherwise provided in the applicable Note Terms
     Certificate, bear interest at the rate determined by reference to the
     applicable Interest Rate Basis or Bases (i) plus or minus the applicable
     Spread, if any, and (ii) multiplied by the applicable Spread Multiplier, if
     any. Commencing on the Initial Interest Reset Date, the rate at which
     interest on such Floating Rate/Fixed Rate Note shall be payable shall be
     reset as of each Interest Reset Date; provided, however, that the interest
     rate in effect for the period commencing on the date specified in the
     applicable Note Terms Certificate (the "Fixed Rate Commencement Date") to
     the Maturity Date shall be the Fixed Interest Rate, if such rate is
     specified in the Note Terms Certificate or, if no such Fixed Interest Rate
     is specified, the interest rate in effect thereon on the day immediately
     preceding the Fixed Rate Commencement Date; and

          (c) If a Note is designated as an Inverse Floating Rate Note, such
     Note shall, except as otherwise provided in the applicable Note Terms
     Certificate, bear interest at the Fixed Interest Rate minus the rate
     determined by reference to the applicable Interest Rate Basis or Bases (i)
     plus or minus the applicable Spread, if any, and (ii) multiplied by the
     applicable Spread Multiplier, if any; provided, however, that, unless
     otherwise specified in the applicable Note Terms Certificate, the interest
     rate thereon shall not be less than zero. Commencing on the Initial
     Interest Reset Date, the rate at which interest on such Inverse Floating
     Rate Note shall be payable shall be reset as of each Interest Reset Date;

provided, however, that, in each case, the interest rate in effect for the
period, if any, from the date of issue to the Initial Interest Reset Date shall
be the initial interest rate of such Note (the "Initial Interest Rate").  If any
Interest Reset Date for any Floating Rate Note would otherwise be a day that is
not a Business Day, such Interest Reset Date shall be postponed to the next
succeeding Business Day, except that in the case of a Floating Rate Note as to
which LIBOR is an applicable Interest Rate Basis and such Business Day falls in
the next succeeding calendar month, such Interest Reset Date shall be the
immediately preceding Business Day.  Notwithstanding the foregoing, a Floating
Rate Note may also have either or both of the following: a maximum interest
rate, or ceiling, that may 

                                       7
<PAGE>
 
accrue during any Interest Period (a "Maximum Interest Rate") and a minimum
interest rate, or floor, that may accrue during any Interest Period (a "Minimum
Interest Rate"). Interest accrued on a Floating Rate Note shall be calculated by
multiplying its principal amount by an accrued interest factor. Such accrued
interest factor shall be computed by adding the interest factor calculated for
each day in the applicable Interest Period. Unless otherwise provided in the
applicable Note Terms Certificate, the interest factor for each such day shall
be computed by dividing the interest rate applicable to such day by 360, in the
case of Floating Rate Notes for which an applicable Interest Rate Basis is the
CD Rate, the Commercial Paper Rate, the Eleventh District Cost of Funds Rate,
the Federal Funds Rate, LIBOR or the Prime Rate, or by the actual number of days
in the year in the case of Floating Rate Notes for which an applicable Interest
Rate Basis is the CMT Rate or the Treasury Rate. Unless otherwise specified in
the applicable Note Terms Certificate, if the interest rate is to be calculated
with reference to two or more Interest Rate Bases, such interest rate shall be
calculated in each Interest Period in the same manner as if only the applicable
Interest Rate Basis specified in the applicable Note Terms Certificate applied.

      Section 2.10  Redemption at the Option of the Issuer.  To the extent an
applicable Note Terms Certificate provides for an Initial Redemption Date, Notes
shall be redeemable on any date on and after such Initial Redemption Date but
prior to their Stated Maturity Date in whole or in part at the option of the
Issuer in accordance with the provisions of Article Twelve of the Indenture;
provided, however, that any partial redemption of Notes shall be in increments
of $1,000 and that any remaining principal amount thereof shall be at least
$1,000.  Any such redemption shall be at the applicable Redemption Price,
together with unpaid interest accrued to the date of redemption.

      Section 2.11  Repayment at the Option of the Holder.  To the extent an
applicable Note Terms Certificate provides for one or more Optional Repayment
Dates, Notes shall be subject to repayment at the option of the Holders thereof
on any such Optional Repayment Date in whole or in part; provided, however, that
any partial repayment of Notes shall be in increments of $1,000 and that any
remaining principal amount thereof shall be at least $1,000.  Any such repayment
shall be at a repayment price of 100% of the unpaid principal amount to be
repaid on such Optional Repayment Date, together with unpaid interest accrued to
the date of repayment.

                                  ARTICLE III

                                 MISCELLANEOUS

      Section 3.1 Counterparts.  This First Supplemental Indenture may be
executed in any number of counterparts, each of which shall be deemed an
original, but all of which shall together constitute but one and the same
instrument.

      Section 3.2  Effect of Headings.  The Article and Section headings herein
and in the Table of Contents are for convenience only and shall not affect the
construction hereof.

      Section 3.3  Provisions for the Sole Benefit of Parties and Holders.
Nothing in the Indenture, as supplemented, amended and modified by this First
Supplemental Indenture, or in the Notes, expressed or implied, shall give or be
construed to give to any person, firm or corporation, other than the parties
hereto and their successors and the Holders, any legal or equitable right,
remedy or claim 

                                       8
<PAGE>
 
under the Indenture, as so supplemented, amended and modified, or under any
covenant or provision herein contained, all such covenants and provisions being
for the sole benefit of the parties hereto and their successors and of the
Holders.

                                       9
<PAGE>
 
     IN WITNESS WHEREOF, the parties hereto have caused this First Supplemental
Indenture to be duly executed and the appropriate corporate seals to be hereunto
affixed and attested, all as of the 5th day of December, 1996.

                                    HALLIBURTON COMPANY


                                    By: /s/ Robert M. Kennedy
                                    Title: Vice President - Legal

Attest:

/s/ Susan S. Keith

Title: Vice President and 
        Secretary


                                    TEXAS COMMERCE BANK NATIONAL
                                         ASSOCIATION


                                    By: /s/ Terry L. Stewart
                                    Title: Assistant Vice President

                                       10
<PAGE>
 
                                                                       EXHIBIT A

                           INTEREST RATE DEFINITIONS

     Unless otherwise specified in the applicable Note Terms Certificate, the
Calculation Agent shall determine each Interest Rate Basis in accordance with
the following provisions.

     CD RATE.  Unless otherwise specified in the applicable Note Terms
Certificate, "CD Rate" means, with respect to any Interest Determination Date
relating to a Floating Rate Note for which the interest rate is determined with
reference to the CD Rate (a "CD Rate Interest Determination Date"), the rate on
such date for negotiable United States dollar certificates of deposit having the
Index Maturity specified in the applicable Note Terms Certificate as published
by the Board of Governors of the Federal Reserve System in "Statistical Release
H. 15(519), Selected Interest Rates" or any successor publication ("H. 15(519)")
under the heading "CDS (Secondary Market)," or, if not published by 3:00 P.M.,
New York City time, on the related Calculation Date, the rate on such CD Rate
Interest Determination Date for negotiable United States dollar certificates of
deposit of the Index Maturity specified in the applicable Note Terms Certificate
as published by the Federal Reserve Bank of New York in its daily statistical
release "Composite 3:30 P.M. Quotations for U.S. Government Securities" or any
successor publication ("Composite Quotations") under the heading "Certificates
of Deposit." If such rate is not yet published in either H.15(519) or Composite
Quotations by 3:00 P.M., New York City time, on the related Calculation Date,
then the CD Rate on such CD Rate Interest Determination Date shall be calculated
by the Calculation Agent as the arithmetic mean of the secondary market offered
rates as of 10:00 A.M., New York City time, on such CD Rate Interest
Determination Date, of three leading nonbank dealers in negotiable United States
dollar certificates of deposit in The City of New York (which may include the
Agents or their affiliates) selected by the Calculation Agent for negotiable
United States dollar certificates of deposit of major United States money center
banks with a remaining maturity closest to the Index Maturity specified in the
applicable Note Terms Certificate in an amount that is representative for a
single transaction in that market at that time; provided, however, that, if the
dealers so selected by the Calculation Agent are not quoting as mentioned in
this sentence, the CD Rate determined as of such CD Rate Interest Determination
Date shall be the CD Rate in effect immediately prior to such CD Rate Interest
Determination Date.

     CMT RATE.  Unless otherwise specified in the applicable Note Terms
Certificate, "CMT Rate" means, with respect to any Interest Determination Date
relating to a Floating Rate Note for which the interest rate is determined with
reference to the CMT Rate (a "CMT Rate Interest Determination Date"), the rate
displayed on the Designated CMT Telerate Page under the caption "... Treasury
Constant Maturities... Federal Reserve Board Release H.15... Mondays
Approximately 3:45 P.M.," under the column for the Designated CMT Index Maturity
for (i), if the Designated CMT Telerate Page is 7055, the rate on such CMT Rate
Interest Determination Date and (ii), if the Designated CMT Telerate Page is
7052, the weekly or monthly average, as specified in the applicable Note Terms
Certificate, for the week or the month, as applicable, ended immediately
preceding the week or the month, as applicable, in which the related CMT Rate
Interest Determination Date falls.  If such rate is no longer displayed on the
relevant page or is not displayed by 3:00 P.M., New York City time, on the
related Calculation Date, then the CMT Rate for such CMT Rate Interest
Determination Date shall be such treasury constant maturity rate for the
Designated CMT Index Maturity for such CMT Rate Interest Determination Date as
published in H.15(519).  If such rate is no longer published or is not published
by 3:00 P.M., New York City time, on the related Calculation Date, then the CMT
Rate for such CMT Rate Interest Determination 

                                       11
<PAGE>
 
Date shall be such treasury constant maturity rate for the Designated CMT Index
Maturity (or such other United States Treasury rate for the Designated CMT Index
Maturity) for such CMT Rate Interest Determination Date as may then be published
by either the Board of Governors of the Federal Reserve System or the United
States Department of the Treasury and as the Calculation Agent determines to be
comparable to the rate formerly displayed on the Designated CMT Telerate Page
and published in H.15(519). If such information is not provided by 3:00 P.M.,
New York City time, on the related Calculation Date, then the CMT Rate on the
CMT Rate Interest Determination Date shall be calculated by the Calculation
Agent as a yield to maturity, based on the arithmetic mean of the secondary
market closing offer prices as of approximately 3:30 P.M., New York City time,
on such CMT Rate Interest Determination Date reported, according to their
written records, by three leading United States government securities dealers in
The City of New York (which may include the Agents or their affiliates) (each, a
"Reference Dealer") selected by the Calculation Agent (from five such Reference
Dealers selected by the Calculation Agent and eliminating the highest quotation
(or, in the event of equality, one of the highest) and the lowest quotation (or,
in the event of equality, one of the lowest)), for the most recently issued
direct noncallable fixed rate obligations of the United States ("Treasury
Notes") with an original maturity of approximately the Designated CMT Index
Maturity and a remaining term to maturity of not less than such Designated CMT
Index Maturity minus one year. If the Calculation Agent is unable to obtain
three such Treasury Note quotations, the CMT Rate on such CMT Rate Interest
Determination Date shall be calculated by the Calculation Agent as a yield to
maturity based on the arithmetic mean of the secondary market offered rates as
of approximately 3:30 P.M., New York City time, on such CMT Rate Interest
Determination Date of three Reference Dealers in The City of New York (from five
such Reference Dealers selected by the Calculation Agent and eliminating the
highest quotation (or, in the event of equality, one of the highest) and the
lowest quotation (or, in the event of equality, one of the lowest)), for
Treasury Notes with an original maturity of the number of years that is the next
highest to the Designated CMT Index Maturity and a remaining term to maturity
closest to the Designated CMT Index Maturity and in an amount of at least $100
million. If three or four (and not five) of such Reference Dealers are quoting
as described above, then the CMT Rate shall be based on the arithmetic mean of
the offered rates obtained and neither the highest nor the lowest of such quotes
shall be eliminated; provided, however, that, if fewer than three Reference
Dealers so selected by the Calculation Agent are quoting as mentioned herein,
the CMT Rate determined as of such CMT Rate Interest Determination Date shall be
the CMT Rate in effect on such CMT Rate Determination Date. If two Treasury
Notes with an original maturity as described in the second preceding sentence
have remaining terms to maturity equally close to the Designated CMT Index
Maturity, the Calculation Agent shall obtain quotations for the Treasury Note
with the shorter remaining term to maturity.
 
     "Designated CMT Telerate Page" means the display on the Dow Jones Telerate
Service (or any successor service) on the page specified in the applicable Note
Terms Certificate (or any other page as may replace such page on such service)
for the purpose of displaying Treasury Constant Maturities as reported in H.
15(519).  If no such page is specified in the applicable Note Terms Certificate,
the Designated CMT Telerate Page shall be 7052 for the most recent week.

                                       12
<PAGE>
 
     "Designated CMT Index Maturity" means the original period to maturity of
the U.S. Treasury securities (either 1, 2, 3, 5, 7, 10, 20 or 30 years)
specified in the applicable Note Terms Certificate with respect to which the CMT
Rate will be calculated or, if no such maturity is specified in the applicable
Note Terms Certificate, 2 years.

     COMMERCIAL PAPER RATE.  Unless otherwise specified in the applicable Note
Terms Certificate, "Commercial Paper Rate" means, with respect to any Interest
Determination Date relating to a Floating Rate Note for which the interest rate
is determined with reference to the Commercial Paper Rate (a "Commercial Paper
Rate Interest Determination Date"), the Money Market Yield (as hereinafter
defined) on such date of the rate for commercial paper having the Index Maturity
specified in the applicable Note Terms Certificate as published in H. 1 5 (519)
under the heading "Commercial Paper." If such rate is not published by 3:00
P.M., New York City time, on the related Calculation Date, then the Commercial
Paper Rate on such Commercial Paper Rate Interest Determination Date shall be
the Money Market Yield of the rate for commercial paper having the Index
Maturity specified in the applicable Note Terms Certificate as published in
Composite Quotations under the heading "Commercial Paper" (with an Index
Maturity of one month or three months being deemed to be equivalent to an Index
Maturity of 30 days or 90 days, respectively).  If such rate is not yet
published in either H.15(519) or Composite Quotations by 3:00 P.M., New York
City time, on the related Calculation Date, then the Commercial Paper Rate on
such Commercial Paper Rate Interest Determination Date shall be calculated by
the Calculation Agent as the Money Market Yield of the arithmetic mean of the
offered rates at approximately 11:00 A.M., New York City time, on such
Commercial Paper Rate Interest Determination Date of three leading dealers of
commercial paper in The City of New York (which may include the Agents or their
affiliates) selected by the Calculation Agent for commercial paper having the
Index Maturity specified in the applicable Note Terms Certificate placed for an
industrial issuer whose bond rating is "Aa," or the equivalent, from a
nationally recognized statistical rating organization; provided, however, that,
if the dealers so selected by the Calculation Agent are not quoting as mentioned
in this sentence, the Commercial Paper Rate determined as of such Commercial
Paper Rate Interest Determination Date will be the Commercial Paper Rate in
effect immediately prior to such Commercial Paper Rate Interest Determination
Date.

     "Money Market Yield" means a yield (expressed as a percentage) calculated
in accordance with the following formula:

     Money Market Yield -             D x 360          x 100
                                      --------              
                                 360 - (D x M)

where "D" refers to the applicable per annum rate for commercial paper quoted on
a bank discount basis and expressed as a decimal, and "M" refers to the actual
number of days in the applicable Interest Reset Period.

     ELEVENTH DISTRICT COST OF FUNDS RATE.  Unless otherwise specified in the
applicable Note Terms Certificate, "Eleventh District Cost of Funds Rate" means,
with respect to any Interest Determination Date relating to a Floating Rate Note
for which the interest rate is determined with reference to the Eleventh
District Cost of Funds Rate (an "Eleventh District Cost of Funds Rate Interest
Determination Date"), the rate equal to the monthly weighted average cost of
funds for the calendar month immediately preceding the month in which such
Eleventh District Cost of Funds Rate 

                                       13
<PAGE>
 
Interest Determination Date falls, as set forth under the caption "11th
District" on Telerate Page 7058 as of 11:00 A.M., San Francisco time, on such
Eleventh District Cost of Funds Rate Interest Determination Date. If such rate
does not appear on Telerate Page 7058 on such Eleventh District Cost of Funds
Rate Interest Determination Date, then the Eleventh District Cost of Funds Rate
on such Eleventh District Cost of Funds Rate Interest Determination Date shall
be the monthly weighted average cost of funds paid by member institutions of the
Eleventh Federal Home Loan Bank District that was most recently announced (the
"Index") by the Federal Home Loan Bank ("FHLB") of San Francisco as such cost of
funds for the calendar month immediately preceding such Eleventh District Cost
of Funds Rate Interest Determination Date. If the FHLB of San Francisco fails to
announce the Index on or prior to such Eleventh District Cost of Funds Rate
Interest Determination Date for the calendar month immediately preceding such
Eleventh District Cost of Funds Rate Interest Determination Date, the Eleventh
District Cost of Funds Rate determined as of such Eleventh District Cost of
Funds Rate Interest Determination Date will be the Eleventh District Cost of
Funds Rate in effect immediately prior to such Eleventh District Cost of Funds
Rate Interest Determination Date.

     FEDERAL FUNDS RATE.  Unless otherwise specified in the applicable Note
Terms Certificate, "Federal Funds Rate" means, with respect to any Interest
Determination Date relating to a Floating Rate Note for which the interest rate
is determined with reference to the Federal Funds Rate (a "Federal Funds Rate
Interest Determination Date"), the rate on such date for United States dollar
federal funds as published in H.15(519) under the heading "Federal Funds
(Effective)" or, if not published by 3:00 P.M., New York City time, on the
related Calculation Date, the rate on such Federal Funds Rate Interest
Determination Date as published in Composite Quotations under the heading
"Federal Funds/Effective Rate." If such rate is not published in either
H.15(519) or Composite Quotations by 3:00 P.M., New York City time, on the
related Calculation Date, then the Federal Funds Rate on such Federal Funds Rate
Interest Determination Date shall be calculated by the Calculation Agent as the
arithmetic mean of the rates for the last transaction in overnight United States
dollar federal funds arranged by three leading brokers of federal funds
transactions in The City of New York (which may include the Agents or their
affiliates) selected by the Calculation Agent prior to 9:00 A.M., New York City
time, on such Federal Funds Rate Interest Determination Date; provided, however,
that, if the brokers so selected by the Calculation Agent are not quoting as
mentioned in this sentence, the Federal Funds Rate determined as of such Federal
Funds Rate Interest Determination Date shall be the Federal Funds Rate in effect
immediately prior to such Federal Funds Rate Interest Determination Date.

     LIBOR.  Unless otherwise specified in the applicable Note Terms
Certificate, "LIBOR" means the rate determined in accordance with the following
provisions:

          (i) With respect to any Interest Determination Date relating to a
     Floating Rate Note for which the interest rate is determined with reference
     to LIBOR (a "LIBOR Interest Determination Date"), LIBOR will be either: (a)
     if "LIBOR Reuters" is specified in the applicable Note Terms Certificate,
     the arithmetic mean of the offered rates (unless the Designated LIBOR Page
     by its terms provides only for a single rate, in which case such single
     rate shall be used) for deposits in United States dollars having the Index
     Maturity specified in such Note Terms Certificate, commencing on the
     applicable Interest Reset Date, that appear on the Designated LIBOR Page as
     of 11:00 A.M., London time, on such LIBOR Interest Determination Date, or
     (b) if "LIBOR Telerate" is specified in the applicable Note 

                                       14
<PAGE>
 
     Terms Certificate or if neither "LIBOR Reuters" nor "LIBOR Telerate" is
     specified in the applicable Note Terms Certificate as the method for
     calculating LIBOR, the rate for deposits in United States dollars having
     the Index Maturity specified in such Note Terms Certificate, commencing on
     such Interest Reset Date, that appears on the Designated LIBOR Page as of
     11:00 A.M., London time, on such LIBOR Interest Determination Date. If
     fewer than two such offered rates so appear, LIBOR on such LIBOR Interest
     Determination Date shall be determined in accordance with the provisions
     described in clause (ii) below.

          (ii) With respect to a LIBOR Interest Determination Date on which
     fewer than two offered rates appear on the Designated LIBOR Page as
     specified in clause (i) above, LIBOR will be the arithmetic mean of the
     quotations for deposits in United States dollars for the period of the
     Index Maturity specified in the applicable Note Terms Certificate,
     commencing on the applicable Interest Reset Date, offered to prime banks in
     the London interbank market by the principal London offices of four major
     reference banks (which may include affiliates of the Agents) in the London
     interbank market, as selected by the Calculation Agent, at approximately
     11:00 A.M., London time, on such LIBOR Interest Determination Date and in a
     principal amount that is representative for a single transaction in United
     States dollars in such market at such time.  If fewer than two such
     quotations are so provided, then LIBOR on such LIBOR Interest Determination
     Date shall be the arithmetic mean of the rates quoted at approximately
     11:00 A.M., in London, England, on such LIBOR Interest Determination Date
     by three major reference banks (which may include affiliates of the Agents)
     in London, England, selected by the Calculation Agent for loans in United
     States dollars to leading European banks, having the Index Maturity
     specified in the applicable Note Terms Certificate and in a principal
     amount that is representative for a single transaction in United States
     dollars in such market at such time; provided, however, that, if the banks
     so selected by the Calculation Agent are not quoting as mentioned in this
     sentence, LIBOR determined as of such LIBOR Interest Determination Date
     shall be LIBOR in effect immediately prior to such LIBOR Interest
     Determination Date.

     "Designated LIBOR Page" means (a) if "LIBOR Reuters" is specified in the
applicable Note Terms Certificate, the display on the Reuter Monitor Money Rates
Service (or any successor service) on the page specified in each Note Terms
Certificate (or any other page as may replace such page on such service) for the
purpose of displaying the London interbank rates of major banks for United
States dollars, or (b) if "LIBOR Telerate" is specified in the applicable Note
Terms Certificate or neither "LIBOR Reuters" nor "LIBOR Telerate" is specified
in the applicable Note Terms Certificate as the method for calculating LIBOR,
the display on the Dow Jones Telerate Service (or any successor service) on the
page specified in such Note Terms Certificate (or any other page as may replace
such page on such service) for the purpose of displaying the London interbank
rates of major banks for United States dollars.

     PRIME RATE.  Unless otherwise specified in the applicable Note Terms
Certificate, "Prime Rate" means, with respect to any Interest Determination Date
relating to a Floating Rate Note for which the interest rate is determined with
reference to the Prime Rate (a "Prime Rate Interest Determination Date"), the
rate on such date as such rate is published in H.15(519) under the heading "Bank
Prime Loan." If such rate is not published prior to 3:00 P.M., New York City
time, on the related Calculation Date, then the Prime Rate shall be the
arithmetic mean of the rates of interest 

                                       15
<PAGE>
 
publicly announced by each bank that appears on the Reuters Screen USPRIME1 Page
(as hereinafter defined) as such bank's prime rate or base lending rate as in
effect for such Prime Rate Interest Determination Date. If fewer than four such
rates appear on the Reuters Screen USPRIME1 Page for such Prime Rate Interest
Determination Date, then the Prime Rate on such Prime Rate Interest
Determination Date shall be the arithmetic mean of the prime rates or base
lending rates quoted on the basis of the actual number of days in the year
divided by a 360-day year as of the close of business on such Prime Rate
Interest Determination Date by four major money center banks (which may include
affiliates of the Agents) in The City of New York selected by the Calculation
Agent. If fewer than four such quotations are so provided, then the Prime Rate
on such Prime Rate Interest Determination Date shall be the arithmetic mean of
four prime rates quoted on the basis of the actual number of days in the year
divided by a 360-day year as of the close of business on such Prime Rate
Interest Determination Date as furnished in The City of New York by the major
money center banks, if any, that have provided such quotations and by a
reasonable number of substitute banks or trust companies (which may include
affiliates of the Agents) to obtain four such prime rate quotations, provided
that such substitute banks or trust companies are organized and doing business
under the laws of the United States, or any State thereof, each having total
equity capital of at least $500 million and being subject to supervision or
examination by Federal or State authority, selected by the Calculation Agent to
provide such rate or rates; provided, however, that, if the banks or trust
companies so selected by the Calculation Agent are not quoting as mentioned in
this sentence, the Prime Rate determined as of such Prime Rate Interest
Determination Date shall be the Prime Rate in effect immediately prior to such
Prime Rate Interest Determination Date.

     "Reuters Screen USPRIME1 Page" means the display on the Reuter Monitor
Money Rates Service (or any successor service) on the "USPRIME1" page (or such
other page as may replace the USPRIME1 page on such service) for the purpose of
displaying prime rates or base lending rates of major United States banks.

     TREASURY RATE.  Unless otherwise specified in the applicable Note Terms
Certificate, "Treasury Rate" means, with respect to any Interest Determination
Date relating to a Floating Rate Note for which the interest rate is determined
by reference to the Treasury Rate (a "Treasury Rate Interest Determination
Date"), the rate from the auction held on such Treasury Rate Interest
Determination Date (the "Auction") of direct obligations of the United States
("Treasury Bills") having the Index Maturity specified in the applicable Note
Terms Certificate, as such rate is published in H.15(519) under the heading
"Treasury Bills-auction average (investment)" or, if not published by 3:00 P.M.,
New York City time, on the related Calculation Date, the auction average rate of
such Treasury Bills (expressed as a bond equivalent on the basis of a year of
365 or 366 days, as applicable, and applied on a daily basis) as otherwise
announced by the United States Department of the Treasury.  If the results of
the Auction of Treasury Bills having the Index Maturity specified in the
applicable Note Terms Certificate are not reported as provided by 3:00 P.M., New
York City time, on the related Calculation Date or if no such Auction is held,
then the Treasury Rate will be calculated by the Calculation Agent as a yield to
maturity (expressed as a bond equivalent on the basis of a year of 365 or 366
days, as applicable, and applied on a daily basis) of the arithmetic mean of the
secondary market bid rates, as of approximately 3:30 P.M., New York City time,
on such Treasury Rate Interest Determination Date, of three leading United
States government securities dealers (which may include the Agents or their
affiliates) selected by the Calculation Agent, for the issue of Treasury Bills
with a remaining maturity closest to the Index Maturity specified in the
applicable Note Terms 

                                       16
<PAGE>
 
Certificate; provided, however, that, if the dealers so selected by the
Calculation Agent are not quoting as mentioned in this sentence, the Treasury
Rate determined as of such Treasury Rate Interest Determination Date will be the
Treasury Rate in effect immediately prior to such Treasury Rate Interest
Determination Date.

OTHER/ADDITIONAL PROVISIONS; ADDENDUM

     Any provisions with respect to the Notes, including the specification and
determination of one or more Interest Rate Bases, the calculation of the
interest rate applicable to a Floating Rate Note, the Interest Payment Dates,
the Stated Maturity Date, any redemption or repayment provisions or any other
term relating thereto, may be modified and/or supplemented as specified under
"Other/Additional Provisions" on the face thereof or in an Addendum relating
thereto, if so specified on the face thereof and described in the applicable
Note Terms Certificate.

DISCOUNT NOTES

     The Company may offer Notes ("Discount Notes") from time to time that have
an Issue Price (as specified in the applicable Note Terms Certificate) that is
less than 100% of the principal amount thereof (i.e., par) by more than a
percentage equal to the product of 0.25% and the number of full years to the
Stated Maturity Date.  Discount Notes may not bear any interest currently or may
bear interest at a rate that is below market rates at the time of issuance.  The
difference between the Issue Price of a Discount Note and par is referred to
herein as the "Discount." In the event of redemption, repayment or acceleration
of maturity of a Discount Note, the amount payable to the Holder of such
Discount Note will be equal to the sum of (i) the Issue Price (increased by any
accruals of Discount) and, in the event of any redemption of such Discount Note
(if applicable), multiplied by the Initial Redemption Percentage (as adjusted by
the Annual Redemption Percentage Reduction, if applicable) and (ii) unpaid
interest, if any, accrued thereon to the date of such redemption, repayment or
acceleration of maturity, as the case may be.

     Unless otherwise specified in the applicable Note Terms Certificate, for
purposes of determining the amount of Discount that has accrued as of any date
on which a redemption, repayment or acceleration of maturity occurs for a
Discount Note, such Discount shall be accrued using a constant yield method.
The constant yield shall be calculated using a 30-day month, 360-day year
convention, a compounding period that, except for the Initial Period (as
hereinafter defined), corresponds to the shortest period between Interest
Payment Dates for the applicable Discount Note (with ratable accruals within a
compounding period), a coupon rate equal to the initial coupon rate applicable
to such Discount Note and an assumption that the maturity of such Discount Note
will not be accelerated.  If, in the case of an interest bearing Discount Note,
the period from the date of issue to the initial Interest Payment Date for a
Discount Note (the "Initial Period") is shorter than the compounding period for
such Discount Note, a proportionate amount of the yield for an entire
compounding period shall be accrued.  If, in such case, the Initial Period is
longer than the compounding period, then such period shall be divided into a
regular compounding period and a short period with the short period being
treated as provided in the preceding sentence.  The accrual of the applicable
Discount may differ from the accrual of original issue discount for purposes of
the Internal Revenue Code of 1986, as amended (the "Code"), certain Discount
Notes may not be treated as having original issue discount within the meaning of
the Code, and Notes other than Discount Notes 

                                       17
<PAGE>
 
may be treated as issued with original issue discount for federal income tax
purposes. See "United States Federal Income Tax Considerations."

INDEXED NOTES

     The Company may from time to time offer Notes ("Indexed Notes") with the
amount of principal, premium or interest payable in respect thereof to be
determined by reference to the price or prices of specified commodities or
stocks or to other items, in each case as specified in the applicable Note Terms
Certificate.  In certain cases, Holders of Indexed Notes may receive a principal
payment on the Maturity Date that is greater than or less than the principal
amount of such Indexed Notes depending upon the relative value on the Maturity
Date of the specified indexed item. Information as to the method for determining
the amount of principal, premium, if any, or interest, if any, payable in
respect of Indexed Notes, certain historical information with respect to the
specified indexed item and any material tax considerations associated with an
investment in Indexed Notes will be specified in the applicable Note Terms
Certificate.

AMORTIZING NOTES

     The Company may from time to time offer Notes ("Amortizing Notes") with the
amount of principal thereof and interest thereon payable in installments over
the term of such Notes.  Unless otherwise specified in the applicable Note Terms
Certificate, interest on each Amortizing Note will be computed on the basis of a
360-day year of twelve 30-day months.  Payments with respect to Amortizing Notes
will be applied first to interest due and payable thereon and then to the
reduction of the unpaid principal amount thereof.  Further information
concerning additional terms and provisions of Amortizing Notes will be specified
in the applicable Note Terms Certificate, including a table setting forth
repayment information for such Amortizing Notes.

                                       18
<PAGE>
 
                         SECOND SUPPLEMENTAL INDENTURE

                         DATED AS OF DECEMBER 12, 1996

                                     AMONG

                             HALLIBURTON COMPANY,

                             HALLIBURTON HOLD CO.

                                      and

                   TEXAS COMMERCE BANK NATIONAL ASSOCIATION

                                  as Trustee



(Second Senior Indenture)
<PAGE>
 
     This Second Supplemental Indenture dated as of December 12, 1996 is among
Halliburton Company, a Delaware corporation (the "Issuer"), Halliburton Hold
Co., a Delaware corporation ("Holding Company"), and Texas Commerce Bank
National Association, a national banking association, as Trustee, and
supplements, amends and modifies that certain Second Senior Indenture dated as
of  December 1, 1996 between the Issuer and the Trustee (the "Second Senior
Indenture"):

                                   RECITALS:

     The Issuer, the Holding Company and Halliburton Merge Co., a Delaware
corporation and an indirect, wholly owned subsidiary of the Issuer ("Mergeco"),
have executed and delivered an Agreement and Plan of Reorganization dated as of
December 11, 1996 pursuant to which Mergeco will be merged with and into the
Issuer (the "Merger"), which will be the corporation surviving the Merger, and
the outstanding capital stock of the Issuer will be converted into capital stock
of the Holding Company.

     To effect the Reorganization, the Issuer has incorporated the Holding
Company as a new first-tier subsidiary corporation, which in turn has
incorporated Halliburton Delaware, Inc., a Delaware corporation ("Newco"), as a
new second-tier subsidiary, which in turn has incorporated Mergeco as a new
third-tier subsidiary corporation.

     As a result of effectuation of the Merger, the Holding Company will become
a holding company and the Issuer will become an indirect wholly-owned subsidiary
of the Holding Company.

     The Merger will be effected pursuant to Section 251(g) of the General
Corporation Law of the State of Delaware ("DGCL"), which permits effectuation of
such a merger without a vote of stockholders of either constituent corporation.

     Pursuant to the Merger, the corporate name of the Issuer will be changed to
"Halliburton Energy Services, Inc." and, immediately thereafter, the corporate
name of the Holding Company will be changed to "Halliburton Company".

     The Issuer and the Trustee have heretofore executed and delivered the First
Supplemental Indenture dated as of December 5, 1996 to the Second Senior
Indenture, which provides for the designation and issuance of a series of
medium-term notes (the "Notes").

     None of the Notes has yet been issued; the Issuer has issued no
indebtedness pursuant to the Second Senior Indenture and will not do so prior to
the Merger.

     The Holding Company and the Issuer intend that the Holding Company shall
assume the obligations of the Issuer with respect to the Second Senior Indenture
and that the Holding Company will be the Issuer with respect to any indebtedness
thereafter issued under the Second Senior Indenture.
<PAGE>
 
     NOW, THEREFORE, in consideration of the premises, the covenants herein
contained  and other good and valuable consideration, the receipt and
sufficiency of which are hereby acknowledged by the parties hereto, the parties
hereto covenant and agree as follows:

                                   ARTICLE I

     Section 1.1    Definitions.  Capitalized terms used but not defined herein
are defined in the Second Senior Indenture and are used herein with the meanings
ascribed to them therein.
 
     Section 1.2    Second Senior Indenture.  The Holding Company shall,
effective as of the effective time of the Merger under the DGCL (the "Effective
Time"), assume, and shall thereafter timely pay, perform and discharge, each and
every obligation of the Issuer under and with respect to the Second Senior
Indenture, including without limitation those certain covenants contained in
Sections 3.6, 3.7 and 3.8 of the Second Senior Indenture  (the "Special
Covenants").  In this regard, the Special Covenants shall be interpreted, from
and after the Effective Time, (i) to apply to the Holding Company, as the
"Issuer" thereunder, and to the Issuer, as a "Restricted Subsidiary" thereunder,
and (ii) not to apply to the Issuer, as the "Issuer" thereunder. From and after
the Effective Time, the Issuer shall have no obligation to pay, perform or
discharge any indebtedness thereafter issued under the Second Senior Indenture,
all such obligations being solely those of the Holding Company.

                                  ARTICLE II

     Section 2.1    Effectiveness.  Although this Second Supplemental Indenture
may be executed and delivered by the parties hereto prior thereto, the
provisions hereof shall not become effective unless and until the Merger becomes
effective under the DGCL and, under such circumstances, shall become effective
concurrently with the Effective Time of such Merger.  From and after the
Effective Time, the Second Senior Indenture, as hereby supplemented, amended and
modified, shall remain in full force and effect.

     Section 2.2    References.  Each reference in the Second Senior Indenture
or this Second Supplemental Indenture to any article, section, term or provision
of the Second Senior Indenture shall mean and be deemed to refer to such
article, section, term or provision of the Second Senior Indenture, as modified
by this Second Supplemental Indenture, except where the context otherwise
indicates.

     Section 2.3    Benefit.  All the covenants, provisions, stipulations and
agreements contained in this Second Supplemental Indenture are and shall be for
the sole and exclusive benefit of the parties hereto, their successors and
assigns, and of the holders and registered owners from time to time of the
Debentures and any other Securities issued and outstanding from time to time
under the Second Senior Indenture, as hereby amended and supplemented.

     Section 2.4    Counterparts. This Second Supplemental Indenture may be
executed in any number of counterparts, each of which shall be deemed an
original and all of which taken together shall be deemed to be a single
instrument.
<PAGE>
 
     Section 2.5    Governing Law.  This Second Supplemental Indenture shall be
deemed to be a contract under the laws of the State of New York, and for all
purposes shall be construed in accordance with the laws of such state without
regard to principles of conflicts of laws, except as may otherwise required by
mandatory provisions of law.

     Section 2.6    Headings.  The Article and Section headings herein are for
convenience only and shall not affect the construction hereof.

     IN WITNESS WHEREOF, the said Halliburton Company, Halliburton Hold Co. and
Texas Commerce Bank National Association have each caused this Second
Supplemental Indenture to be executed in its corporate name by the officer whose
name is subscribed below, thereunto duly authorized, and its corporate seal to
be hereunto affixed and, in the cases of Halliburton Company and Halliburton
Hold Co., attested by its Secretary or Assistant Secretary, all as of the day
and year first above written.

                                       HALLIBURTON COMPANY


                                       By  /s/ Lester L. Coleman
Attest:                                Name:  Lester L. Coleman
                                       Title: Executive Vice President

By  /s/ Susan S. Keith
Name:  Susan S. Keith
Title: Vice President and 
        Secretary

                                       HALLIBURTON HOLD CO.


                                       By  /s/ Robert M. Kennedy
Attest:                                Name:  Robert M. Kennedy
                                       Title: Vice President

By  /s/ Susan S. Keith
Name:  Susan S. Keith
Title: Secretary

                                       TEXAS COMMERCE BANK
                                            NATIONAL ASSOCIATION


                                       By  /s/ Terry L. Stewart
                                       Name:  Terry L. Stewart
                                       Title: Assistant Vice President


<PAGE>
 
                                                                     EXHIBIT 4.3

                         FIRST SUPPLEMENTAL INDENTURE

                         DATED AS OF DECEMBER 12, 1996

                                 BETWEEN AMONG

                             HALLIBURTON COMPANY,

                             HALLIBURTON HOLD CO.

                                      and

                   TEXAS COMMERCE BANK NATIONAL ASSOCIATION

                                  as Trustee



(Subordinated Indenture)
<PAGE>
 
     This First Supplemental Indenture dated as of December 12, 1996 is among
Halliburton Company, a Delaware corporation (the "Issuer"), Halliburton Hold
Co., a Delaware corporation ("Holding Company"), and Texas Commerce Bank
National Association, a national banking association, as Trustee, and
supplements, amends and modifies that certain Subordinated Indenture dated as of
January 2, 1991 between the Issuer and the Trustee (the "Subordinated
Indenture"):

                                   RECITALS:

     The Issuer, the Holding Company and Halliburton Merge Co., a Delaware
corporation and an indirect, wholly owned subsidiary of the Issuer ("Mergeco"),
have executed and delivered an Agreement and Plan of Reorganization dated as of
December 11, 1996 pursuant to which Mergeco will be merged with and into the
Issuer (the "Merger"), which will be the corporation surviving the Merger, and
the outstanding capital stock of the Issuer will be converted into capital stock
of the Holding Company.

     To effect the Reorganization, the Issuer has incorporated the Holding
Company as a new first-tier subsidiary corporation, which in turn has
incorporated Halliburton Delaware, Inc., a Delaware corporation ("Newco"), as a
new second-tier subsidiary, which in turn has incorporated Mergeco as a new
third-tier subsidiary corporation.

     As a result of effectuation of the Merger, the Holding Company will become
a holding company and the Issuer will become an indirect wholly-owned subsidiary
of the Holding Company.

     The Merger will be effected pursuant to Section 251(g) of the General
Corporation Law of the State of Delaware ("DGCL"), which permits effectuation of
such a merger without a vote of stockholders of either constituent corporation.

     Pursuant to the Merger, the corporate name of the Issuer will be changed to
"Halliburton Energy Services, Inc." and, immediately thereafter, the corporate
name of the Holding Company will be changed to "Halliburton Company".

     No indebtedness of the Issuer is outstanding under the Subordinated
Indenture.

     The Holding Company and the Issuer intend that the Holding Company shall
assume the obligations of the Issuer with respect to the Subordinated Indenture
and that the Holding Company will be the Issuer with respect to any indebtedness
thereafter issued under the Subordinated Indenture.

     NOW, THEREFORE, in consideration of the premises, the covenants herein
contained  and other good and valuable consideration, the receipt and
sufficiency of which are hereby acknowledged by the parties hereto, the parties
hereto covenant and agree as follows:
<PAGE>
 
                                   ARTICLE I

     Section 1.1    Definitions.  Capitalized terms used but not defined herein
are defined in the Subordinated Indenture and are used herein with the meanings
ascribed to them therein.
 
     Section 1.2    Subordinated Indenture. The Holding Company shall, effective
as of the effective time of the Merger under the DGCL (the "Effective Time"),
assume, and shall thereafter timely pay, perform and discharge, each and every
obligation of the Issuer under and with respect to the Subordinated Indenture.
From and after the Effective Time, the Issuer shall have no obligation to pay,
perform or discharge any indebtedness thereafter issued under the Subordinated
Indenture, all such obligations being solely those of the Holding Company.

                                   ARTICLE II

     Section 2.1    Effectiveness.  Although this First Supplemental Indenture
may be executed and delivered by the parties hereto prior thereto, the
provisions hereof shall not become effective unless and until the Merger becomes
effective under the DGCL and, under such circumstances, shall become effective
concurrently with the Effective Time of such Merger.  From and after the
Effective Time, the Subordinated Indenture, as hereby supplemented, amended and
modified, shall remain in full force and effect.

     Section 2.2    References.  Each reference in the Subordinated Indenture or
this First Supplemental Indenture to any article, section, term or provision of
the Subordinated Indenture shall mean and be deemed to refer to such article,
section, term or provision of the Subordinated Indenture, as modified by this
First Supplemental Indenture, except where the context otherwise indicates.

     Section 2.3    Benefit. All the covenants, provisions, stipulations and
agreements contained in this First Supplemental Indenture are and shall be for
the sole and exclusive benefit of the parties hereto, their successors and
assigns, and of the holders and registered owners from time to time of the
Debentures and any other Securities issued and outstanding from time to time
under the Subordinated Indenture, as hereby amended and supplemented.

     Section 2.4    Counterparts. This First Supplemental Indenture may be
executed in any number of counterparts, each of which shall be deemed an
original and all of which taken together shall be deemed to be a single
instrument.

     Section 2.5    Governing Law.  This First Supplemental Indenture shall be
deemed to be a contract under the laws of the State of New York, and for all
purposes shall be construed in accordance with the laws of such state without
regard to principles of conflicts of laws, except as may otherwise required by
mandatory provisions of law.

     Section 2.6    Headings.  The Article and Section headings herein are for
convenience only and shall not affect the construction hereof.
<PAGE>
 
     IN WITNESS WHEREOF, the said Halliburton Company, Halliburton Hold Co. and
Texas Commerce Bank National Association have each caused this First
Supplemental Indenture to be executed in its corporate name by the officer whose
name is subscribed below, thereunto duly authorized, and its corporate seal to
be hereunto affixed and, in the cases of Halliburton Company and Halliburton
Hold Co.,  attested by its Secretary or Assistant Secretary, all as of the day
and year first above written.

                                    HALLIBURTON COMPANY


                                    By /s/ Lester L. Coleman  
                                       _____________________________
Attest:                             
                                    Name:  Lester L. Coleman

                                    Title:  Executive Vice President

By /s/ Susan S. Keith
  __________________________________

Name: Susan S. Keith

Title:  Vice President and Secretary


                                    HALLIBURTON HOLD CO.


                                    By  /s/ Robert M. Kennedy
                                      _________________________
Attest:                             
                                    Name:  Robert M. Kennedy

                                    Title:  Vice President

By  /s/ Susan S. Keith
  __________________________

Name:  Susan S. Keith

Title:  Secretary

                                    TEXAS COMMERCE BANK
                                         NATIONAL ASSOCIATION


                                    By  /s/ Terry L. Stewart
                                      ______________________________

                                    Name: Terry L. Stewart 

                                    Title:  Assistant Vice President



<PAGE>
 
                                                                     EXHIBIT 4.4

- --------------------------------------------------------------------------------

                              HALLIBURTON COMPANY

                                      and

                   CHASEMELLON SHAREHOLDER SERVICES, L.L.C.

                                 Rights Agent



                                   RESTATED*
                               RIGHTS AGREEMENT


                         Dated as of December 1, 1996

*  This Rights Agreement has been restated without amendment to reflect a change
of corporate name.

- --------------------------------------------------------------------------------
<PAGE>
 
                               TABLE OF CONTENTS


<TABLE>
<CAPTION>
                                                                                         Page
                                                                                         ----
<S>                                                                                      <C>
Exhibit.................................................................................  ii

Section 1.     Certain Definitions......................................................   1
               -------------------

Section 2.     Appointment of Rights Agent..............................................   7
               ---------------------------

Section 3.     Issue of Right Certificates..............................................   7
               ---------------------------

Section 4.     Form of Right Certificates...............................................   9
               --------------------------

Section 5.     Execution, Authentication and Delivery...................................  10
               --------------------------------------

Section 6.     Registration, Registration of Transfer and Exchange......................  11
               ---------------------------------------------------

Section 7.     Mutilated, Destroyed, Lost and Stolen Right Certificates.................  12
               --------------------------------------------------------

Section 8.     Exercise of Rights; Purchase Price; Expiration Date of Rights............  12
               -------------------------------------------------------------

Section 9.     Cancellation and Destruction of Right Certificates.......................  13
               --------------------------------------------------

Section 10.    Reservation and Availability of Shares...................................  13
               --------------------------------------

Section 11.    Record Date..............................................................  14
               -----------

Section 12.    Adjustment of Purchase Price, Number of Shares or Number of Rights.......  15
               ------------------------------------------------------------------

Section 13.    Certificate of Adjusted Purchase Price or Number of Shares...............  20
               ----------------------------------------------------------

Section 14.    Consolidation, Merger or Sale or Transfer of Assets or Earning Power.....  21
               --------------------------------------------------------------------

Section 15.    Fractional Rights and Fractional Shares..................................  23
               ---------------------------------------

Section 16.    Rights of Action.........................................................  24
               ----------------

Section 17.    Agreement of Right Holders...............................................  24
               --------------------------

Section 18.    Right Certificate Holder Not Deemed a Stockholder........................  25
               -------------------------------------------------
</TABLE>

                                      -i-
<PAGE>
 
<TABLE>
<S>                                                                                      <C>
Section 19.    Concerning the Rights Agent..............................................  25
               ---------------------------

Section 20.    Duties of Rights Agent...................................................  25
               ----------------------

Section 21.    Merger or Consolidation or Change of Name of Rights Agent................  27
               ---------------------------------------------------------

Section 22.    Change of Rights Agent...................................................  28
               ----------------------

Section 23.    Issuance of New Right Certificates.......................................  28
               ----------------------------------

Section 24.    Redemption...............................................................  28
               ----------

Section 25.    Mandatory Redemption and Exchange........................................  29
               ---------------------------------

Section 26.    Notice of Certain Events.................................................  30
               ------------------------

Section 27.    Securities Laws Registrations............................................  31
               -----------------------------

Section 28.    Notices..................................................................  32
               -------

Section 29.    Supplements and Amendments...............................................  32
               --------------------------

Section 30.    Successors...............................................................  33
               ----------

Section 31.    Benefits of this Agreement...............................................  33
               --------------------------

Section 32.    Severability.............................................................  33
               ------------

Section 33.    Governing Law............................................................  33
               -------------

Section 34.    Counterparts.............................................................  33
               ------------

Section 35.    Descriptive Headings.....................................................  33
               --------------------

Section 36.    Effective Date...........................................................  33
               --------------
</TABLE>
 
- ---------------------

Exhibit A --  Form of Right Certificate

Exhibit B --   Certificate of Designation, Rights and Preferences of Series A
               Junior Participating Preferred Stock

                                     -ii-
<PAGE>
 
     This Restated/1/ Rights Agreement, dated as of December 1, 1995, is between
Halliburton Company, a Delaware corporation (the "Company"), and ChaseMellon
Shareholder Services, L.L.C., a New Jersey limited liability company, as Rights
Agent.


                                   RECITALS:

     The Company (formerly Halliburton Hold Co., a Delaware corporation) is a
holding company organized to succeed by reorganization ("Reorganization") to
Halliburton Company (now Halliburton Energy Services, Inc, a Delaware
corporation and a wholly owned subsidiary of the Company and herein called the
"Predecessor Company").

     The name of the Company was changed in connection with the Reorganization
from Halliburton Hold Co. to Halliburton Company.

     The Reorganization included the merger (the "Merger") of the Predecessor
Company with one of its indirect,  wholly owned subsidiaries under Section
251(g) of the Delaware General Corporation Law (the "DGCL").

     The Predecessor Company was a party to a Second Amended and Restated Rights
Agreement dated December 15, 1995 with the Rights Agent (the "Predecessor Rights
Agreement") pursuant to which rights to purchase preferred stock were
outstanding on the basis of one right for each share of outstanding common stock
of the Predecessor Company.

     Section 251(g) of the DGCL requires that the holding company resulting from
the Reorganization contemplated thereby shall have the same authorized and
outstanding capitalization as its predecessor.

     The certificate of incorporation of the Company is such that, upon
completion of the Reorganization, the authorized, issued and outstanding capital
stock of the Company, including its preferred stock and common stock,
immediately following the Merger would be identical to that of the Predecessor
Company immediately prior to the Merger.

     Accordingly, to conform the Company's capitalization to that of the
Predecessor Company as it related to the Predecessor Rights Agreement, the Board
of Directors of the Company has authorized and declared a dividend distribution
of one right (a "Right") for each share of Common Stock, par value $2.50, of the
Company ("Common Stock") outstanding at the Close of Business on the Effective
Date (as such terms are hereinafter defined) and has authorized the issuance of
one Right with respect to each share of Common Stock that shall hereafter be
issued out of authorized but unissued Common Stock or out of treasury between
the Effective Date and the earlier of the Distribution Date or the Expiration
Date (as such terms are hereinafter defined) or the date, if any, on which such
Rights are redeemed, each Right representing the right to purchase one

- -----------------

     /1/  This Rights Agreement has been restated without amendment to reflect
the change of corporate name of the Company from Halliburton Hold Co. to
Halliburton Company.
<PAGE>
 
one-hundredth of a share of Series A Junior Participating Preferred Stock of the
Company, having the rights and preferences set forth in the form of Certificate
of Designation, Rights and Preferences of Series A Junior Participating
Preferred Stock attached hereto as Exhibit B, upon the terms and subject to the
conditions hereinafter set forth.

     The Board of Directors of the Company has directed that the terms and
conditions under which the Rights are to be distributed, including without
limitation those affecting the exercise thereof, the securities or other
property to be acquired thereby and the purchase price to be paid therefor,
shall be set forth in a written agreement between the Company and a rights agent
made for the benefit of the holders of the Rights to the extent so provided
therein.
 
     NOW, THEREFORE, in consideration of the premises and the mutual agreements
herein set forth, the parties hereto agree as follows:

     Section 1.    Certain Definitions.  For purposes of this Agreement, the
                   -------------------                                      
following terms shall have the meanings indicated:

          "Acquiring Person" shall mean any Person who or which, together with
     all Affiliates and Associates of such Person, shall be the Beneficial Owner
     of 15% or more of the Voting Shares of the Company then outstanding, but
     shall not include the Company, any Subsidiary of the Company, any employee
     benefit plan of the Company or any Subsidiary of the Company or any entity
     holding Voting Shares for or pursuant to any such plan.  Notwithstanding
     the foregoing, no Person shall become an "Acquiring Person" as the result
     of an acquisition of Voting Shares by the Company which, by reducing the
     number of shares outstanding, increases the proportionate number of shares
     beneficially owned by such Person to 15% or more of the Voting Shares of
     the Company then outstanding; provided, however, that, if a Person shall
     become the Beneficial Owner of 15% or more of the Voting Shares of the
     Company then outstanding by reason of share purchases by the Company and
     shall, after such share purchases by the Company and at a time when such
     Person is the Beneficial Owner of 15% or more of the Voting Shares of the
     Company then outstanding, become the Beneficial Owner of any additional
     Voting Shares of the Company, then such Person shall be deemed to be an
     "Acquiring Person".  Notwithstanding the foregoing, any Person who has
     reported or is required to report such ownership (but who is the Beneficial
     Owner of less than 20% of the outstanding Common Shares of the Company) on
     Schedule 13G under the Exchange Act (or any comparable or successor
     reporting form) or on Schedule 13D under the Exchange Act (or any
     comparable or successor reporting form) which Schedule 13D does not state
     any intention or reserve the right to control or influence the management
     or policies of the Company or engage in any of the actions specified in
     Item 4 of such Schedule (other than the disposition of the Common Shares)
     and, within ten Business Days of being requested by the Company to advise
     it regarding the same, certifies to the Company that such Person acquired
     Common Shares in excess of 14.9% of the outstanding Common Shares of the
     Company inadvertently or without knowledge of the terms of the Rights and
     who, together with all such Person's Affiliates and Associates, thereafter
     does not acquire additional 

                                      -2-
<PAGE>
 
     Common Shares while being the Beneficial Owner of 15% or more of the
     outstanding Common Shares of the Company shall not be deemed to be an
     "Acquiring Person"; provided, however, that, if the Person requested so to
     certify fails to do so within ten Business Days, then such Person shall
     become an Acquiring Person immediately after such ten day period.

          "Agreement" shall mean this Restated Rights Agreement as hereafter
     amended from time to time.

          "Affiliate" and "Associate" shall have the respective meanings
     ascribed to such terms in Rule 12b-2 of the General Rules and Regulations
     under the Exchange Act as in effect on the date of this Agreement.

          A Person shall be deemed the "Beneficial Owner" of and shall be deemed
     to "own beneficially" any securities which (without duplication):

          (i)    such Person or any of such Person's Affiliates or Associates
     beneficially owns, directly or indirectly, within the meaning of either
     Section 13 or 16 of the Exchange Act;

          (ii)   such Person or any of such Person's Affiliates or Associates
     has (A) the right to acquire (whether such right is exercisable immediately
     or only after the passage of time) pursuant to any agreement, arrangement
     or understanding (other than customary agreements with and between
     underwriters and selling group members with respect to a bona fide public
     offering of securities), or upon the exercise of conversion rights,
     exchange rights, rights (other than these Rights), warrants or options, or
     otherwise; or (B) the right to vote pursuant to any agreement, arrangement
     or understanding; or

          (iii)  are beneficially owned, directly or indirectly, by any other
     Person with which such Person or any of such Person's Affiliates or
     Associates has any agreement, arrangement or understanding (other than
     customary agreements with and between underwriters and selling group
     members with respect to a bona fide public offering of securities) for the
     purpose of acquiring, holding, voting or disposing of any securities of the
     Company; provided, however, that, for purposes of each clause of this
     definition, a Person shall not be deemed the Beneficial Owner of, or to own
     beneficially, securities tendered pursuant to a tender or exchange offer
     made by or on behalf of such Person or any of such Person's Affiliates or
     Associates until such tendered securities are accepted for purchase or
     exchange; and provided, further, that, for purposes of each clause of this
     definition, a Person shall not be deemed the Beneficial Owner of, or to own
     beneficially, any security as a result of any agreement, arrangement or
     understanding to vote such security if such agreement, arrangement, or
     understanding (1) arises solely from a revocable proxy or consent given to
     such Person in response to a public proxy or consent solicitation made
     pursuant to, and in accordance with, the applicable rules and regulations
     promulgated under the Exchange Act and (2) is not also then reportable on
     Schedule 13D under the Exchange Act (or any comparable or successor
     report).

                                      -3-
<PAGE>
 
          Notwithstanding anything in this definition to the contrary, the
     phrase "then outstanding", when used with reference to a Person's
     Beneficial Ownership of securities of the Company (or to the number of such
     securities "beneficially owned"), shall mean the number of such securities
     then issued and outstanding together with the number of such securities not
     then actually issued and outstanding which such Person would be deemed to
     own beneficially hereunder.

          "Business Day" shall mean any day other than a Saturday, Sunday or a
     day on which banking institutions in the State of Texas are authorized or
     obligated by law or executive order to close.

          "Close of Business" on any given date shall mean 5:00 P.M., Dallas
     time, on such date; provided, however, that, if such date is not a Business
     Day it shall mean 5:00 P.M., Dallas time, on the next succeeding Business
     Day.

          "Closing Price", with respect to any security, shall mean the last
     sale price, regular way, on a specific Trading Day or, in case no such sale
     takes place on such Trading Day, the average of the closing bid and asked
     prices, regular way, in either case as reported in the principal
     consolidated transaction reporting system with respect to securities listed
     or admitted to trading on the New York Stock Exchange or, if such security
     is not then listed or admitted to trading on the New York Stock Exchange,
     as reported in the principal consolidated transaction reporting system with
     respect to securities listed on the principal national securities exchange
     on which the such security is listed or admitted to trading or, if such
     security is not then listed or admitted to trading on any national
     securities exchange, the last quoted price or, if not so quoted, the
     average of the high bid and low asked prices in the  over-the-counter
     market, as reported by the National Association of Securities Dealers, Inc.
     Automated Quotations System or such other system then in use, or, if on any
     such Trading Day such security is not quoted by any such organization, the
     average of the closing bid and asked prices as furnished by a professional
     market maker making a market in such security selected by the Board of
     Directors of the Company.  If such security is not publicly held or so
     listed or traded, "Closing Price" shall mean the fair value per unit of
     such security as determined in good faith by the Board of Directors of the
     Company, whose determination shall be described and the Closing Price set
     forth in a statement filed with the Rights Agent.

          "Common Shares" when used with reference to the Company shall mean
     shares of capital stock of the Company which have no preference over any
     other class of stock with respect to dividends or assets, which are not
     redeemable at the option of the Company and with respect to which no
     sinking, purchase or similar fund is provided and shall initially mean the
     shares of Common Stock, par value $2.50, of the Company.  "Common Shares"
     when used with reference to any Person other than the Company shall, if
     used with reference to a corporation, mean the capital stock (or equity
     interest) with the greatest voting power of such other Person or, if such
     other Person is a Subsidiary of another Person, the Person or Persons which
     ultimately control such first-mentioned Person and, if used with reference
     to  any other 

                                      -4-
<PAGE>
 
     Person, mean the equity interest in such Person (or, if the net worth
     determined in accordance with generally accepted accounting principles of
     another Person which controls such first-mentioned Person is greater than
     such first-mentioned Person, then such other Person) with the greatest
     voting power or managerial power with respect to the business and affairs
     of such Person.

          "Common Stock" shall have the meaning ascribed to such term in the
     Recitals to this Agreement.

          "Company" shall mean Halliburton Company, a Delaware corporation, and
     its successors.

          "Company Order" means a written request or order signed in the name of
     the Company by its Chairman of the Board, its President or a Vice
     President, and by its Treasurer, an Assistant Treasurer, its Secretary or
     an Assistant Secretary, and delivered to the Rights Agent.

          "Corporate Trust Office" means the principal office of the Rights
     Agent at which it administers its corporate trust business, which, in the
     case of ChaseMellon Shareholders Services, L.L.C., shall, until hereafter
     changed, be its office at 2323 Bryan Street, Suite 2300, Dallas, Texas
     75201.

          "DGCL" shall have the meaning ascribed to such term in the Recitals to
     this Agreement.

          "Distribution Date" shall mean the earlier of (i) the tenth Business
     Day after the Shares Acquisition Date or (ii) the tenth Business Day (or
     such later date as may be determined by action of the Board of Directors
     prior to such time as any Person becomes an Acquiring Person) after the
     date of commencement by any Person (other than the Company, any Subsidiary
     of the Company, any employee benefit plan of the Company or any Subsidiary
     of the Company, or any entity holding Voting Shares for or pursuant to the
     terms of any such plan) of, or after the date of the first public
     announcement of the intention of any Person (other than the Company, any
     Subsidiary of the Company, any employee benefit plan of the Company or any
     Subsidiary of the Company, or any entity holding Voting Shares for or
     pursuant to the terms of any such plan) to commence, a tender or exchange
     offer the consummation of which would result in any Person becoming the
     Beneficial Owner of 15% or more of the then outstanding Voting Shares of
     the Company; provided, however, that an occurrence described in clause (ii)
     of this definition above shall not cause the occurrence of the Distribution
     Date if the Board of Directors of the Company shall, prior to such tenth
     Business Day (or such later date as described in clause (ii) above),
     determine that such tender or exchange offer is spurious, unless,
     thereafter, the Board of Directors of the Company shall make a contrary
     determination, in which event the Distribution Date shall occur on the
     later 

                                      -5-
<PAGE>
 
     to occur of such tenth Business Day (or such later date as described in
     clause (ii) above) and the date of such latter determination.

          "Effective Date" shall mean December 11, 1996.

          "Exchange Act" shall mean the Securities Exchange Act of 1934, as
     amended, and any successor statute thereto.

          "Final Expiration Date" shall mean the Close of Business on December
     15, 2005.

          "Merger" shall have the meaning ascribed to such term in the Recitals
     to this Agreement.

          "Reorganization" shall have the meaning ascribed to such term in the
     Recitals to this Agreement.

          "Person" shall mean any individual, firm, corporation, partnership,
     limited partnership, trust or other entity, and shall include any successor
     (by merger or otherwise ) of such entity.

          "Predecessor Company" shall have the meaning ascribed to such term in
     the Recitals to this Agreement.

          "Preferred Shares" shall mean shares of the Company's currently
     authorized Series A Junior Participating Preferred Stock, without par
     value.

          "Principal Party" shall have the meaning ascribed to such term in
     Section 14(b).

          "Purchase Price" shall mean the price at which the holder of a Right
     may, subject to the terms and conditions of this Agreement, purchase one
     one-hundredth (1/100) of a Preferred Share (which, initially, is as set
     forth in Section 8(b) hereof), as such price shall be adjusted pursuant to
     the terms of this Agreement.

          "Redemption Date" shall mean the time at which the Rights are redeemed
     pursuant to Section 24 herein or the time at which all of the Rights are
     mandatorily redeemed and exchanged pursuant to Section 25 hereof.

          "Redemption Price" shall have the meaning specified in Section 24(b)
     herein.

          "Right" shall mean one preferred share purchase right which initially
     represents the right of the registered holder thereof to purchase one one-
     hundredth (1/100) of a Preferred Share upon the terms and subject to the
     conditions herein set forth.

                                      -6-
<PAGE>
 
          "Right Certificate" shall mean a certificate, in substantially the
     form of Exhibit A attached to this Rights Agreement, evidencing the Rights
     registered in the name of the holder thereof.

          "Rights Agent" shall mean ChaseMellon Shareholder Services, L.L.C., a
     New Jersey limited liability company, and any successor thereto appointed
     in accordance with the terms hereof, in its capacity as agent for the
     Company and the holders of the Rights pursuant to this Agreement.

          "Rights Register" and "Rights Registrar" shall have the meanings
     specified in Section 6.

          "Shares Acquisition Date" shall mean the first date of public
     announcement (which for purposes of this definition shall include without
     limitation a report filed pursuant to Section 13(d) or Section 16(a) of the
     Exchange Act) by the Company or an Acquiring Person that an Acquiring
     Person has become such.

          "Subsidiary" of any Person shall mean any corporation or other entity
     of which a majority of the outstanding capital stock or other equity
     interests having ordinary voting power in the election of directors or
     similar officials is owned, directly or indirectly, by such Person.

          "Trading Day" shall mean a day on which the principal national
     securities exchange on which any of the Voting Shares of the Company are
     listed or admitted to trading is open for the transaction of business or,
     if none of the Voting Shares of the Company is listed or admitted to
     trading on any national stock exchange, a Business Day.

          "Voting Shares" shall mean (i) the Common Shares of the Company and
     (ii) any other shares of capital stock of the Company entitled to vote
     generally in the election of directors or entitled to vote together with
     the Common Shares in respect of any merger or consolidation of the Company,
     any sale of all or substantially all of the Company's assets or any
     liquidation, dissolution or winding up of the Company.  Whenever any
     provision of this Agreement requires a determination of whether a number of
     Voting Shares comprising a specified percentage of such Voting Shares is,
     was or will be beneficially owned or has been voted, tendered, acquired,
     sold or otherwise disposed of or a determination of whether a Person has
     offered or proposed to acquire a number of Voting Shares comprising such
     specified percentage, the number of Voting Shares comprising such specified
     percentage of Voting Shares shall, subject to its provisions of the
     definition in this Section 1(a) of "Beneficial Owner", in every such case
     be deemed to be the number of Voting Shares comprising the specified
     percentage of all the Company's then outstanding Voting Shares.

          "Wholly-Owned Subsidiary" of a Person shall mean any corporation or
     other entity all the outstanding capital stock or other equity interests of
     which having ordinary voting 

                                      -7-
<PAGE>
 
     power in the election of directors or similar officials (other than
     directors' qualifying shares or similar interest) are owned, directly or
     indirectly, by such Person.

      Section 2.    Appointment of Rights Agent.  The Company hereby appoints
                    ---------------------------                              
the Rights Agent to act as agent for the Company and the holders of the Rights
(who, in accordance with Section 3 hereof, shall prior to the Distribution Date
also be the holders of the Common Shares of the Company) in accordance with the
terms and conditions hereof, and the Rights Agent hereby accepts such
appointment. The Company may from time to time appoint such co-Rights Agents as
it may deem necessary or desirable.

      Section 3.    Issue of Right Certificates.   From and after the date of
                    ---------------------------                              
this Agreement until the Distribution Date, (i) outstanding Rights will be
evidenced (subject to the provisions of paragraph (b) of this Section 3) by the
certificates for outstanding Common Shares of the Company and not by separate
Right Certificates, and (ii) the right to receive Right Certificates will be
transferable only in connection with the transfer of Common Shares of the
Company.  As soon as practicable after the Distribution Date, the Rights Agent
will send, by first-class, insured, postage-prepaid mail, to each record holder
of Common Shares of the Company as of the Close of Business on the Distribution
Date, at the address of such holder shown on the stock transfer records of the
Company, a Right Certificate evidencing one Right for each Common Share so held.
From and after the Distribution Date, the Rights will be evidenced solely by
such Right Certificates.

     (b)  With respect to Common Shares of the Company outstanding on the date
of this Agreement, the certificates evidencing such Common Shares shall
thereafter also evidence the outstanding Rights (as such Rights have been or
shall be amended and supplemented) previously distributed with respect thereto
until the earlier of the Distribution Date or the date of surrender thereof to
the Company's transfer agent for registration or transfer of such Common Shares.
Moreover, Common Shares of the Company issued pursuant to the Merger will
continue to be evidenced, as permitted by the provisions of Section 251(g) of
the DGCL, by the certificates that formerly evidenced the common stock of the
Predecessor Company. Until the Distribution Date (or, if earlier, the Redemption
Date or Final Expiration Date), the surrender for registration of transfer or
exchange of any certificate for Common Shares of the Company outstanding as of
the Close of Business on the date of this Agreement or issued pursuant to the
Merger shall also constitute the surrender for registration of transfer or
exchange of the outstanding Rights associated with the Common Shares represented
thereby.

     (c)  The Company agrees that, at any time after the date of this Agreement
and prior to the Distribution Date at which it issues any of its Common Shares
upon original issue or out of treasury, it will concurrently distribute to the
holder of such Common Shares one Right for each such Common Share, which Right
shall be subject to the terms and provisions of this Agreement and will evidence
the right to purchase the same number of one one-hundredths of a Preferred Share
at the same Purchase Price as the Rights then outstanding.

                                      -8-
<PAGE>
 
     (d)  Certificates for Common Shares of the Company issued after the date of
this Rights Agreement (other than pursuant to the Merger) but prior to the
earliest of the Distribution Date, the Redemption Date and the Final Expiration
Date, whether upon registration of transfer or exchange of such Common Shares
outstanding on the date of this Agreement (or issued pursuant to the Merger) or
upon original issue or out of treasury thereafter, shall have impressed on,
printed on, written on or otherwise affixed to them the following legend:

          This certificate also evidences and entitles the holder hereof to
     certain Rights as set forth in a Restated Rights Agreement between
     Halliburton Company and a Rights Agent dated as of December 1, 1996 (the
     "Rights Agreement"), the terms of which are hereby incorporated herein by
     reference and a copy of which is on file at the principal executive offices
     of Halliburton Company. Under certain circumstances as set forth in the
     Rights Agreement, such Rights will be evidenced by separate certificates
     and will no longer be evidenced by this certificate. Halliburton Company
     will mail to the holder of this certificate a copy of the Rights Agreement
     without charge after receipt of a written request therefor. As described in
     the Rights Agreement, Rights issued to or acquired by any Acquiring Person
     (as defined in the Rights Agreement) shall, under certain circumstances,
     become null and void.

With respect to certificates evidencing  Common Shares of the Company
outstanding on the date of this Agreement, issued pursuant to the Merger or
issued with the foregoing legend, until the Distribution Date, outstanding
Rights associated with the Common Shares of the Company represented by such
certificates shall be evidenced by such certificates alone, and the surrender of
any such certificate for registration of transfer or exchange of the Common
Shares evidenced thereby shall also constitute surrender for registration of
transfer or exchange of outstanding Rights (as such Rights have been or shall be
amended and supplemented) associated with the Common Shares represented thereby.

     (e)  If the Company purchases or acquires any of its Common Shares after
the date hereof but prior to the Distribution Date, any Rights associated with
such Common Shares shall be deemed canceled and retired so that the Company
shall not be entitled to exercise any Rights associated with the Common Shares
which are no longer outstanding.

     Section 4.    Form of Right Certificates.  The form of Right Certificates
                   --------------------------                                 
(and the forms of election to purchase Preferred Shares (or other securities)
and of assignment to be printed on the reverse thereof) shall in form and
substance be substantially the same as Exhibit A hereto and may have such marks
of identification or designation and such legends, summaries or endorsements
printed thereon as the Company may deem appropriate and as are not inconsistent
with the provisions of this Agreement, as may be required to comply with any
applicable law or with any rule or regulation made pursuant thereto or with any
rule or regulation of any stock exchange on which the Rights may from time to
time be listed or as may be necessary to conform to usage.  Subject to the
provisions of Section 23 hereof, the Right Certificates, whenever issued, shall
be dated as of the date 

                                      -9-
<PAGE>
 
of authentication thereof, but, regardless of any adjustments of the Purchase
Price or the number of Preferred Shares (or other securities) as to which a
Right is exercisable (whether pursuant to this Agreement or any future
amendments or supplements to this Agreement), or both, occurring after the
Effective Date and prior to the date of such authentication, such Right
Certificates may, on their face, without invalidating or otherwise affecting any
such adjustment, expressly entitle the holders thereof to purchase such number
of Preferred Shares at the Purchase Price per one one-hundredth (1/100) of a
Preferred Share as to which a Right would be exercisable if the Distribution
Date were the date of this Agreement; no adjustment of the Purchase Price or the
number of Preferred Shares (or other securities) as to which a Right is
exercisable, or both, effected subsequent to the date of authentication of any
Right Certificate shall be invalidated or otherwise affected by the fact that
such adjustment is not expressly reflected on the face or in the provisions of
such Right Certificate.

     Pending the preparation of definitive Right Certificates, the Company may
execute, and upon Company Order the Rights Agent shall authenticate and send, by
first-class, insured, postage-prepaid mail, to each record holder of Common
Shares of the Company as of the Close of Business on the Distribution Date,
temporary Right Certificates which are printed, lithographed, typewritten,
mimeographed or otherwise produced substantially of the tenor of the definitive
Right Certificates in lieu of which they are issued and with such appropriate
insertions, omissions, substitutions and other variations as the officers
executing such Right Certificates may determine, as evidenced by their execution
of such Right Certificates.

     If temporary Right Certificates are issued, the Company will cause
definitive Right Certificates to be prepared without unreasonable delay.  After
the preparation of definitive Right Certificates, the temporary Right
Certificates shall be exchangeable for definitive Right Certificates, upon
surrender of the temporary Right Certificates at the Corporate Trust Office of
the Rights Agent, without charge to the holder.  Upon surrender for cancellation
of any one or more temporary Right Certificates, the Company shall execute and
the Rights Agent shall authenticate and deliver in exchange therefor one or more
definitive Right Certificates, evidencing a like number of Rights.  Until so
exchanged, the temporary Right Certificates shall in all respects be entitled to
the same benefits under this Agreement as definitive Right Certificates.

     Section 5.    Execution, Authentication and Delivery.  The Right
                   --------------------------------------            
Certificates shall be executed on behalf of the Company by its Chairman of the
Board, its President or one of its Vice Presidents, under its corporate seal
reproduced thereon attested by its Secretary or one of its Assistant
Secretaries.  The signature of any of these officers on the Right Certificates
may be manual or facsimile.

     Right Certificates bearing the manual or facsimile signatures of
individuals who were at any time the proper officers of the Company shall bind
the Company, notwithstanding that such individuals or any of them have ceased to
hold such officers prior to the authentication and delivery of such Right
Certificates or did not hold such offices at the date of authentication of such
Right Certificates.  At any time and from time to time after the execution and
delivery of this Agreement and prior to the Distribution Date, the Company may
deliver Right Certificates executed by the 

                                      -10-
<PAGE>
 
Company to the Rights Agent for authentication, together with a Company Order
for the authentication and delivery of such Right Certificates; and the Rights
Agent in accordance with such Company Order shall authenticate and deliver such
Right Certificates as in this Agreement provided and not otherwise.

     No Right Certificate shall be entitled to any benefit under this Agreement
or be valid or obligatory for any purpose unless there appears on such Right
Certificate a certificate of authentication substantially in the form provided
for herein executed by the Rights Agent by manual signature, and such
certificate upon any Right Certificate shall be conclusive evidence and the only
evidence that such Right Certificate has been duly authenticated and delivered
hereunder.

     Section 6.    Registration, Registration of Transfer and Exchange.  From
                   ---------------------------------------------------       
and after the Distribution Date and prior to the earlier of the Redemption Date
and the Final Expiration Date, the Company shall cause to be kept at the
Corporate Trust Office of the Rights Agent a Rights Register (a "Rights
Register") in which, subject to such reasonable regulations as it may prescribe,
the Company shall provide for the registration of Right Certificates and of
transfers of Rights.  The Rights Agent is hereby appointed the registrar and
transfer agent (the "Rights Registrar") for the purpose of registering Right
Certificates and transfers of Rights as herein provided and the Rights Agent
agrees to maintain such Rights Register in accordance with such regulations so
long as it continues to be designated as Rights Registrar hereunder.

     Upon surrender to the Rights Agent for registration of transfer of any
Right Certificate, the Company shall execute, and the Rights Agent shall
authenticate and deliver, in the name of the designated transferee or
transferees, one or more new Right Certificates evidencing a like number of
Rights.

     At the option of the holder, Right Certificates may be exchanged for other
Right Certificates upon surrender of the Right Certificates to be exchanged to
the Rights Agent.  Whenever any Right Certificates are so surrendered for
exchange, the Company shall execute, and the Rights Agent shall authenticate and
deliver, the Right Certificates which the holder making the exchange is entitled
to receive.

     All Right Certificates issued upon any registration of transfer or exchange
of Right Certificates shall be the valid obligations of the Company, evidencing
the same Rights, and entitled to the same benefits under this Agreement, as the
Right Certificates surrendered upon such registration of transfer or exchange.

     Every Right Certificate presented or surrendered for registration of
transfer or exchange shall (if so required by the Company or the Rights Agent)
be duly endorsed, or accompanied by a written instrument of transfer in form
satisfactory to the Company and the Rights Registrar duly executed, by the
holder thereof or his attorney duly authorized in writing.

                                      -11-
<PAGE>
 
     No service charge shall be made for any registration of transfer or
exchange of Right Certificates, but the Company may require payment of a sum
sufficient to cover any tax or other governmental charge that may be imposed in
connection with any registration of transfer or exchange of Right Certificates,
other than exchanges not involving any transfer.

     The provisions of this Section 6 shall be subject to the provisions of
Section 15.

     Section 7.    Mutilated, Destroyed, Lost and Stolen Right Certificates.
                   --------------------------------------------------------  
If any mutilated Right Certificate is surrendered to the Rights Agent, the
Company shall execute and the Rights Agent shall authenticate and deliver in
exchange therefor a new Right Certificate of like tenor, for a like number of
Rights and bearing a registration number not contemporaneously outstanding.

     If there shall be delivered to the Company and the Rights Agent (i)
evidence to their satisfaction of the destruction, loss or theft of a Right
Certificate and (ii) such security or indemnity, if any, as may be required by
them to save each of them and any agent of either of them harmless, then, in the
absence of notice to the Company or the Rights Agent that such Right Certificate
has been acquired by a bona fide purchaser, the Company shall execute and upon
its request the Rights Agent shall authenticate and deliver, in lieu of any such
destroyed, lost or stolen Right Certificate, a new Right Certificate of like
tenor, for a like number of Rights and bearing a registration number not
contemporaneously outstanding.

     Upon the issuance of any new Right Certificate under this Section, the
Company may require the payment of a sum sufficient to cover any tax or other
governmental charge that may be imposed in relation thereto and any other
expenses (including the fees and expenses of the Rights Agent) connected
therewith.

     Every new Right Certificate issued pursuant to this Section in lieu of any
destroyed, lost or stolen Right Certificate shall constitute an additional
contractual obligation of the Company, whether or not the destroyed, lost or
stolen Right Certificate shall be at any time enforceable by anyone, and shall
be entitled to all the benefits of this Agreement equally and proportionately
with any and all other Right Certificates duly issued hereunder.

     The provisions of this Section are exclusive and shall preclude (to the
extent lawful) all other rights and remedies with respect to the replacement or
payment of mutilated, destroyed, lost or stolen Right Certificates.

     Section 8.    Exercise of Rights; Purchase Price; Expiration Date of
                   ------------------------------------------------------
Rights.  (a) The registered holder of any Right Certificate may exercise the
- ------                                                                      
Rights evidenced thereby (except as otherwise provided herein) in whole or in
part at any time after the Distribution Date upon surrender of the Right
Certificate, with the form of election to purchase on the reverse side thereof
duly executed, to the Rights Agent at its Corporate Trust Office, together with
payment of the Purchase Price for each one one-hundredth (1/100) of a Preferred
Share (or other securities) as to which the Rights are exercised, at or prior to
the earliest of (i) the Close of Business on the Final Expiration 

                                      -12-
<PAGE>
 
Date, (ii) the time of redemption on the Redemption Date or (iii) the time at
which such Rights are mandatorily redeemed and exchanged as provided in Section
25 hereof.

     (b)  The Purchase Price for each one one-hundredth (1/100) of a Preferred
Share pursuant to the exercise of a Right shall initially be one hundred fifty
dollars ($150.00), shall be subject to adjustment from time to time as provided
in Sections 12 and 14 hereof and shall be payable in lawful money of the United
States of America in accordance with paragraph (c) below.

     (c)  Upon receipt of a Right Certificate representing exercisable Rights,
with the form of election to purchase duly executed, accompanied by payment of
the Purchase Price for the securities to be purchased and an amount equal to any
applicable transfer tax required to be paid by the holder of such Right
Certificate in accordance with Section 10 in cash, or by certified check or
cashier's check payable to the order of the Company, the Rights Agent shall
thereupon promptly (i) (A) requisition from any transfer agent of the Preferred
Shares (or other securities) certificates for such number of one one-hundredths
of a Preferred Share (or other securities) as are to be purchased and registered
in such name or names as may be designated by the registered holder of such
Right Certificate or, if appropriate, in the name of a depositary agent or its
nominee, and the Company hereby irrevocably authorizes its transfer agent to
comply with all such requests, and (B) requisition from a depositary agent
appointed by the Company, if any, depositary receipts representing such number
of one one-hundredths of a Preferred Share as are to be purchased and registered
in such name or names as may be designated by such holder (in which case
certificates for the Preferred Shares represented by such receipts shall be
deposited by the transfer agent with such depositary agent), and the Company
hereby directs such depositary agent to comply with all such requests, (ii) when
appropriate, requisition from the Company the amount of cash to be paid in lieu
of issuance of fractional shares in accordance with Section 15, (iii) promptly
after receipt of such certificates or depositary receipts registered in such
name or names as may be designated by such holder, cause the same to be
delivered to or upon the order of the registered holder of such Right
Certificate and (iv) when appropriate, after receipt, promptly deliver such cash
to or upon the order of such holder.

     (d)  If the registered holder of the Right Certificate shall exercise less
than all the Rights evidenced thereby, a new Right Certificate evidencing Rights
equal to the Rights remaining unexercised shall be issued by the Rights Agent to
the registered holder of such Right Certificate or to his duly authorized
assigns, subject to the provisions of Section 15 hereof.

     Section 9.    Cancellation and Destruction of Right Certificates.  All
                   --------------------------------------------------      
Right Certificates surrendered for the purpose of exercise, transfer or exchange
shall, if surrendered to the Company or to any of its other agents, be delivered
to the Rights Agent for such purpose and for cancellation or, if surrendered to
the Rights Agent for such purpose, shall be canceled by it.  No Right
Certificates shall be authenticated in lieu of or in exchange for any Right
Certificates canceled as provided in this Section except as expressly permitted
by any of the provisions of this Agreement.  The Company shall deliver to the
Rights Agent for cancellation, and the Rights Agent shall so cancel, any other
Right Certificate purchased or acquired by the Company.  The Rights Agent shall
deliver all canceled Right 

                                      -13-
<PAGE>
 
Certificates to the Company, or shall, pursuant to a Company Order, destroy such
canceled Right Certificates and in such case shall deliver a certificate of
destruction thereof to the Company.

     Section 10.     Reservation and Availability of Shares.  The Company
                     --------------------------------------              
covenants and agrees that it will cause to be reserved and kept available out of
its authorized and unissued Preferred Shares or any Preferred Shares held in its
treasury, the number of Preferred Shares that will be sufficient to permit the
exercise in full of all outstanding Rights.

     The Company further covenants and agrees that it will, from and after the
Distribution Date, cause to be reserved and kept available out of its authorized
and unissued Common Shares or any Common Shares held in its treasury, the number
of Common Shares of the Company that will be sufficient to permit the exercise
in full of all outstanding Rights if adjusted pursuant to Section 12(a)(ii).

     The Company covenants and agrees that it will take all such action as may
be necessary to ensure that all Preferred Shares or Common Shares of the Company
issued upon exercise of Rights shall (subject to payment of the Purchase Price)
be duly authorized, validly issued, fully paid and nonassessable.  The Company
further covenants and agrees that it will pay when due and payable any and all
federal and state transfer taxes and charges which may be payable in respect of
the issuance or delivery of the Right Certificates or of any Preferred Shares
(or depositary receipts therefor) or Common Shares of the Company upon the
exercise of Rights.  The Company shall not, however, be required to pay any
transfer tax that may be payable in respect of any transfer or delivery of Right
Certificates to a Person other than, or in respect of the issuance or delivery
of certificates or depositary receipts for the Preferred Shares or Common Shares
of the Company upon exercise of Rights evidenced by Right Certificates in a name
other than that of, the registered holder of the Right Certificate evidencing
Rights surrendered for transfer or exercise or to issue or deliver any
certificates or depositary receipts for Preferred Shares or Common Shares of the
Company upon the exercise of any Rights until any such tax shall have been paid
(any such tax being payable by the holder of such Right Certificate at the time
of surrender thereof) or until it has been established to the Company's
reasonable satisfaction that no such tax is due.

     Section 11.   Record Date.  Each Person in whose name any certificate for
                   -----------                                                
Preferred Shares or Common Shares of the Company is issued upon the exercise of,
or upon mandatory redemption and exchange of, Rights shall for all purposes be
deemed to have become the holder of record of the Preferred Shares or Common
Shares represented thereby on, and such certificate shall be dated, (i) in the
case of the exercise of Rights, the date upon which the Right Certificate
evidencing such Rights was duly surrendered and payment of the Purchase Price
(and any applicable transfer taxes) was made, or (ii) in the case of the
mandatory redemption and exchange of Rights, the date of such mandatory
redemption and exchange; provided, however, that, if the date of such surrender
and payment or mandatory redemption and exchange is a date upon which the
transfer books of the Company for its Preferred Shares or Common Shares, as the
case may be, are closed, such Person shall be deemed to have become the record
holder of such shares on, and such certificate shall be dated, the next
succeeding Business Day on which such transfer books of the Company are open.

                                      -14-
<PAGE>
 
Prior to the exercise of (or the mandatory redemption and exchange of) the
Rights evidenced thereby, the holder of a Right Certificate shall not be
entitled to any rights of a holder of Preferred Shares (or Common Shares of the
Company) for which the Rights shall be exercisable, including without limitation
the rights to vote, to receive dividends or other distributions or to exercise
any preemptive rights, and shall not be entitled to receive any notice of any
proceedings of the Company, except as provided herein.

      Section 12.   Adjustment of Purchase Price, Number of Shares or Number of
                    -----------------------------------------------------------
Rights.  The Purchase Price, the number and kind of shares of capital stock of
- ------                                                                        
the Company covered by each Right and the number of Rights outstanding are
subject to adjustment from time to time as provided in this Section 12.

     (a)  (i)    If the Company shall at any time (A) declare a dividend on the
Preferred Shares payable in Preferred Shares, (B) subdivide the outstanding
Preferred Shares, (C) combine the outstanding Preferred Shares into a smaller
number of Preferred Shares or (D) issue any shares of its capital stock in a
reclassification of the Preferred Shares (including any such reclassification in
connection with a consolidation or merger in which the Company is the continuing
or surviving corporation), except as otherwise provided in this Section 12(a),
the Purchase Price in effect at the time of the record date for such dividend or
of the effective date of such subdivision, combination or reclassification, and
the number and kind of shares of capital stock issuable on such date, shall be
proportionately adjusted so that the holder of any Right exercised thereafter
shall be entitled to receive, upon payment of the Purchase Price for the number
of one one-hundredths of  a Preferred Share for which a Right was exercisable
immediately prior to such date, the aggregate number and kind of shares of
capital stock which, if such Right had been duly exercised immediately prior to
such date (at a time when the Preferred Shares transfer books of the Company
were open), such holder would have acquired upon such exercise and been entitled
to receive upon payment or effectuation of such dividend, subdivision,
combination or reclassification; provided, however, that in no event shall the
consideration to be paid upon the exercise of one Right be less than the
aggregate par value of the shares of capital stock of the Company issuable upon
exercise of one Right. If an event occurs which would require an adjustment
under both Section 12(a)(i) and Section 12(a)(ii), the adjustment provided for
in this Section 12(a)(i) shall be in addition to, and shall be made prior to,
any adjustment required pursuant to Section 12(a)(ii).

          (ii)   Subject to action of the Board of Directors of the Company
pursuant to Section 25 of this Agreement, if any Person shall become an
Acquiring Person, each other holder of a Right shall, from and after the Close
of Business on the tenth Business Day after the Shares Acquisition Date, have a
right to receive, upon exercise thereof at a price equal to the then current
Purchase Price multiplied by the number of one one-hundredths of a Preferred
Share for which a Right is then exercisable, in accordance with the terms of
this Agreement and in lieu of Preferred Shares, such number of Common Shares of
the Company as shall equal the result obtained by (x) multiplying the then
current Purchase Price by the number of one one-hundredths of a Preferred Share
for which a Right is then exercisable and dividing that product by (y) 50% of
the then current per share market price of the Company's Common Shares
(determined pursuant to Section 12(d)) on 

                                      -15-
<PAGE>
 
the date such Person became an Acquiring Person. If any Person shall become an
Acquiring Person and the Rights shall then be outstanding, the Company shall not
take any action which would eliminate or diminish the benefits intended to be
afforded by the Rights.

     Notwithstanding any other provision of this Agreement, from and after the
time any Person shall become an Acquiring Person, any Rights that are or were
acquired or beneficially owned by any such Acquiring Person (or any Associate or
Affiliate of such Acquiring Person) shall be null and void and any holder of
such Rights shall thereafter have no right to exercise such Rights under any
provision of this Agreement.  No Right Certificate shall be issued pursuant to
this Agreement that represents Rights beneficially owned by an Acquiring Person
whose Rights would be null and void pursuant to the preceding sentence or by any
Associate or Affiliate thereof; no Right Certificate shall be issued at any time
upon the transfer of any Rights to an Acquiring Person whose Rights would be
null and void pursuant to the preceding sentence or to any Associate or
Affiliate thereof or to any nominee (acting in its capacity as such) of such
Acquiring Person, Associate or Affiliate; and any Right Certificate delivered to
the Rights Agent for transfer to an Acquiring Person whose Rights would be null
and void pursuant to the preceding sentence or to any Associate or Affiliate
thereof or to any nominee (acting in its capacity as such) of such Acquiring
Person, Associate or Affiliate shall be canceled.

          (iii)  If on or after the Distribution Date there shall not be
sufficient Common Shares of the Company issued but not outstanding, or
authorized but unissued, to permit the exercise in full of all outstanding
Rights in accordance with the foregoing subparagraph (ii), the Company agrees to
take all such action as is within its power, including without limitation
appropriate action by its Board of Directors, as may be necessary to amend the
Company's charter to authorize additional Common Shares for issuance upon
exercise of the Rights.  If, notwithstanding the foregoing, the shareholders
shall not approve an amendment to the Company's charter authorizing such
additional Common Shares, the adjustment prescribed in Section 12(a)(ii) shall
not be made but, in lieu thereof, each holder of a Right shall thereafter have
the right to receive, upon exercise thereof in accordance with the terms of this
Agreement, such number of one one-hundredths of Preferred Shares as shall equal
the result obtained by (x) multiplying the then current Purchase Price by the
number of one one-hundredths of a Preferred Share for which a Right is then
exercisable and dividing that product by (y) 50% of the then current per share
market price of one one-hundredth of a Preferred Share (determined pursuant to
Section 12(d)) on the date such Person became an Acquiring Person.

     (b)  If the Company shall fix a record date for the issuance of rights,
options or  warrants to all holders of Preferred Shares entitling them (for a
period expiring within 45 calendar days after such record date) to subscribe for
or purchase Preferred Shares (or shares having the same rights, privileges and
preferences as the Preferred Shares ("equivalent preferred shares")) or
securities convertible into or exchangeable for Preferred Shares or equivalent
preferred shares at a price per Preferred Share or equivalent preferred share
(together with any additional consideration required upon conversion or exchange
in the case of a security convertible into or exchangeable for Preferred Shares
or equivalent preferred shares), less than the current per share market price of
the Preferred Shares (determined pursuant to Section 12(d) on such record date),
the Purchase Price to be in effect 

                                      -16-
<PAGE>
 
after such record date shall be determined by multiplying the Purchase Price in
effect immediately prior to such record date by a fraction, the numerator of
which shall be the number of Preferred Shares outstanding on such record date
plus the number of Preferred Shares which the aggregate offering price of the
total number of Preferred Shares and/or equivalent preferred shares so to be
offered (together with the aggregate of any additional consideration required
upon conversion or exchange in the case of any convertible or exchangeable
securities so to be offered) would purchase at such current market price and the
denominator of which shall be the number of Preferred Shares outstanding on such
record date plus the number of additional Preferred Shares and/or equivalent
preferred shares to be offered for subscription or purchase (or into or for
which the convertible or exchangeable securities so to be offered are initially
convertible or exchangeable); provided, however, that in no event shall the
consideration to be paid upon the exercise of one Right be less than the
aggregate par value of the shares of capital stock of the Company issuable upon
exercise of one Right. In case all or part of such subscription or purchase
price may be paid in a form other than cash, the value of such consideration
shall be as determined in good faith by the Board of Directors of the Company,
whose determination shall be described in a statement filed with the Rights
Agent. Preferred Shares owned by or held for the account of the Company or any
of its Subsidiaries shall not be deemed outstanding for the purpose of any
computation described in this Section 12(b). The adjustment described in this
Section 12(b) shall be made successively whenever such record date is fixed;
and, if none of such rights, options or warrants is so issued, the Purchase
Price shall be adjusted to be the Purchase Price which would then be in effect
if such record date had not been fixed.

     (c)  If the Company shall fix a record date for the making of a
distribution to all holders of the Preferred Shares (including any such
distribution made in connection with a consolidation or merger in which the
Company is the continuing or surviving corporation) of evidences of indebtedness
or assets (other than a regular quarterly cash dividend or a dividend payable in
Preferred Shares) or subscription rights or warrants (excluding those referred
to in Section 12(b)), the Purchase Price to be in effect after such record date
shall be determined by multiplying the Purchase Price in effect immediately
prior to such record date by a fraction, the numerator of which shall be the
then current per share market price of the Preferred Shares (determined pursuant
to Section 12(d)) on such record date, less the fair market value (as determined
in good faith by the Board of Directors of the Company, whose determination
shall be described in a statement filed with the Rights Agent) of the portion of
the assets or evidences of indebtedness so to be distributed or of such
subscription rights or warrants applicable to one Preferred Share and the
denominator of which shall be such current per share market price of the
Preferred Shares; provided, however, that in no event shall the consideration to
be paid upon the exercise of one Right be less than the aggregate par value of
the shares of capital stock of the Company to be issued upon the exercise of one
Right. Such adjustments shall be made successively whenever such a record date
is fixed; and, if such distribution is not so made, the Purchase Price shall
again be adjusted to be the Purchase Price which would then be in effect if such
record date had not been fixed.

     (d)  (i)  For the purpose of any computation hereunder, the "current per
share market price" of the Common Shares on any date shall be deemed to be the
average of the daily Closing Prices per share of such Common Shares for the 30
consecutive Trading Days immediately prior to 

                                      -17-
<PAGE>
 
such date; provided, however, that, if the issuer of such Common Shares shall
announce (A) a dividend or distribution on such Common Shares payable in such
Common Shares or securities convertible into such Common Shares or (B) any
subdivision, combination or reclassification of such Common Shares, and the ex-
dividend date for such dividend or distribution, or the record date for such
subdivision, combination or reclassification, shall occur during such period of
30 Trading Days, then, and in each such case, the current per share market price
of the Common Shares shall be appropriately adjusted to reflect the current
market price per Common Share equivalent.

          (ii)   For the purpose of any computation hereunder, the "current per
share market price" of the Preferred Shares shall be determined in the same
manner as set forth above for Common Shares in paragraph (i) of this Section
12(d).  If the current per share market price of the Preferred Shares cannot be
determined in the manner provided above, the "current per share market price" of
the Preferred Shares shall be conclusively deemed to be the current per share
market price of the Common Shares (determined in the manner provided above)
multiplied by one hundred.

     (e)  No adjustment in the Purchase Price shall be required unless such
adjustment would require an increase or decrease of at least 1% in the Purchase
Price; provided, however, that any adjustments which by reason of this Section
12(e) are not required to be made shall be carried forward and taken into
account in any subsequent adjustment.  All calculations under this Section 12
shall be made to the nearest cent or to the nearest ten-thousandth of a Common
Share or other share or one-millionth of a Preferred Share, as the case may be,
and references herein to the "number of one one-hundredths of a Preferred Share"
(or similar phrases) shall be construed to include fractions of one one-
hundredth of a Preferred Share.  Notwithstanding the first sentence of this
Section 12(e), any adjustment required by this Section 12 shall be made no later
than the earlier of (i) three years from the date of the transaction which
requires such adjustment or (ii) the thirtieth day preceding the Final
Expiration Date.

     (f)  If as a result of an adjustment made pursuant to Section 12(a), the
holder of any Right thereafter exercised shall become entitled to receive any
shares of capital stock of the Company other than Preferred Shares, thereafter
the number of such other shares so receivable upon exercise of any Right shall
be subject to adjustment from time to time in a manner and on terms as nearly
equivalent as practicable to the provisions with respect to the shares contained
in this Section 12, and the provisions of this Agreement, including without
limitation Sections 8, 10, 11 and 14, with respect to the Preferred Shares shall
apply on like terms to any such other shares.

     (g)  All Rights originally issued by the Company subsequent to any
adjustment made to the Purchase Price hereunder shall, whether or not the Right
Certificate evidencing such Rights reflects such adjusted Purchase Price,
evidence the right to purchase, at the adjusted Purchase Price, the number of
one one-hundredths of a Preferred Share purchasable from time to time hereunder
upon exercise of the Rights, all subject to further adjustment as provided
herein.

     (h)  Unless the Company shall have exercised its election as provided in
Section 12(i), upon each adjustment of the Purchase Price pursuant to Section
12(b) or 12(c), each Right 

                                      -18-
<PAGE>
 
outstanding immediately prior to the making of such adjustment shall thereafter
evidence the right to purchase, at the adjusted Purchase Price per one one-
hundredth of a Preferred Share, that number of one one-hundredths of a Preferred
Share obtained by (i) multiplying (x) the number of one-hundredths of a share
covered by a Right immediately prior to this adjustment by (y) the Purchase
Price in effect immediately prior to such adjustment of the Purchase Price and
(ii) dividing the product so obtained by the Purchase Price in effect
immediately after such adjustment of the Purchase Price.

     (i)  The Company may elect on or after the date of any adjustment of the
Purchase Price to adjust the number of Rights outstanding in lieu of any
adjustment in the number of one one-hundredths of a Preferred Share purchasable
upon the exercise of a Right.  Each Right outstanding after such adjustment of
the number of Rights shall be exercisable for the number of one one-hundredths
of a Preferred Share for which a right was exercisable immediately prior to such
adjustment of the Purchase Price.  Each Right held of record prior to such
adjustment of the number of Rights shall become that number of Rights
(calculated to the nearest one ten-thousandth) obtained by dividing the Purchase
Price in effect immediately prior to adjustment of the Purchase Price by the
Purchase Price in effect immediately after adjustment of the Purchase Price.
The Company shall make a public announcement of its election to adjust the
number of Rights, indicating the record date for the adjustment, and, if known
at the time, the amount of the adjustment to be made.  This record date may be
the date on which the Purchase Price is adjusted or any day thereafter, but, if
the Right Certificates have been issued, shall be at least 10 days later than
the date of the public announcement.  (Until such record date, however, any
adjustment in the number of one one-hundredths of a Preferred Share for which a
Right shall be exercisable made as required by this Agreement shall remain in
effect.)  If Right Certificates have been issued, upon each adjustment of the
number of Rights pursuant to this Section 12(i), the Company shall, as promptly
as practicable, cause to be distributed to holders of record of Right
Certificates on such record date Right Certificates evidencing, subject to
Section 15 hereof, the additional Rights to which such holders shall be entitled
as a result of such adjustment, or, at the option of the Company, shall cause to
be distributed to such holders of record in substitution and replacement for the
Right Certificates held by such holders prior to the date of adjustment, and
upon surrender thereof, if required by the Company, new Right Certificates
evidencing all the Rights to which such holders shall be entitled after such
adjustment.  Right Certificates so to be distributed shall be issued, executed
and authenticated in the manner provided for herein and shall be registered in
the names of the holders of record of Right Certificates on the record date
specified in the public announcement.

     (j)  Irrespective of any adjustment or change in the Purchase Price or the
number of one one-hundredths of a Preferred Share issuable upon the exercise of
the Rights, the Right Certificates theretofore and thereafter issued may
continue to express the Purchase Price and the number of one one-hundredths of a
Preferred Share that were expressed in the initial Right Certificates issued
hereunder.

     (k)  Before taking any action that would cause an adjustment reducing the
Purchase Price below one one-hundredth of the amount of consideration per
Preferred Share determined by the Board of Directors of the Company to be
capital, or below one one-hundredth of the par value, if any, 

                                      -19-
<PAGE>
 
per Preferred Share issuable upon exercise of the Rights, the Company agrees to
take such corporate action as is within its power, including without limitation
appropriate action by its Board of Directors, and which is, in the opinion of
its counsel, necessary in order that the Company may validly and legally issue
fully paid and nonassessable one one-hundredths of Preferred Shares at such
adjusted Purchase Price.

     (l)  In any case in which this Section 12 shall require that an adjustment
in the Purchase Price be made effective as of a record date for a specified
event, the Company may elect to defer until the occurrence of such event the
issuance to the holder of any Right exercised after such record date of the
Preferred Shares or other capital stock or securities of the Company, if any,
issuable upon such exercise over and above the Preferred Shares or other capital
stock or securities of the Company, if any, issuable upon such exercise on the
basis of the Purchase Price in effect prior to such adjustment; provided,
however, that the Company shall deliver to such holder a due bill or other
appropriate instrument evidencing such holder's right to receive such additional
securities upon the occurrence of the event requiring such adjustment.

     (m)  Anything in this Section 12 to the contrary notwithstanding, the
Company shall be entitled to make such reductions in the Purchase Price, in
addition to those adjustments expressly required by this Section 12, as and to
the extent that it in its sole discretion shall determine to be advisable in
order that any combination or subdivision of the Preferred Shares, issuance
wholly for cash of any of the Preferred Shares at less than the current market
price, issuance wholly for cash of Preferred Shares or securities which by their
terms are convertible into or exchangeable for Preferred Shares, dividends on
Preferred Shares payable in Preferred Shares or issuance of rights, options or
warrants referred to in subsection (b) of this Section 12, hereafter effected by
the Company to holders of its Preferred Shares shall not be taxable to such
shareholders.

     (n)  If at any time prior to the Distribution Date, the Company shall (i)
declare or pay any dividend on the Common Shares of the Company payable in such
Common Shares or (ii) effect a subdivision or combination of such Common Shares
(by reclassification or otherwise than by payment of dividends in Common Shares)
into a greater or lesser number of Common Shares, then in any such case (A) the
number of one one-hundredths of a Preferred Share purchasable after such event
upon proper exercise of each Right shall be determined by multiplying the number
of one one-hundredths of a Preferred Share so purchasable immediately prior to
such event by a fraction, the numerator of which is the number of Common Shares
of the Company outstanding immediately before such event and the denominator of
which is the number of such Common Shares outstanding immediately after such
event, and (B) each such Common Share outstanding immediately after such event
shall have issued with respect to it that number of Rights which each such
Common Share outstanding immediately prior to such event had issued with respect
to it.  The adjustment provided for in this Section 12(n) shall be made
successively whenever such a dividend is declared or paid or such a subdivision
or combination is effected.  If an event occurs which would require an
adjustment under Section 12(a)(ii) and this Section 12(n), the adjustments
provided for in this Section 12(n) shall be in addition and prior to any
adjustment required pursuant to Section 12(a)(ii).

                                      -20-
<PAGE>
 
      Section 13.   Certificate of Adjusted Purchase Price or Number of Shares.
                    ----------------------------------------------------------  
Whenever an adjustment is made as provided in Section 12 or 14 hereof, the
Company shall (a) promptly prepare a certificate setting forth such adjustment,
and a brief statement of the facts accounting for such adjustment, (b) promptly
file with the Rights Agent and with each transfer agent for the Common Shares of
the Company and the Preferred Shares a copy of such certificate and (c) mail a
brief summary thereof to each holder of record of a Right Certificate in
accordance with Section 28 hereof.

      Section 14.   Consolidation, Merger or Sale or Transfer of Assets or
                    ------------------------------------------------------
Earning Power.  (a) If, directly or indirectly, at any time after a Person has
- -------------                                                                 
become an Acquiring Person, (i) the Company shall consolidate with, or merge
with and into, any other Person, (ii) any Person shall merge with and into the
Company and the Company shall be the continuing or surviving corporation of such
merger and, in connection with any such merger, all or part of the Common Shares
of the Company shall be changed into or exchanged for stock or other securities
of any other Person (or the Company) or cash or any other property, or (iii) the
Company shall sell or otherwise transfer (or one or more of its Subsidiaries
shall sell or otherwise transfer), in one or a series of two or more
transactions, assets of the Company or its Subsidiaries which constitute more
than 50% of the assets or which produce more than 50% of the earning power or
cash flow of the Company and its Subsidiaries (taken as a whole) to any Person
other than the Company or one or more of its Wholly-Owned Subsidiaries, then,
and in each such case, the Company agrees that, as a condition to engaging in
any such transaction, it will make or cause to be made proper provision so that
(i) each holder of a Right (except as otherwise provided herein) shall
thereafter have the right to receive, upon the exercise thereof in accordance
with the terms of this Agreement and in lieu of Preferred Shares, such number of
Common Shares of the Principal Party (as such term is hereinafter defined) as
shall be equal to the result obtained by (X) multiplying the then current
Purchase Price by the number of one one-hundredths of a Preferred Share for
which a Right is then exercisable (without taking into account any adjustment
previously made pursuant to Section 12(a)(ii)) and dividing that product by (Y)
50% of the current per share market price of the Common Shares of such other
Person (determined pursuant to Section 12(d)) on the date of consummation of
such consolidation, merger, sale or transfer; (ii) such Principal Party shall
thereafter be liable for, and shall assume, by virtue of such consolidation,
merger, sale or transfer, all the obligations and duties of the Company pursuant
to this Agreement; (iii) the term "Company," as used herein, shall thereafter be
deemed to refer to such Principal Party; and (iv) the Principal Party shall take
such steps (including without limitation the reservation of a sufficient number
of shares of its Common Shares in accordance with Section 10) in connection with
such consummation as may be necessary to assure that the provisions hereof shall
thereafter be applicable, as nearly as reasonably may be, in relation to the
Common Shares thereafter deliverable upon the exercise of the Rights.  The
Company shall not enter into any transaction of the kind referred to in this
Section 14 if at the time of such transaction there are outstanding any rights,
warrants, instruments or securities or any agreement or arrangements which, as a
result of the consummation of such transaction, would substantially diminish or
otherwise eliminate the benefits intended to be afforded by the Rights.  The
provisions of this Section 14 shall similarly apply to successive mergers or
consolidations or sales or other transfers.  For the purposes of this Section
14, 50% of the assets of the Company and its Subsidiaries shall be determined by
reference to the book value of such assets as set forth in the most recent
consolidated balance sheet of the Company and its Subsidiaries (which 

                                      -21-
<PAGE>
 
need not be audited) and 50% of the earning power or cash flow of the Company
and its Subsidiaries shall be determined by reference to the mathematical
average of the operating income or cash flow, respectively, resulting from the
operations of the Company and its Subsidiaries for the two most recent full
fiscal years as set forth in the consolidated and consolidating financial
statements of the Company and its Subsidiaries for such years; provided,
however, that, if the Company has, during such period, engaged in one or more
transactions to which purchase accounting is applicable, such determination
shall be made by reference to the pro forma operating income of the Company and
its Subsidiaries giving effect to such transactions as if they had occurred at
the commencement of such two-year period.

     (b)  The term "Principal Party" shall mean:  (i) in the case of any
transaction described in clause (i) or (ii) of the first sentence of Section
14(a), the Person that is the issuer of any securities into which Common Shares
of the Company are converted in such merger or consolidation, and, if no
securities are so issued, the Person that is the other party to such merger or
consolidation; and (ii) in the case of any transaction described in clause (iii)
of the first sentence of Section 14(a), the Person that is the party receiving
the greatest portion of the assets transferred pursuant to such transaction or
transactions; provided, however, that in any such case (1) if the Common Shares
of such Person is not at such time and has not been continuously over the
preceding twelve months registered under Section 12 of the Exchange Act and such
Person is a direct or indirect subsidiary of another Person the Common Shares of
which is and has been so registered, the term "Principal Party" shall refer to
such other Person; and (2) in case such Person is a Subsidiary, directly or
indirectly, of more than one Person, the Common Shares of two or more of which
are and have been so registered, the term "Principal Party" shall refer to
whichever of such Persons is the issuer of the Common Shares having the greatest
aggregate market value.

     (c)  The Company shall not consummate any such consolidation, merger, sale
or transfer unless the Principal Party shall have a sufficient number of
authorized Common Shares which have not been issued or reserved for issuance to
permit the exercise in full of the Rights in accordance with this Section 14 and
unless prior thereto the Company and such Principal Party shall have executed
and delivered to the Rights Agent a supplemental agreement to this Agreement
providing for the terms set forth in subsections (a) and (b) of this Section 14
and further providing that, as soon as practicable after the date of any
consolidation, merger, sale or transfer of assets referenced in the first
sentence of Section 14(a), the Principal Party shall:  (i) prepare and file a
registration statement under the Securities Act with respect to the Rights and
the securities purchasable upon exercise of the Rights on an appropriate form,
and shall use its best efforts to cause such registration statement to (A)
become effective as soon as practicable after such filing and (B) remain
effective (with a prospectus at all times meeting the requirements of the
Securities Act) until the Final Expiration Date; and (ii) shall deliver to
holders of the Rights historical financial statements for the Principal Party
and each  of its Affiliates which comply in all respects with the requirements
for registration of a class of securities under the Exchange Act.  The
provisions of this Section 14 shall similarly apply to successive mergers,
consolidations, sale or other transfers of assets. If an event subject to this
Section 14 shall occur at any time after the occurrence of an event subject to
Section 12(a)(ii), the 

                                      -22-
<PAGE>
 
Rights that have not theretofore been exercised shall thereafter become
exercisable in the manner described in Section 14(a).

      Section 15.   Fractional Rights and Fractional Shares.  (a) the Company
                    ---------------------------------------                  
shall not be required to issue or distribute Right Certificates which evidence
fractional Rights.  If, on the Distribution Date or thereafter, as a result of
any adjustment effected pursuant to Section 12(i) or otherwise hereunder, a
Person would otherwise be entitled to receive a Right Certificate evidencing a
fractional Right, the Company shall, in lieu thereof, pay or cause to be paid to
such Person an amount in cash equal to the same fraction of the current market
value of a whole Right.  For the purpose of this Section 15(a), the current
market value of a whole Right shall be the Closing Price of the Rights for the
Trading Day immediately prior to the date on which such fractional Rights would
have been otherwise issuable.

     (b)  The Company shall not be required to issue fractions of Preferred
Shares (other than fractions which are integral multiples of one one-hundredth
of a Preferred Share) upon exercise of the Rights or to distribute certificates
which evidence fractional Preferred Shares (other than fractions which are
integral multiples of one one-hundredth of a Preferred Share).  Fractions of
Preferred Shares in integral multiples of one one-hundredth of a Preferred Share
may, at the election of the Company, be evidenced by depositary receipts,
pursuant to an appropriate agreement between the Company and a depositary
selected by it, provided that such agreement shall provide that the holders of
such depositary receipts shall have all the rights, privileges and preferences
to which they are entitled as beneficial owners of the Preferred Shares
represented by such depository shares.  If, on the Distribution Date or
thereafter, as a result of any adjustment effected hereunder in the number of
one one-hundredths of a Preferred Share as to which a Right has become
exercisable, a Person would otherwise be entitled to receive a fractional
Preferred Share that is not an integral multiple of one one-hundredth of a
Preferred Share, the Company shall, in lieu thereof, pay to such Person at the
time such Right is exercised as herein provided an amount in cash equal to the
same fraction (which is not an integral multiple of one one-hundredth of a
Preferred Share) of the current market value of one Preferred Share.  For
purposes of this Section 15(b), the current market value of a Preferred Share
shall be the Closing Price of a Preferred Share for the Trading Day immediately
prior to the date of such exercise.

     (c)  Should any adjustment contemplated by Section 12(a)(ii) or any
mandatory redemption and exchange contemplated by Section 25 occur, the Company
shall not be required to issue fractions of Common Shares of the Company upon
exercise of the Rights or to distribute certificates which evidence fractional
Common Shares.  If, after any such adjustment or mandatory redemption and
exchange, a Person would otherwise be entitled to receive a fractional Common
Share of the Company upon exercise of any Right Certificate or upon mandatory
redemption and exchange as contemplated by Section 25, the Company shall, in
lieu thereof, pay to such Person at the time such Right is exercised as herein
provided or upon such mandatory redemption and exchange an amount in cash equal
to the same fraction of the current market value of one Common Share.  For
purposes of this Section 15(c), the current market value of a Common Share of
the Company shall be the Closing Price of such a Common Share for the Trading
Day immediately prior to the date of such exercise or the date of such mandatory
redemption and exchange.

                                      -23-
<PAGE>
 
     (d)  The holder of a Right by the acceptance thereof expressly waives his
right to receive any fractional Rights or any fractional shares upon exercise or
mandatory redemption and exchange of a Right (except as provided above).

      Section 16.   Rights of Action.  (a) All rights of action in respect of
                    ----------------                                         
the obligations and duties owed to the holders of the Rights under this
Agreement are vested in the registered holders of the Rights; and, without the
consent of the Rights Agent or of the holder of any other Rights, any registered
holder of any Rights may, in his own behalf and for his own benefit, enforce,
and may institute and maintain any suit, action or proceeding, judicial or
otherwise, against the Company to enforce, or otherwise to act in respect of,
such holder's right to exercise such Rights in the manner provided in the Right
Certificate evidencing such Rights and in this Agreement.  Without limiting the
foregoing or any remedies available to the holders of Rights, it is specifically
acknowledged that the holders of Rights would not have an adequate remedy at law
for any breach of this Agreement and will be entitled to specific performance of
the obligations under, and injunctive relief against actual or threatened
violations of, the obligations of any Person subject to this Agreement.

     (b)  No right or remedy herein conferred upon or reserved to the registered
holder of Rights is intended to be exclusive of any other right or remedy, and
every right and remedy shall, to the extent permitted by law, be cumulative and
in addition to every other right and remedy given hereunder or now or hereafter
existing at law or in equity or otherwise.  The assertion or employment of any
right or remedy, whether hereunder or otherwise, shall not prevent the
concurrent assertion or employment of any other appropriate right or remedy.

     (c)  No delay or omission of any registered holder of Rights to exercise
any right or remedy accruing hereunder shall impair any such right or remedy or
constitute a waiver of any default hereunder or an acquiescence therein. Every
right and remedy given hereunder or by law to such holders may be exercised from
time to time, and as often as may be deemed expedient, by such holders.

      Section 17.   Agreement of Right Holders.  Every holder of a Right, by
                    --------------------------                              
accepting the same, consents and agrees with the Company and the Rights Agent
and with every other holder of a Right that:

          (a)  prior to the Distribution Date, the Rights will be transferable
     only in connection with the transfer of the Common Shares of the Company;

          (b)  after the Distribution Date, the Right Certificates are
     transferable only on the registry books of the Rights Agent if surrendered
     at the Corporate Trust Office of the Rights Agent duly endorsed or
     accompanied by a proper instrument of transfer; and

          (c)  the Company and the Rights Agent may deem and treat the person in
     whose name the Right Certificate (or, prior to the Distribution Date, the
     associated Common Shares certificate) is registered as the absolute owner
     thereof and of the Rights evidenced thereby 

                                      -24-
<PAGE>
 
     (notwithstanding any notations of ownership or writing on the Right
     Certificates or the associated Common Shares certificate made by anyone
     other than the Company or the Rights Agent) for all purposes, and neither
     the Company nor the Rights Agent shall be affected by any notice to the
     contrary.

      Section 18.   Right Certificate Holder Not Deemed a Stockholder.  No
                    -------------------------------------------------     
holder, as such, of any Right (whether or not then evidenced by a Right
Certificate) shall be entitled to vote, receive dividends or be deemed for any
purpose to be the holder of Preferred Shares, Common Shares of the Company or
any other securities of the Company which may at any time be issuable on the
exercise (or mandatory redemption and exchange) of the Rights represented
thereby, nor shall anything contained herein or in any Right Certificate be
construed to confer upon any such holder, as such, any of the rights of a
stockholder of the Company, including without limitation any right to vote for
the election of directors or upon any matter submitted to stockholders at any
meeting thereof, to give or withhold consent to any corporate action, to receive
notice of meetings or other actions affecting stockholders (except as provided
in Section 26) or to receive dividends or subscription rights until the Right or
Rights evidenced by such Right Certificate shall have been exercised (or
mandatorily redeemed and exchanged) in accordance with the provisions hereof.

      Section 19.   Concerning the Rights Agent.  The Company agrees to pay to
                    ---------------------------                               
the Rights Agent reasonable compensation for all services rendered by it
hereunder and, from time to time, on demand of the Rights Agent, its reasonable
expenses and counsel fees and other disbursements incurred in the administration
and execution of this Agreement and the exercise and performance of its duties
hereunder. The Company also agrees to indemnify the Rights Agent for, and to
hold it harmless against, any loss, liability or expense, incurred without
negligence, bad faith or willful misconduct on the part of the Rights Agent, for
anything done or omitted by the Rights Agent in connection with the acceptance
and administration of this Agreement, including the costs and expenses of
defending against any claim of liability in the premises.

     The Rights Agent shall be protected and shall incur no liability for, or in
respect of any action taken, suffered or omitted by it in connection with, its
administration of this Agreement in reliance upon any Right Certificate or
certificate for Preferred Shares, Common Shares of the Company or other
securities of the Company, Company Order, instrument of assignment or transfer,
power of attorney, endorsement, affidavit, letter, notice, direction, consent,
certificate, statement, or other paper or document believed by it to be genuine
and to be executed and, where necessary, verified or acknowledged, by the proper
person or persons, or otherwise upon the advice of its counsel as set forth in
Section 20 hereof.

      Section 20.   Duties of Rights Agent.  The Rights Agent undertakes the
                    ----------------------                                  
duties and obligations imposed by this Agreement upon the following terms and
conditions, by all of which the Company and the holders of Right Certificates,
by their acceptance thereof, shall be bound:

     (a)  The Rights Agent may consult with legal counsel (who may be legal
counsel for the Company), and the opinion of such counsel shall be full and
complete authorization and protection 

                                      -25-
<PAGE>
 
to the Rights Agent as to any action taken or omitted by it in good faith and in
accordance with such opinion.

     (b)  Whenever in the performance of its duties under this Agreement the
Rights Agent shall deem it necessary or desirable that any fact or matter be
proved or established by the Company prior to taking or suffering any action
hereunder, such fact or matter (unless other evidence in respect thereof be
herein specifically prescribed) may be deemed to be conclusively proved and
established by a certificate signed by any one of the Chairman of the Board, the
President, any Vice President, the Treasurer, any Assistant Treasurer, the
Secretary or any Assistant Secretary of the Company and delivered to the Rights
Agent; and such certificate shall be full authorization to the Rights Agent for
any action taken or suffered in good faith by it under the provisions of this
Agreement in reliance upon such certificate.

     (c)  The Rights Agent shall be liable hereunder to the Company or any other
Person only for its own negligence, bad faith or willful misconduct.

     (d)  The Rights Agent shall not be liable for or by reason of any of the
statements of fact or recitals contained in this Agreement or in the Right
Certificates (except its authentication thereof) or be required to verify the
same, but all such statements and recitals are and shall be deemed to have been
made by the Company only.

     (e)  The Rights Agent shall not have any responsibility with respect to the
validity of this Agreement or the execution and delivery hereof (except the due
execution hereof by the Rights Agent) or with respect to the validity or
execution of any Right Certificate (except its authentication thereof); nor
shall it be responsible for any breach by the Company of any covenant or
condition contained in this Agreement or in any Right Certificate; nor shall it
be responsible for any change in the exercisability of the Rights (including the
Rights becoming void pursuant to Section 12(a)(ii) hereof) or any adjustment in
the terms of the Rights (including the manner, method, or amount thereof)
provided for in Sections 3, 12, 14, 24 and 25, or the ascertainment of the
existence of facts that would require any such change or adjustment (except with
respect to the exercise of Rights evidenced by Right Certificates after actual
notice that such change or adjustment is required); nor shall it by any act
hereunder be deemed to make any representation or warranty as to the
authorization or reservation of any Preferred Shares or Common Shares to be
issued pursuant to this Agreement or any Right Certificate or as to whether any
Preferred Shares or Common Shares will, when issued, be duly authorized, validly
issued, fully paid and nonassessable.

     (f)  The Company agrees that it will perform, execute, acknowledge and
deliver or cause to be performed, executed, acknowledged and delivered all such
further and other acts, instruments and assurances as may reasonably be required
by the Rights Agent for the carrying out or performing by the Rights Agent of
the provisions of this Agreement.

     (g)  The Rights Agent is hereby authorized and directed to accept
instructions with respect to the performance of its duties hereunder from any
one of the Chairman of the Board, the President, 

                                      -26-
<PAGE>
 
any Vice President, the Treasurer, any Assistant Treasurer, the Secretary or any
Assistant Secretary of the Company, and to apply to such officers for advice or
instructions in connection with its duties, and it shall not be liable for any
action taken or suffered to be taken by it in good faith in accordance with
instructions of any such officer.

     (h)  The Rights Agent and any shareholder, director, officer or employee of
the Rights Agent may buy, sell or deal in any of the Rights or other securities
of the Company or become pecuniarily interested in any transaction in which the
Company may be interested, or contract with or lend money to the Company or
otherwise act as fully and freely as though it were not Rights Agent under this
Agreement. Nothing herein shall preclude the Rights Agent from acting in any
other capacity for the Company.

     (i)  The Rights Agent may execute and exercise any of the rights or powers
hereby vested in it or perform any duty hereunder either itself or by or through
its attorneys or agents, and the Rights Agent shall not be answerable or
accountable for any act, default, neglect or misconduct of any such attorneys or
agents or for any loss of the Company resulting from any such act, default,
neglect or misconduct, provided that reasonable care was exercised in the
selection and continued employment thereof.

      Section 21.   Merger or Consolidation or Change of Name of Rights Agent.
                    ---------------------------------------------------------  
Any corporation into which the Rights Agent or any successor Rights Agent may be
merged or with which it may be consolidated, or any corporation resulting from
any merger or consolidation to which the Rights Agent or any successor Rights
Agent shall be a party, or any corporation succeeding the corporate trust
business of the Rights Agent or any successor Rights Agent, shall be the
successor to the Rights Agent under this Agreement without the execution or
filing of any paper or any further act on the part of any of the parties hereto,
provided that such corporation would be eligible for appointment as a successor
Rights Agent under the provisions of Section 22.  If at the time such successor
Rights Agent shall succeed to the agency created by this Agreement any of the
Right Certificates shall have been authenticated but not delivered, any such
successor Rights Agent may adopt the authentication of the predecessor Rights
Agent and deliver such Right Certificates so authenticated, and, if at that time
any of the Right Certificates shall not have been authenticated, any successor
Rights Agent may authenticate such Right Certificates either in the name of the
predecessor Rights Agent or in the name of the successor Rights Agent; and in
all such cases such Right Certificates shall have the full force provided in the
Right Certificates and in this Agreement.

     If at any time the name of the Rights Agent shall be changed and at such
time any of the Right Certificates shall have been authenticated but not
delivered, the Rights Agent may adopt the authentication under its prior name
and deliver Right Certificates so authenticated; and, in case at that time any
of the Right Certificates shall not have been authenticated, the Rights Agent
may authenticate such Right Certificates either in its prior name or in its
changed name; and in all such cases such Right Certificates shall have the full
force provided in the Right Certificates and in this Agreement.

                                      -27-
<PAGE>
 
      Section 22.   Change of Rights Agent.  The Rights Agent or any successor
                    ----------------------                                    
Rights Agent may resign and be discharged from its duties under this Agreement
upon 30 days' notice in writing mailed to the Company and to each transfer agent
for the Common Shares of the Company and the Preferred Shares by registered or
certified mail, and to the holders of the Right Certificates by first-class
mail.  The Company may remove the Rights Agent or any successor Rights Agent
upon 30 days' notice in writing, mailed to the Rights Agent or successor Rights
Agent, as the case may be, and to each transfer agent for the Common Shares of
the Company and the Preferred Shares by registered or certified mail, and to the
holders of the Right Certificates by first-class mail.  If the Rights Agent
shall resign or be removed or shall otherwise become incapable of acting, the
Company shall appoint a successor to the Rights Agent.  If the Company shall
fail to make such appointment within a period of 30 days after giving notice of
such removal or after it has been notified in writing of such resignation or
incapacity by the resigning or incapacitated Rights Agent or by the registered
holder of a Right Certificate (or, prior to the Distribution Date, of Common
Shares), then any registered holder of a Right Certificate (or, prior to the
Distribution Date, of Common Shares) may apply to any court of competent
jurisdiction for the appointment of a new Rights Agent.  Any successor Rights
Agent, whether appointed by the Company or by such a court, shall be a
corporation or other legal entity organized, doing business and in good standing
under the laws of the United States or of any state of the United States, which
is authorized to exercise corporate securities transfer powers in the State of
Texas and has at the time of its appointment as Rights Agent a combined capital
and surplus of at least $25 million.  After appointment, the successor Rights
Agent shall be vested with the same powers, rights, duties and responsibilities
as if it had been originally named as Rights Agent without further act or deed;
but the predecessor Rights Agent shall deliver and transfer to the successor
Rights Agent any property at the time held by it hereunder, and execute and
deliver any further assurance, conveyance, act or deed necessary for the
purpose.  Not later than the effective date of any such appointment, the Company
shall file notice thereof in writing with the predecessor Rights Agent and each
transfer agent for the Common Shares of the Company and the Preferred Shares,
and mail a notice thereof in writing to the registered holders of the Right
Certificates.  Failure to give any notice provided for in this Section 22,
however, or any defect therein, shall not affect the legality or validity of the
resignation or removal of the Rights Agent or the appointment of the successor
Rights Agent, as the case may be.

      Section 23.   Issuance of New Right Certificates.  Notwithstanding any of
                    ----------------------------------                         
the provisions of this Agreement or of the Rights to the contrary, the Company
may, at its option, issue new Rights Certificates evidencing Rights in such form
as may be approved by its Board of Directors to reflect any adjustment or change
in the Purchase Price per share and the number or kind or class of shares or
other securities purchasable under the Right Certificates made in accordance
with the provisions of this Agreement.

     Section 24.    Redemption.  (a) The Rights may be redeemed by action of the
                    ----------                                                  
Board of Directors of the Company pursuant to paragraph (b) of this Section 24,
or may be redeemed and exchanged by action of the Board of Directors of the
Company pursuant to Section 25 herein, but shall not be redeemed in any other
manner.

                                      -28-
<PAGE>
 
     (b)  The Board of Directors of the Company may, at its option, at any time
prior to the Close of Business on the Shares Acquisition Date redeem all but not
less than all the then outstanding Rights at a redemption price of one cent
($0.01) per Right then outstanding, appropriately adjusted to reflect any
adjustment in the number of Rights outstanding pursuant to Section 12(i) herein
(such redemption price being hereinafter referred to as the "Redemption Price").
Any such redemption of the Rights by the Board of Directors may be made
effective at such time, on such basis and with such conditions as the Board of
Directors in its sole discretion may establish.

     (c)  The right of the registered holders of Right Certificates to exercise
the Rights evidenced thereby or, if the Distribution Date has not theretofore
occurred, the inchoate right of the registered holders of Rights to exercise the
same shall, without notice to such holders or to the Rights Agent and without
further action, terminate and be of no further force or effect effective as of
the time of adoption by the Board of Directors of the Company of a resolution
authorizing and directing the redemption of the Rights pursuant to paragraph (b)
of this Section 24 (or, alternatively, if the Board of Directors qualified such
action as to time, basis or conditions, then at such time, on such basis and
with such conditions as the Board of Directors may have established pursuant to
such paragraph (b)); thereafter, the only right of the holders of Rights shall
be to receive the Redemption Price.  The Company shall promptly give public
notice of any redemption resolution pursuant to paragraph (b) of this Section
24; provided, however, that the failure to give, or any defect in, any such
notice shall not affect the validity of such redemption.  Within 10 days after
the adoption of any redemption resolution pursuant to paragraph (b) of this
Section 24, the Company shall give notice of such redemption to the holders of
the then outstanding Rights by mailing such notice to all such holders at their
last addresses as they appear upon the registry books of the Rights Agent or,
prior to the Distribution Date, on the registry books of the transfer agents for
the Common Shares of the Company.  Any notice which is mailed in the manner
herein provided shall be deemed given, whether or not the holder receives the
notice.  Each such notice of redemption shall state the method by which the
payment of the Redemption Price will be made.

     (d)  Neither the Company nor any of its Affiliates or associates may
acquire (other than, in the case of such Affiliates and Associates, in their
capacity as holders of Common Shares of the Company), redeem or purchase for
value any Rights at any time in any manner other than as specifically set forth
in this Section 24 or in Section 25 herein, and other than in connection with
the purchase of Common Shares of the Company prior to the Distribution Date.

      Section 25.   Mandatory Redemption and Exchange.  (a) The Board of
                    ---------------------------------                   
Directors of the Company may, at its option, at any time after the Close of
Business on the Shares Acquisition Date, issue Common Shares of the Company in
mandatory redemption of, and in exchange for, all or part of the then
outstanding and exercisable Rights (which shall not include Rights that have
become null and void pursuant to the provisions of Section 12(a)(ii) hereof) at
an exchange ratio of one Common Share for each two Common Shares for which each
Right is then exercisable pursuant to the provisions of Section 12(a)(ii)
hereof.  Notwithstanding the foregoing, the Board of Directors shall not be
empowered to effect such redemption and exchange at any time after any Person
(other than the Company, any Subsidiary of the Company, any employee benefit
plan of the Company or any such Subsidiary, or any entity holding Voting Shares
for or pursuant to the terms of any such plan) 

                                      -29-
<PAGE>
 
together with all Affiliates and Associates of such Person, becomes the
Beneficial Owner of 50% or more of the Voting Shares then outstanding.

     (b)  As of the Close of Business on such date as the Board of Directors of
the Company shall order the mandatory redemption and exchange of any Rights
pursuant to subsection (a) of this Section 25 and without any further action and
without any notice, the right to exercise such Rights shall terminate and the
only right thereafter of a holder of such Rights shall be to receive such number
of Common Shares as is provided in paragraph (a) of this Section 25.  The
Company shall promptly give public notice of any such redemption and exchange;
provided, however, that the failure to give, or any defect in, such notice shall
not affect the validity of such redemption and exchange.  The Company promptly
shall  mail a notice of any such redemption and exchange to all the holders of
such Rights at their last addresses as they appear upon the registry books of
the Rights Agent.  Any notice which is mailed in the manner herein provided
shall be deemed given, whether or not the holder receives the notice.  Each such
notice of mandatory redemption and exchange shall state the method by which the
redemption and exchange of the Common Shares for Rights will be effected and, in
the event of any partial redemption and exchange, the number of Rights which
will be redeemed and exchanged.  Any partial redemption and exchange shall be
effected pro rata based on the number of Rights (other than Rights which have
become null and void pursuant to the provisions of Section 12(a)(ii) hereof)
held by each holder of Rights.

     (c)  If there shall not be sufficient Common Shares of the Company issued
but not outstanding, or authorized but unissued, to permit a mandatory
redemption and exchange of Rights in accordance with the provisions of this
Section 25, the Company agrees to take all such action as is within its power,
including without limitation appropriate action by its Board of Directors, as
may be necessary to amend the Company's charter to authorize additional Common
Shares for issuance upon such mandatory redemption and exchange.  If,
notwithstanding the foregoing, the shareholders shall not approve an amendment
to the Company's charter authorizing such additional Common Shares, the Company,
at its option, may substitute Preferred Shares (or equivalent preferred shares,
as such term is defined in Section 12(b) hereof) for Common Shares of the
Company, at the initial rate of one one-hundredth of a Preferred Share (or
equivalent preferred share) for each Common Share, as appropriately adjusted.

      Section 26.   Notice of Certain Events.  If the Company shall, on or after
                    ------------------------                                    
the Distribution Date, propose (a) to pay any dividend or other distribution
payable in stock of any class of the Company or any Subsidiary of the Company to
the holders of its Preferred Shares, (b) to distribute to the holders of its
Preferred Shares rights or warrants to subscribe for or to purchase any
additional Preferred Shares or shares of stock of any class or any other
securities, rights or options, (c) to make any other distribution to the holders
of its Preferred Shares (other than a regular quarterly cash dividend, (d) to
effect any reclassification of its Preferred Shares (other than a
reclassification involving only the subdivision of outstanding Preferred
Shares), (e) to effect any consolidation or merger into or with, or to effect
any sale or other transfer (or to permit one or more of its Subsidiaries to
effect any sale or other transfer), in one or more transactions, of more than
50% of the assets or earning power or cash flow of the Company and its
Subsidiaries (determined as provided in Section 14 herein) to, any other Person
( other than the Company or a Wholly-Owned Subsidiary 

                                      -30-
<PAGE>
 
or Wholly-Owned Subsidiaries), (f) to effect the liquidation, dissolution or
winding up of the Company or (g) if the Rights have theretofore become
exercisable with respect to Common Shares of the Company pursuant to Section
12(a)(ii) herein, to declare or pay any dividend or other distribution on the
Common Shares payable in Common Shares or in stock of any other class of the
Company or any Subsidiary of the Company or to effect a subdivision or
combination of the Common Shares (by reclassification or otherwise than by
payment of dividends in Common Shares) then, in each such case, the Company
shall give to each holder of a Right Certificate, in accordance with Section 28
hereof, notice of such proposed action, which shall specify the date of
authorization of such action by the Board of Directors of the Company and (i)
record date for such dividend or other distribution or (ii) the date on which
such reclassification, consolidation, merger, sale, transfer, liquidation,
dissolution, winding up, subdivision or combination is to take place and the
date of participation therein by the holders of the Common Shares of the Company
or the Preferred Shares, or both, if any such date is to be fixed. Such notice
shall be so given in the case of any action covered by clause (a), (b) or (g)
above at least 20 days prior to the record date for determining holders of the
Preferred Shares or of the Common Shares of the Company, as the case as may be,
for purposes of such action, and, in the case of any such other action, at least
20 days prior to the date of the taking of such proposed action or the date of
participation therein by the holders of the Preferred Shares or Common Shares of
the Company, as the case may be, whichever shall be the earlier.

     If any of the events set forth in Section 12(a)(ii) of this Agreement shall
occur, then, in any such case, the Company shall as soon as practicable
thereafter give to each holder of a Right Certificate, in accordance with
Section 28 hereof, a notice of the occurrence of such event, which shall specify
the event and the consequences of the event to holders of Rights under Section
12(a)(ii) hereof.

      Section 27.   Securities Laws Registrations.  To the extent legally
                    -----------------------------                        
required, the Company agrees that it will prepare and file, no later than the
Distribution Date, and will sue its best efforts to cause to be declared
effective, a registration statement under the Securities Act of 1933, as
amended, registering the offering, sale and delivery of the Preferred Shares
issuable upon exercise of the Rights, and the Company will, thereafter, use its
best efforts to maintain such registration statement (or another) continuously
in effect so long as any Rights remain outstanding and exercisable with respect
to Preferred Shares.  Should the Rights become exercisable with respect to
securities of the Company or one of its Subsidiaries other than Preferred
Shares, the Company agrees that it will, to the extent legally required,
promptly thereafter prepare and file, or cause to be prepared and filed, and
will use its best efforts to cause to be declared effective, a registration
statement under such Act registering the offering, sale and delivery of such
other securities and the Company will, thereafter, use its best efforts to
maintain such registration statement (or another) continuously in effect so long
as any outstanding Rights are exercisable with respect to such securities.  The
Company further agrees to use its best efforts, from and after the Distribution
Date, to qualify or register for sale the Preferred Shares or other securities
of the Company or one of its Subsidiaries issuable upon exercise of the Rights
under the securities or "blue sky" laws (to the extent legally required
thereunder) of all jurisdictions in which registered holders of Right
Certificates reside determined by reference to the Rights Register.

                                      -31-
<PAGE>
 
      Section 28.   Notices.  Notices or demands authorized by this Agreement to
                    -------                                                     
be given or made by the Rights Agent or by the holder of any Right Certificate
to or on the Company shall be sufficiently given to made if sent by first-class
mail, postage prepaid, addressed (until another address is filed in writing with
the Rights Agent) as follows:

               Halliburton Company
               3600 Lincoln Plaza
               500 N. Akard Street
               Dallas, Texas 75201-3391

               Attention: Secretary

Subject to the provisions of Section 22 hereof, any notice or demand authorized
by this Agreement to be given or made by the Company or by the holder of any
Right Certificate to or on the Rights Agent shall be sufficiently given or made
if sent by first-class mail, postage prepaid, addressed (until another address
is filed in writing with the Company) as follows:

               ChaseMellon Shareholder Services, L.L.C.
               2323 Bryan Street
               Suite 2300
               Dallas, Texas 75201

               Attention:  Administration

Notices or demands authorized by this Agreement to be given or made by the
Company or the Rights Agent to the holder of any Right Certificate shall be
sufficiently given or made if sent by first-class mail, postage prepaid,
addressed to such holder at the address of such holder as shown on the Rights
Register of the Company or, prior to the Distribution Date, on the stock
transfer records for the Common Shares of the Company.

      Section 29.   Supplements and Amendments.  The Company and the Rights
                    --------------------------                             
Agent may from  time to time supplement or amend this Agreement without the
approval of any holders of Right Certificates in order to cure any ambiguity, to
correct or supplement any provision contained herein which may be defective or
inconsistent with any other provisions herein, or to make any other provisions
in regard to matters or questions arising hereunder, which the Company and the
Rights Agent may deem necessary or desirable, including without limitation
extending the Final Expiration Date and, provided that at the time of such
amendment or supplement the Distribution Date has not occurred, the period
during which the Rights may be redeemed; provided, however, that, after the
Distribution Date, any such amendment or supplement shall not materially and
adversely affect the interests of the holders of Right Certificates.  Without
limiting the foregoing, the Board of Directors of the Company may by resolution
adopted at any time prior to such time as any Person becomes an Acquiring Person
amend this Agreement to lower the threshold set forth in the definitions of
Acquiring Person and Distribution Date in Section 1 from 15% to a percentage not
less than the greater of (i) any percentage greater than the largest percentage
of the outstanding Voting Shares 

                                      -32-
<PAGE>
 
then known to the Company to be beneficially owned by any Person (other than the
Company, any Subsidiary of the Company, any employee benefit plan of the Company
or any Subsidiary of the Company, or any entity holding Voting Shares for or
pursuant to the terms of any such plan), and (ii) 10%.

     Section 30.   Successors.  All the covenants and provisions of this
                    ----------                                           
Agreement by or for the benefit of the Company or the Rights Agent shall bind
and inure to the benefit of their respective successors and assigns hereunder.

     Section 31.   Benefits of this Agreement.  Nothing in this Agreement shall
                    --------------------------                                  
be construed to give to any Person other than the Company, the Rights Agent and
the registered holders of the Rights any legal or equitable right, remedy or
claim under this Agreement; but this Agreement shall be for the sole and
exclusive benefit of the Company, the Rights Agent and the registered holders of
the Rights.

     Section 32.   Severability.  If any term, provision, covenant or
                    ------------                                      
restriction of this Agreement is held by a court of competent jurisdiction or
other authority to be invalid, void or unenforceable, the remainder of the
terms, provisions, covenants and restrictions of this Agreement shall remain in
full force and effect and shall in no way be affected, impaired or invalidated.

     Section 33.   Governing Law.  This Agreement and each Right Certificate
                    -------------                                            
issued hereunder shall be deemed to be a contract made under the laws of the
State of Delaware and for all purposes shall be governed by and construed in
accordance with the laws of such State applicable to contracts to be made and
performed entirely within such State.

     Section 34.   Counterparts.  This Agreement may be executed in any number
                    ------------                                               
of counterparts and each of such counterparts shall for all purposes be deemed
to be an original, and all such counterparts shall together constitute but one
and the same instrument.

     Section 35.   Descriptive Headings.  Descriptive headings of the several
                    --------------------                                      
Sections of this Agreement are inserted for convenience only and shall not
control or affect the meaning or construction of any of the provisions hereof.

     Section 36.    Effective Date.  This Restated Rights Agreement shall become
                    --------------                                              
effective at the opening of business on December 11, 1996.

     IN WITNESS WHEREOF, the parties hereto have caused this Agreement to be
duly executed and their respective corporate seals to be hereunto affixed and
attested, all as of the day and year first above written.

                                       HALLIBURTON COMPANY
Attest:

By /s/ Robert M. Kennedy               By /s/ Susan S. Keith     
   ------------------------               -----------------------------------
Title:  Assistant Secretary                   Vice President

                                      -33-
<PAGE>
 
                                       CHASEMELLON SHAREHOLDER
                                       SERVICES, L.L.C.
                                       As Rights Agent
Attest:

By /s/ R. John Davis                   By /s/ Margaret W. Grubb
   ----------------------                 -----------------------------------
Title: Authorized Officer                          Authorized Officer

                                      -34-
<PAGE>
 
                                                                       Exhibit A
                                                                       ---------

                          [Form of Right Certificate]

Certificate No. R-                            ____________ Rights

          NOT EXERCISABLE AFTER DECEMBER 15, 2005 OR EARLIER IF REDEMPTION OR
          EXCHANGE OCCURS.  THE RIGHTS ARE SUBJECT TO REDEMPTION AT $.01 PER
          RIGHT AND TO EXCHANGE ON THE TERMS SET FORTH IN THE RIGHTS AGREEMENT.
          UNDER CERTAIN CIRCUMSTANCES, RIGHTS BENEFICIALLY OWNED BY ACQUIRING
          PERSONS (AS DEFINED IN SECTION 1 OF THE RIGHTS AGREEMENT) OR ANY
          SUBSEQUENT HOLDER OF SUCH RIGHTS MAY BECOME NULL AND VOID.

                               Right Certificate

                              HALLIBURTON COMPANY

     This certifies that ___________________________________________, or
registered assigns, is the registered owner of the number of Rights set forth
above, each of which entitles the owner thereof, subject to the terms,
provisions and conditions of the Restated Rights Agreement dated as of December
1, 1996 (the "Rights Agreement") between Halliburton Company, a Delaware
corporation ("the Company"), and ChaseMellon Shareholder Services, L.L.P., a New
Jersey limited liability company (the "Rights Agent"), to purchase from the
Company at any time after the Distribution Date (as such term is defined in the
Rights Agreement) and prior to 5:00 P.M. (Dallas time) on December 15, 2005 at
the Corporate Trust Office of the Rights Agent, one one-hundredth (1/100) of a
fully paid nonassessable share of Series A Junior Participating Preferred Stock,
without par value (the "Preferred Shares"), of the Company, at a purchase price
of one hundred and fifty dollars ($150.00) per one one-hundredth (1/100) of a
Preferred Share (the "Purchase Price"), upon presentation and surrender of this
Right Certificate with the Form of Election to Purchase duly executed.  The
number of Rights evidenced by this Right Certificate (and the number of
Preferred Shares which may be purchased upon exercise thereof) set forth above,
and the Purchase Price per share set forth above, are the number and Purchase
Price as of December 11, 1996, based on the Preferred Shares as constituted at
such date.

     As provided in the Rights Agreement, the Purchase Price and the number of
one one-hundredths of a Preferred Share which may be purchased upon the exercise
of Rights evidenced by this Right Certificate are subject to modification and
adjustment upon the occurrence of certain events.

                                      A-1
<PAGE>
 
     The Right Certificate is subject to all the terms, provisions and
conditions of the Rights Agreement, which terms, provisions and conditions are
hereby incorporated herein by reference and to which Rights Agreement reference
is hereby made for a full description of the rights, limitations of rights,
obligations, duties and immunities hereunder of the Rights Agent, the Company
and the holders of the Right Certificates. Copies of the Rights Agreement are on
file at the principal executive offices of the Company and the Corporate Trust
Office of the Rights Agent.

     This Right Certificate, with or without other Right Certificates, upon
surrender hereof at the Corporate Trust Office of the Rights Agent, may be
exchanged for another Right Certificate or Right Certificates of like tenor
evidencing Rights entitling the holder to purchase a like aggregate number of
Preferred Shares as the Rights evidenced by the Right Certificate or Right
Certificates surrendered shall have entitled such holder to purchase.  If this
Right Certificate shall be exercised in part, the holder shall be entitled to
receive upon surrender hereof another Right Certificate or Right Certificates
for the number of whole Rights not exercised.

     Subject to the provisions of the Rights Agreement, the Rights evidenced by
this Certificate (i) may be redeemed by the Company at a redemption price of one
cent ($0.01) per Right or (ii) may be mandatorily redeemed and exchanged by the
Company in whole or in part for Preferred Shares or shares of the Company's
common stock, par value $2.50 per share.

     No fractional Preferred Shares will be issued upon the exercise of any
Right or Rights evidenced hereby (other than fractions which are integral
multiples of one one-hundredth of a Preferred Share, which may, at the election
of the Company, be evidenced by depositary receipts), but in lieu thereof a cash
payment will be made as provided in the Rights Agreement.

     No holder of this Right Certificate shall be entitled to vote or receive
dividends or be deemed for any purpose the holder of the Preferred Shares or of
any other securities of the Company which may at any time be issuable on the
exercise hereof, not shall anything contained in the Rights Agreement or herein
be construed to confer upon the holder hereof, as such, any of the rights of a
stockholder of the Company, including without limitation any right to vote for
the election of directors or upon any matter submitted to stockholders at any
meeting thereof, to give or withhold consent to any corporate action, to receive
notice of meetings or other actions affecting stockholders (except as provided
in the Rights Agreement) or to receive dividends or subscription rights, until
the Right or Rights evidenced by this Right Certificate shall have been
exercised or such Right or Rights shall have been mandatorily redeemed and
exchanged by the Company as provided in the Rights Agreement.

     This Right Certificate shall not be entitled to any benefit under the
Rights Agreement or be valid or obligatory for any purpose until it shall have
been authenticated by the Rights Agent.

                                      A-2
<PAGE>
 
     WITNESS the facsimile signatures of the proper officers of the Company and
its corporate seal.
Dated as of ____________________, 19__.

ATTEST:                                HALLIBURTON COMPANY


____________________                   By: __________________________________
________
     Secretary

Authentication:

This is one of the Right Certificates referred to in the within-mentioned Rights
Agreement.

ChaseMellon Shareholder Services, L.L.C. as Rights Agent


By: ______________________________
         Authorized Signature

                                      A-3
<PAGE>
 
                  [Form of Reverse Side of Right Certificate]


                              FORM OF ASSIGNMENT
                              ------------------

               (To be executed by the registered holder if such
               holder desires to transfer the Right Certificate)


          FOR VALUE RECEIVED __________________________ hereby sells, assigns
and transfers unto ___________________________________________________________
______________________________________________________________________________
                 (Please print name and address of transferee)

_______________________________________________________________________________
this Right Certificate, together with all right, title and interest therein, and
does hereby irrevocably constitute and appoint ____________________ Attorney, to
transfer the within Right Certificate on the books of the within-named
corporation, with full power of substitution.


Dated:  ____________________, 19___.


                                  ___________________________________________
                                  Signature

Signature Guaranteed:

     Signatures must be guaranteed by a member firm of a registered national
securities exchange, a member of the National Association of Securities Dealers,
Inc., or a commercial bank or trust company having an office or correspondent in
the United States of America.

_______________________________________________________________________________
                   (To be executed if a statement is correct)

The undersigned hereby certifies that the Rights evidenced by this Right
Certificate are not beneficially owned by an Acquiring Person or an Affiliate or
Associate thereof (as defined in the Rights Agreement).

                                  _____________________________________________
                                  Signature

           [Form of Reverse Side of Right Certificate -- continued]

                                      A-4
<PAGE>
 
                         FORM OF ELECTION TO PURCHASE
                         ----------------------------

                     (To be executed if holder desires to
                        exercise the Right Certificate)


To:  HALLIBURTON COMPANY

          The undersigned hereby irrevocably elects to exercise _______________
Rights represented by this Right Certificate to purchase the Preferred Shares
(or other securities) issuable upon the exercise of such Rights and requests
that certificates for such Preferred Shares (or for such other securities) be
issued in the name of:

Please insert social security
or other identifying number:___________________________________________________

_______________________________________________________________________________
                        (Please print name and address)

_______________________________________________________________________________

If such number of Rights shall not be all the Rights evidenced by this Right
Certificate, a new Right Certificate for the balance remaining of such Rights
shall be registered in the name of and delivered to:

Please insert social security
or other identifying number:___________________________________________________

_______________________________________________________________________________
                        (Please print name and address)

_______________________________________________________________________________


Dated:_______________, 19___           ________________________________________
                                       Signature

           [Form of Reverse Side of Right Certificate -- continued]


Signature Guaranteed:

                                      A-5
<PAGE>
 
     Signatures must be guaranteed by a member firm of a registered national
securities exchange, a member of the National Association of Securities Dealers,
Inc., or a commercial bank or trust company having an office or correspondent in
the United States.


_______________________________________________________________________________

                    (To be executed if statement is correct)

The undersigned hereby certifies that the Rights evidenced by this Right
Certificate are not beneficially owned by an Acquiring Person or an Affiliate or
Associate thereof (as defined in the Rights Agreement).


                                       ________________________________________


_______________________________________________________________________________


                                    NOTICE
                                    ------

     The signature in the foregoing Forms of Assignment and Election must
correspond to the name as written upon the face of this Right Certificate in
every particular, without alteration or enlargement or any change whatsoever.

     If the certification set forth above in the Form of Assignment or the Form
of Election to Purchase, as the case may be, is not completed, the Company and
the Rights Agent will deem the beneficial owner of the Rights evidenced by this
Right Certificate to be an Acquiring Person or an Affiliate or Associate thereof
(as defined in the Rights Agreement) and such Assignment or Election will not be
honored.

                                      A-6
<PAGE>

                                  Exhibit B
 
                          CERTIFICATE OF DESIGNATION,

                            RIGHTS AND PREFERENCES


                                      OF

                    SERIES A JUNIOR PARTICIPATING PREFERRED
                           STOCK, WITHOUT PAR VALUE

                                      of

                             HALLIBURTON HOLD CO.



     Halliburton Hold Co., a corporation organized and existing under and by
virtue of the General Corporation Law of the State of Delaware, DOES HEREBY
CERTIFY:

     That at a meeting of the Board of Directors of Halliburton Hold Co. ("Hold
Co.") the following resolution, creating a series of two (2) million shares of
Preferred Stock, designated as Series A Junior Participating Preferred Stock was
duly adopted pursuant to the authority granted to and vested in the Board of
Directors of this corporation in accordance with the provisions of its
Certificate of Incorporation:

          RESOLVED, that, pursuant to the authority granted to and vested in the
     Board of Directors of Hold Co. in accordance with the provisions of the
     Certificate of Incorporation of Hold Co., a series of 2,000,000 shares of
     Series A Junior Participating Preferred Stock, without par value, of Hold
     Co. (the "Preferred Shares") be, and hereby is, created, and that the
     designation and amount thereof and the relative rights, preferences and
     limitations thereof (in addition to the provisions set forth in the
     Certificate of Incorporation of Hold Co. which are applicable to the
     Preferred Stock of all series) are as follows:

     I.   Designation and Amount. The shares of such series shall be designated
          -----------------------                                              
as the "Series A Junior Participating Preferred Stock" (the "Junior Preferred
Stock") and the number of shares constituting such series shall be two (2)
million.  Such number of shares may be increased or decreased by resolution of
the Board of Directors; provided, that no decrease shall reduce the number of
                        --------                                             
shares of Junior Preferred Stock to a number less than that of the shares then
outstanding plus the number of shares issuable upon exercise of outstanding
rights, options or warrants or upon conversion of outstanding securities issued
by the corporation.
<PAGE>
 
     II.  Dividends and Distributions.
          ----------------------------

          (A)  Subject to the prior and superior rights of the holders of any
     shares of any series of Preferred Stock ranking prior and superior to the
     shares of Junior Preferred Stock with respect to dividends, the holders of
     shares of Junior Preferred Stock, in preference to the holders of common
     stock, $2.50 par value, of the corporation (the "Common Stock") and of any
     other stock ranking junior (as to dividends) to Junior Preferred Stock,
     shall be entitled to receive, when, as and if declared by the Board of
     Directors out of funds legally available for the purpose, cumulative
     quarterly dividends payable in cash or in kind, as hereinafter provided, on
     the last day of March, June, September and December in each year (each such
     date being referred to herein as a "Quarterly Dividend Payment Date"),
     commencing on the first Quarterly Dividend Payment Date after the first
     issuance of a share or fraction of a share of Junior Preferred Stock, in an
     amount per share (rounded to the nearest cent) equal to the greater of (a)
     $1.00 (payable in cash) or (b) subject to the provision for adjustment
     hereinafter set forth, 100 times the aggregate per share amount (payable in
     cash) of all cash dividends, and 100 times the aggregate per share amount
     (payable in kind) of all non-cash dividends or other distributions, other
     than a dividend payable in shares of Common Stock (by reclassification or
     otherwise), declared on the Common Stock since the immediately preceding
     Quarterly Dividend Payment Date or, with respect to the first Quarterly
     Dividend Payment Date, since the first issuance of any share or fraction of
     a share of Junior Preferred Stock.  If the corporation shall at any time
     declare or pay any dividend on Common Stock payable in shares of Common
     Stock or effect a subdivision or combination of the outstanding shares of
     Common Stock (by reclassification or otherwise), into a greater or lesser
     number of shares of Common Stock, then in each such case the amount to
     which holders of shares of Junior Preferred Stock were entitled immediately
     prior to such event under clause (b) of the preceding sentence shall be
     adjusted by multiplying such amount by a fraction the numerator of which is
     the number of shares of Common Stock outstanding immediately after such
     event and the denominator of which is the number of shares of Common Stock
     that was outstanding immediately prior to such event.

          (B)  The corporation shall declare a dividend or distribution on the
     Junior Preferred Stock as provided in paragraph (A) of this Section
     immediately after it declares a dividend or distribution on the Common
     Stock (other than a dividend payable in shares of Common Stock); provided
     that, if no dividend or distribution shall have been declared on the Common
     Stock during the period between any Quarterly Dividend Payment Date and the
     next subsequent Quarterly Dividend Payment Date, a dividend of $1.00 per
     share on the Junior Preferred Stock shall nevertheless accrue and be
     cumulative on the outstanding shares of Junior Preferred Stock as provided
     in paragraph (C) of this Section.

          (C)  Dividends shall begin to accrue and be cumulative on outstanding
     shares of Junior Preferred Stock from the Quarterly Dividend Payment Date
     next preceding the date of issue of such shares of Junior Preferred Stock,
     unless the date of issue of such 

                                       2
<PAGE>
 
     shares is prior to the record date for the first Quarterly Dividend Payment
     Date, in which case dividends on such shares shall begin to accrue from the
     date of issue of such shares, or unless the date of issue is a Quarterly
     Dividend Payment Date or is a date after the record date for the
     determination of holders of shares of Junior Preferred Stock entitled to
     receive a quarterly dividend and before such Quarterly Dividend Payment
     Date, in either of which events such dividends shall begin to accrue and be
     cumulative from such Quarterly Dividend Payment Date. Accrued but unpaid
     dividends shall not bear interest. Dividends paid on the shares of Junior
     Preferred Stock in an amount less than the total amount of such dividends
     at the time accrued and payable on such shares shall be allocated pro rata
     on a share by share basis among all such shares at the time outstanding.
     The Board of Directors may fix a record date for the determination of
     holders of shares of Junior Preferred Stock entitled to receive payment of
     a dividend or distribution declared thereon, which record date shall be not
     more than 60 days prior to the date fixed for the payment thereof.

     III. Voting Rights.  The holders of shares of Junior Preferred Stock
          --------------                                                 
shall have the following voting rights:

          (A)  Subject to the provision for adjustment hereinafter set forth,
     each share of Junior Preferred Stock shall entitle the holder thereof to
     100 votes on all matters submitted to a vote of the shareholders of the
     corporation.  If the corporation shall at any time declare or pay any
     dividend on Common Stock payable in shares of Common Stock, or effect a
     subdivision or combination of the outstanding shares of Common Stock (by
     reclassification or otherwise) into a greater or lesser number of shares of
     Common Stock, then in each such case the number of votes per share to which
     holders of shares of Junior Preferred Stock were entitled immediately prior
     to such event shall be adjusted by multiplying such number by a fraction
     the numerator of which is the number of shares of Common Stock outstanding
     immediately after such event and the denominator of which is the number of
     shares of Common Stock that were outstanding immediately prior to such
     event.

          (B)  Except as otherwise provided in the Certificate of Incorporation
     or by law, the holders of shares of Junior Preferred Stock and the holders
     of shares of Common Stock shall vote together as one class on all matters
     submitted to a vote of shareholders of the corporation.

     IV.  Certain Restrictions.
          ---------------------

          (A)  Whenever quarterly dividends or other dividends or distributions
     payable on the Junior Preferred Stock as provided in Section II are in
     arrears, thereafter and until all accrued and unpaid dividends and
     distributions, whether or not declared, on shares of Junior Preferred Stock
     outstanding shall have been paid in full, the corporation shall not:

                                       3
<PAGE>
 
          (i)    declare or pay dividends on, make any other distributions on,
                 or redeem or purchase or otherwise acquire for consideration
                 any shares of stock ranking junior (as to dividends) to the
                 Junior Preferred Stock;

          (ii)   declare or pay dividends on or make any other distributions on
                 any shares of stock ranking on a parity (as to dividends) with
                 the Junior Preferred Stock, except dividends paid ratably on
                 the Junior Preferred Stock and all such parity stock on which
                 dividends are payable or in arrears in proportion to the total
                 amounts to which the holders of all such shares are then
                 entitled; or

          (iii)  purchase or otherwise acquire for consideration any shares of
                 Junior Preferred Stock, or any shares of stock ranking on a
                 parity (as to dividends) with the Junior Preferred Stock,
                 except in accordance with a purchase offer made in writing or
                 by publication (as determined by the Board of Directors) to all
                 holders of such shares upon such terms as the Board of
                 Directors, after consideration of the respective annual
                 dividend rates and other relative rights and preferences of the
                 respective series and classes, shall determine in good faith
                 will result in fair and equitable treatment among the
                 respective series or classes.

          (B)  The corporation shall not permit any subsidiary of the
     corporation to purchase or otherwise acquire for consideration any shares
     of stock of the corporation unless the corporation could, under paragraph
     (A) of this Section IV, purchase or otherwise acquire such shares at such
     time and in such manner.

     V.   Reacquired Shares.  Any shares of Junior Preferred Stock purchased or
          ------------------                                                   
otherwise acquired by the corporation in any manner whatsoever shall be retired
and cancelled promptly after the acquisition thereof.  All such shares shall
upon their cancellation become authorized but unissued shares of Preferred Stock
and may be reissued as part of a series of Preferred Stock to be created by
resolution or resolutions of the Board of Directors, subject to the conditions
and restrictions on issuance set forth herein.

     VI.  Liquidation, Dissolution or Winding Up.  Upon any liquidation,
          ---------------------------------------                       
dissolution or winding up of the corporation, no distribution shall be made (1)
to the holders of shares of stock ranking junior (as to amounts payable upon
liquidation, dissolution or winding up) to the Junior Preferred Stock unless,
prior thereto, the holders of Junior Preferred Stock shall have received an
amount per share (rounded to the nearest cent) equal to the greater of (a)
$100.00 per share, or (b) an amount per share, subject to the provision for
adjustment hereinafter set forth, equal to 100 times the aggregate amount to be
distributed per share to holders of Common Stock, plus, in either case, an
amount equal to accrued and unpaid dividends and distributions thereon, whether
or not declared, to the date of such payment, or (2) to the holders of stock
ranking on a parity (as to amounts payable or upon liquidation, dissolution or
winding up) with the Junior Preferred Stock, except distributions made ratably
on the 

                                       4
<PAGE>
 
Junior Preferred Stock and all other such parity stock in proportion to
the total amounts to which the holders of all such shares are entitled upon such
liquidation, dissolution or winding up.  If the corporation shall at any time
declare or pay any dividend on Common Stock payable in shares of Common Stock,
or effect a subdivision or combination of the outstanding shares of Common Stock
(by reclassification or otherwise) into a greater or lesser number of shares of
Common Stock, then in each such case the aggregate amount to which holders of
shares of Junior Preferred Stock were entitled immediately prior to such event
under the provision in clause (1) (b) of the preceding sentence shall be
adjusted by multiplying such amount by a fraction the numerator of which is the
number of shares of Common Stock outstanding immediately after such event and
the denominator of which is the number of shares of Common Stock that were
outstanding immediately prior to such event.

     VII.    Consolidation, Merger, etc.  If the corporation shall enter
             ---------------------------                                
into any consolidation, merger, combination or other transaction in which the
shares of Common Stock are exchanged for or changed into other stock or
securities, cash or any other property, or any combination thereof, then in any
such case the shares of Junior Preferred Stock shall at the same time be
similarly exchanged or changed in an amount per share (subject to the provision
for adjustment hereinafter set forth) equal to 100 times the aggregate amount of
stock, securities, cash or any other property, or any combination thereof, into
which or for which each share of Common Stock is changed or exchanged.  If the
corporation shall at any time declare or pay any dividend on Common Stock
payable in shares of Common Stock, or effect a subdivision or combination of the
outstanding shares of Common Stock (by reclassification or otherwise) into a
greater or lesser number of shares of Common Stock, then in each such case the
amount set forth in the preceding sentence with respect to the exchange or
change of shares of Junior Preferred Stock shall be adjusted by multiplying such
amount by a fraction the numerator of which is the number of shares of Common
Stock outstanding immediately after such event and the denominator of which is
the number of shares of Common Stock that were outstanding immediately prior to
such event.

     VIII.   No Redemption.  The shares of Junior Preferred Stock shall not
             --------------                                                
be redeemable.  So long as any shares of Junior Preferred Stock remain
outstanding, the corporation shall not purchase or otherwise acquire for
consideration any shares of stock ranking junior (either as to dividends or upon
liquidation, dissolution or winding up) to the Junior Preferred Stock unless the
corporation shall substantially concurrently also purchase or acquire for
consideration a proportionate number of shares of Junior Preferred Stock.

     IX.     Rank.  Except as otherwise provided in its Certificate of
             -----                                                    
Incorporation, the corporation may authorize or create any series of Preferred
Stock ranking prior to or on a parity with the Junior Preferred Stock as to
dividends or as to distribution of assets upon liquidation, dissolution or
winding up.

     X.      Amendment.  The Certificate of Incorporation of the corporation 
             ---------
shall not be amended in any manner which would materially alter or change the
powers, preferences or special rights of the Junior Preferred Stock so as to
affect them adversely without the affirmative vote of the holders of a majority
of the outstanding shares of Junior Preferred Stock, voting together as a single
class.

                                       5
<PAGE>
 
     The foregoing resolution was adopted by the Board of Directors of the
corporation, pursuant to the authority vested in it by the Certificate of
Incorporation of the corporation, at a meeting of the Board of Directors duly
held on the ___ day of ________, 1996.

     IN WITNESS WHEREOF, this Certificate has been executed on behalf of the
Corporation by its ______________ this ___ day of ________, 1996.

                               HALLIBURTON HOLD CO.



                                By:_________________

                                   _________________

                                   _________________


                                       6

<PAGE>
 
                                                                     EXHIBIT 8.1

(713) 758-2192                                                    (713) 615-5210

                                December 4, 1996


Halliburton Company
3600 Lincoln Plaza
500 North Akard Street
Dallas, Texas 75201-3391

     Re: Halliburton Company Reorganization

Gentlemen:

     You have requested our opinion with respect to certain federal income tax
consequences of an internal reorganization of Halliburton Company
("Halliburton") involving, among other things, (i) the implementation of a new
holding company structure for the Halliburton group of companies (the "Holding
Company Reorganization") and (ii) the distribution by Halliburton of the stock
of four subsidiaries to Halliburton Delaware, Inc. ("HDI"), as hereinafter
described (the "Spinoffs").  Our opinion is based upon (i) the Agreement and
Plan of Reorganization (the "Reorganization Agreement") to be entered into among
Halliburton, Halliburton Hold Co. ("Holdco") and Halliburton Merge Co. ("Merger
Sub"), (ii) the financial statements and other information you furnished to us
with respect to Halliburton and its subsidiaries, and (iii) the facts,
representations, law and analysis hereinafter set forth./1/

     As set forth in detail below, in our opinion, the Holding Company
Reorganization will constitute a tax-free reorganization under section 368(a) of
the Internal Revenue Code of 1986, as amended,/2/ and the Spinoffs will be tax-
free under section 355 of the Code.  As a result, no gain or loss will be
recognized for federal income tax purposes by Halliburton, HDI or the
stockholders of Halliburton by reason of the Holding Company Reorganization or
the Spinoffs.

- ------------------
     /1/ Capitalized terms used but not defined herein have the meanings
ascribed to them in the Reorganization Agreement.

     /2/ Hereinafter referred to as the "Code". All section references herein
are to the Code unless otherwise noted.
<PAGE>
 
Halliburton Company
Page 2
December 4, 1996
                                     FACTS

THE PARTIES

HALLIBURTON.  Halliburton is a Delaware corporation with its principal office at
3600 Lincoln Plaza, 500 North Akard Street, Dallas, Texas 75201-3391.
Halliburton maintains its books and records on an accrual basis of accounting
and its taxable year ends on December 31.  Halliburton is the common parent of
an affiliated group of corporations that files consolidated federal income tax
returns. Halliburton's common stock is widely-held and traded on the New York
Stock Exchange and certain foreign exchanges.

          Halliburton owns all of the outstanding stock of the following
subsidiaries (individually, a "Distributed Subsidiary" and, collectively, the
"Distributed Subsidiaries"): (i) Brown & Root Holdings, Inc. ("BRHI"), (ii)
Halliburton International, Inc. ("HII"), (iii) Landmark Graphics Corporation
("Landmark"), and (iv) Halliburton Affiliates Corporation ("HAC").

          For each of the five years preceding the Spinoffs, Halliburton has
been directly engaged, and through its subsidiaries indirectly engaged, in the
energy services business, and through its subsidiaries, indirectly engaged in
the engineering and construction services business.

          Halliburton's energy services business is conducted through
Halliburton Energy Services Division (a division of Halliburton), foreign
branches of Halliburton, certain domestic and foreign subsidiaries of
Halliburton and other legal entities in which Halliburton has an interest
(sometimes collectively referred to herein as the "Energy Services Group").  The
Energy Services Group offers a wide range of services and products to provide
integrated solutions to customers in the exploration, development and production
of oil and natural gas.  The Energy Services Group operates worldwide serving
major oil and gas companies, independent operators and national oil and gas
companies with certain of its operations being conducted by and through domestic
and foreign subsidiaries including HII (a first-tier subsidiary of Halliburton)
and certain of its subsidiaries.  The services and products provided by the
Energy Services Group include cementing, casing equipment and water control
services; completion and production products; directional drilling systems,
measurement while drilling, logging while drilling, and mud logging services;
open and cased hole logging and perforating services and logging and perforating
products; well testing, reservoir description and evaluation services, tubing
conveyed well completion systems and reservoir engineering services;
stimulation, sand control services and coiled tubing services; and wellhead
pressure control equipment, well control, hydraulic workover and downhole video
services.

          Halliburton's engineering and construction business is conducted
through another group of Halliburton domestic and foreign subsidiaries and other
entities in which Halliburton owns an indirect interest, headed primarily by
BRHI and including certain subsidiaries of HII (sometimes collectively referred
to herein as the "Engineering and Construction Services Group").  The
Engineering and Construction Services Group provides engineering and
construction services for
<PAGE>
 
Halliburton Company
Page 3
December 4, 1996

both land and marine activities throughout the world.  Included are technical
and economic feasibility studies, site evaluation, licensing, conceptual design,
process design, detailed engineering, procurement, project and construction
management; construction and start-up assistance of electric utility plants,
chemical and petrochemical plants, refineries, pulp and paper mills, metal
processing plants, highways and bridges; subsea construction, fabrication and
installation of subsea pipelines, offshore platforms, production platform
facilities, marine engineering and other marine related projects; contract
maintenance and operations and maintenance services for both industry and
government; engineering and environmental consulting and waste management
services for industry, utilities and government; and remedial engineering and
construction services for hazardous waste sites.

          Halliburton's authorized capital stock consists of (i) 200,000,000
shares of common stock, par value $2.50 per share ("Halliburton Common Stock"),
of which 125,258,208 shares were issued and outstanding as of November 30, 1996,
and (ii) 5,000,000 shares of preferred stock, par value $1.00 per share, of
which none is issued and outstanding.  Halliburton also has outstanding
preferred share purchase rights ("Halliburton Rights") each of which entitle the
holder to purchase from Halliburton 1/100 of a share of Series A Junior
Participating Preferred Stock exercisable solely upon the occurrence of certain
takeover-type events.  The Halliburton Rights are similar to the rights
described in Rev. Rul. 90-11, 1990-1 C.B. 10.

HOLDCO.  Holdco is a wholly-owned subsidiary of Halliburton, incorporated in
Delaware on November 7, 1996 for the purpose of acting as a holding company for
the Halliburton group of companies.  Prior to the Holding Company
Reorganization, Holdco will have no significant assets or liabilities.  The
issued and outstanding capital stock of Holdco consists of 1,000 shares of
common stock, par value $2.50 per share, all of which are directly owned by
Halliburton.

HDI.  HDI is a wholly-owned subsidiary of Holdco, incorporated in Delaware on
November 7, 1996.  Prior to the Holding Company Reorganization, HDI will have no
significant assets or liabilities.  The issued and outstanding capital stock of
HDI consists of 1,000 shares of common stock, par value $1.00 per share, all of
which are directly owned by Holdco.

MERGER SUB.  Merger Sub is a wholly-owned subsidiary of HDI, incorporated in
Delaware on November 7, 1996 for the sole purpose of the Holding Company
Reorganization.  Prior to the Holding Company Reorganization, Merger Sub will
have no significant assets or liabilities.  The issued and outstanding capital
stock of Merger Sub consists of 1,000 shares of common stock, par value $1.00
per share, all of which are directly owned by HDI.

HAC.  HAC is a wholly-owned subsidiary of Halliburton, incorporated in Delaware
on November 7, 1996.  Prior to the Holding Company Reorganization, HAC will have
no significant assets or liabilities.  The issued and outstanding capital stock
of HAC consists of 1,000 shares of common stock, par value $1.00 per share, all
of which are directly owned by Halliburton.
<PAGE>
 
Halliburton Company
Page 4
December 4, 1996

THE HOLDING COMPANY REORGANIZATION

          As noted above, Halliburton conducts its energy services business
through its Energy Services Group, comprised of Halliburton Energy Services
Division, certain foreign branches, first or lower tier foreign and domestic
subsidiaries and certain other entities in which Halliburton owns an interest.
Its other businesses, comprising its Engineering and Construction Services
Group, are conducted in other corporations which are first or lower tier
domestic or foreign subsidiaries of Halliburton and in certain other legal
entities in which Halliburton or such subsidiaries own an interest.  Thus,
Halliburton functions both as an operating company with respect to Halliburton
Energy Services Division and Halliburton's foreign branches, and as a holding
company with respect to other parts of its Energy Services Group and its
Engineering and Construction Services Group. For the business reasons set forth
below, management of Halliburton has determined that it would be advisable and
in the best interests of Halliburton and its subsidiaries to implement a new
holding company structure.  The holding company structure will be accomplished
as follows:

          (i) Merger Sub will merge with and into Halliburton pursuant to the
     provisions of the General Corporation Law of the State of Delaware (the
     "DGCL") hereinafter described (the "Halliburton Merger") pursuant to which
     Halliburton would be the surviving corporation, and

          (ii) pursuant to the Halliburton Merger, each share of Halliburton
     Common Stock issued at the Effective Time of the Halliburton Merger would
     be converted into one share of common stock of Holdco, par value $2.50 per
     share ("Holdco Common Stock").

As a result of the Halliburton Merger, (i) each shareholder of Halliburton
immediately prior to the Effective Time of the Halliburton Merger will own,
immediately after the Effective Time of the Halliburton Merger, a number of
shares of Holdco Common Stock exactly equal to the number of shares of
Halliburton Common Stock held immediately prior to the Halliburton Merger, (ii)
Holdco will own all of the issued and outstanding stock of HDI; and (iii) HDI
will own all of the issued and outstanding stock of Halliburton.  Holdco will
also have outstanding rights equivalent to the Halliburton Rights.  Holdco will
assume the public indebtedness and certain other obligations of Halliburton.

          The Halliburton Merger will be accomplished pursuant to section 251(g)
of the DGCL which permits a Delaware corporation to reorganize as a holding
company without stockholder approval. Section 251(g) eliminates the requirement
for a stockholder vote on such a merger by containing several provisions
designed to ensure that the rights of stockholders are not changed by or as a
result of the merger.  Appraisal rights are not available to dissenting
stockholders in a merger that qualifies under section 251(g) of the DGCL.

          Thus, in the Halliburton Merger (i) shareholder approval will not be
sought nor is it required under section 251(g) of the DGCL; (ii) under section
262(b) of the DGCL, holders of Halliburton
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Halliburton Company
Page 5
December 4, 1996

Common Stock will not be entitled to dissenters' appraisal rights; (iii) the
Halliburton Common Stock will be automatically converted into Holdco Common
Stock evidencing the same proportional interests in Holdco; (iv) the businesses
conducted by Halliburton and its affiliates will not change as a result of the
Halliburton Merger; (v) the board of directors of Holdco will be identical to
the board of directors of Halliburton that existed immediately prior to the
Halliburton Merger; (vi) the rights and interests of the holders of Holdco
Common Stock will be substantially the same as those of holders of Halliburton
Common Stock immediately prior to the Halliburton Merger; (vii) Holdco will be a
newly-formed corporation and, immediately prior to the Halliburton Merger, will
have no significant assets or liabilities; (viii) immediately following
consummation of the Halliburton Merger, on a consolidated basis Holdco will have
substantially the same assets and liabilities as Halliburton had prior to
consummation of the Halliburton Merger; and (ix) the Holdco Common Stock will be
issued solely as part of a reorganization of Halliburton into a holding company
structure.

          Halliburton holds, in its treasury, shares of Halliburton Common Stock
(the "Halliburton Treasury Shares"); as of November 30, 1996 there were
4,012,502 Halliburton Treasury Shares. Pursuant to section 251(g) of the DGCL
the capital structure of Holdco following the Halliburton Merger will mirror
that of Halliburton immediately prior to the Halliburton Merger, such that
Holdco similarly will hold in its treasury a number of shares of Holdco Common
Stock immediately following the Halliburton Merger (the "Holdco Treasury
Shares") equal to the number of Halliburton Treasury Shares immediately prior to
the Merger.  This will be accomplished by the contribution by Halliburton of the
Halliburton Treasury Shares to Holdco immediately prior to the Halliburton
Merger.

THE SPINOFFS

          Halliburton has determined that following the Halliburton Merger the
Distributed Subsidiaries should be owned directly by HDI in order to permit HDI
to function as the company which holds the stock of certain of the principal
subsidiaries of Halliburton and for other business reasons which are detailed in
the section which follows entitled "Business Purpose for the Holding Company
Reorganization and the Spinoffs."  Accordingly, following the Halliburton
Merger, (i) Halliburton will contribute the stock of certain first-tier
controlled foreign corporations ("CFCs") to HAC in exchange for cash in the
amount of $1,000, and (ii) Halliburton will distribute to HDI all of the
outstanding stock of the Distributed Subsidiaries.

          Thus, following the distribution of the Distributed Subsidiaries to
HDI, Halliburton's assets will be comprised of the domestic assets of
Halliburton Energy Services Division, certain foreign branch assets, and the
stock of certain domestic and foreign subsidiaries whose operations are related
to the Halliburton Energy Services Division.
<PAGE>
 
Halliburton Company
Page 6
December 4, 1996

RELATED TRANSACTIONS

          Prior to or in connection with the Holding Company Reorganization and
the Spinoffs, the following related transactions will occur:
 
          (i)    BRHI will contribute its stock in Halliburton Holdings, Inc.
                 ("HHI") to Brown & Root, Inc. ("B&R").

          (ii)   Halliburton will contribute its stock in HHI to HII.
 
          (iii)  Pursuant to a certificate of merger filed with the Halliburton
                 will change its name to Halliburton Secretary of State of
                 Delaware, Energy Services, Inc.

          (iv)   Pursuant to the filing of an amended certificate of
                 incorporation, Holdco will change its name to Halliburton
                 Company immediately after the Effective Time.
                 
          (v)    Following the consummation of the Holding Company
                 Reorganization, Halliburton may distribute cash to HDI, which
                 in turn may distribute such cash to Holdco. Following such
                 distribution, Holdco may make a loan of an equivalent amount of
                 cash to Halliburton.                 

ACTIVE BUSINESSES

BRHI.  BRHI was incorporated in Delaware on December 14, 1989 and has its
principal office at 4100 Clinton Drive, Houston, Texas 77020.  BRHI, through its
subsidiaries, provides engineering and construction services for both land and
marine activities throughout the world.

HII.  HII was incorporated in Delaware on September 30, 1991 and has its
principal office at 3600 Lincoln Plaza, 500 North Akard Street, Dallas, Texas
75201-3391.  HII provides energy services and engineering and construction
services throughout the world.

LANDMARK.  Landmark was incorporated in Delaware on June 29, 1996 and has its
principal office at 15150 Memorial Drive, Houston, Texas 77070-4304.  On October
4, 1996,  the former Landmark Graphics Corporation ("Old Landmark") merged into
Landmark pursuant to a reorganization described in sections 368(a)(1)(A) and
368(a)(2)(D) of the Code.  Following the merger of Old Landmark into Landmark,
Landmark continued the historic business of Old Landmark.

          Landmark offers an extensive line of integrated software applications
to the oil and gas exploration, development and production industry for seismic
processing, three dimensional and two dimensional seismic interpretations,
geologic and petrophysical interpretation, including reservoir analysis, mapping
and modeling of geophysical information, well log and production analysis,
drilling and production engineering and data management.  In addition to
designing, producing and
<PAGE>
 
Halliburton Company
Page 7
December 4, 1996

marketing software products, Landmark is a value-added reseller of workstations
and other hardware and provides a range of services related to its products,
including software and systems support and training, systems configuration and
network design and data loading and management.

BUSINESS PURPOSE FOR THE HOLDING COMPANY REORGANIZATION AND THE SPINOFFS

          Management of Halliburton believes that the full implementation of a
course of action that includes the Holding Company Reorganization and the
Spinoffs will provide numerous benefits to Halliburton and its subsidiaries,
taken as a whole, and that a number of valid business reasons for taking such
actions exist, among which are:

          (a) Reduction of state franchise and income taxes on an ongoing basis,
estimated to result in as much as $4 million annual savings.

          (b) Creation of an organizational structure where major components of
the Energy Services Group and the Engineering and Construction Services Group
(e.g., Halliburton, BRHI, HII, Landmark and HAC) are on structural parity
(rather than lower level subsidiaries of Halliburton).

          (c) Clarification of the role of the ultimate parent company as the
provider of consolidated management, financing, investor relations and certain
other staff services to the organization as a whole.

          (d) Elimination of the need for the public board of directors to take
numerous actions of the nature required for the operations of Halliburton Energy
Services Division and Halliburton's numerous foreign branches, the effect of
which will allow the board of directors of the ultimate parent to concentrate on
high level policy and other management issues while at the same time
facilitating the day to day operations of Halliburton Energy Services Division
and foreign branches of Halliburton through actions of a subsidiary board of
directors.

          (e) Providing through HDI and Holdco structural flexibility in
planning for, and structuring or restructuring of, the overall Halliburton group
of companies to meet business needs in present and future years.

          (f) Financing alternatives are expected to be improved by the holding
company structure in that planning of financings best suited to the varying
needs and circumstances of Halliburton and the Distributed Subsidiaries should
be facilitated.

          (g) A reduction in exposure of the stock of the Distributed
Subsidiaries to liabilities of Halliburton.

          (h) A reduction in exposure of Halliburton to liabilities of the 
Distributed Subsidiaries.
<PAGE>
 
Halliburton Company
Page 8
December 4, 1996

                                REPRESENTATIONS

          1.  No indebtedness will exist between any of the Distributed
Subsidiaries and Halliburton except for intercompany accounts which arise in the
ordinary course of business and are not evidenced by a written instrument.

          2.  No part of the Distributed Subsidiaries stock to be distributed by
Halliburton in the Spinoffs will be received by HDI in any capacity other than
that of a shareholder of Halliburton.

          3.  The five years of financial information supplied to us with
respect to each active business of Halliburton and the Distributed Subsidiaries,
as defined in section 355(b) of the Code (an "Active Business"), is
representative of the present operations of each Active Business, and there have
been no substantial operational changes since the date of the last financial
statement, except for the addition or deletion of certain products or services
lines of business.

          4.  Following the Spinoffs, at least 90 percent of the fair market
value of the gross assets of BRHI and HAC, respectively, will consist of stock
and securities of 80 percent or more owned subsidiaries that are directly
engaged in an Active Business.  For purposes of this representation, a
subsidiary corporation is only treated as being engaged in the active conduct of
a trade or business if at least 5 percent of its gross assets are utilized in an
Active Business.

          5.  Following the Spinoffs, at least 5 percent of the fair market
value of the gross assets of each of Halliburton, Landmark, and HII,
respectively, will be directly utilized in an Active Business.

          6.  Following the Spinoffs, Halliburton and the Distributed
Subsidiaries will each continue the active conduct of their respective
businesses, independently and with their separate employees.

          7.  The Holding Company Reorganization and the Spinoffs are motivated
and carried out to accomplish real and substantial non-Federal tax purposes
germane to the business of Halliburton and the Distributed Subsidiaries.

          8.  There is no plan or intention by HDI to sell, exchange, or
otherwise dispose of any of the shares of the Distributed Subsidiaries stock
received in the Spinoffs or shares of Halliburton stock following the Spinoffs.

          9.  There is no plan or intention by either Halliburton or any
Distributed Subsidiary, directly or through any subsidiary, to purchase any of
its outstanding stock following the Spinoffs.

          10.  There is no plan or intention to liquidate either Halliburton or
any Distributed Subsidiary, to merge either Halliburton or any Distributed
Subsidiary with any other corporation, or,
<PAGE>
 
Halliburton Company
Page 9
December 4, 1996

except for cash dividends, to sell or otherwise dispose of the assets of either
Halliburton or any Distributed Subsidiary, after the Spinoffs, except in the
ordinary course of business.
 
          11.  The total adjusted basis and the fair market value of the assets
transferred to a Distributed Subsidiary by Halliburton each equals or exceeds
the sum of any liabilities assumed by the Distributed Subsidiary plus any
liabilities to which the transferred assets are subject.  Any liabilities
assumed and any liabilities to which the transferred assets are subject were
incurred in the ordinary course of business and are associated with the assets
being transferred.

          12.  Payments made in connection with all continuing transactions
between Halliburton and a Distributed Subsidiary will be for fair market value
based on terms and conditions that would be arrived at by the parties if
bargaining at arm's length.

          13.  Less than 80 percent of the total assets of Halliburton are held
for investment.  For purposes of this representation Halliburton shall be
treated as owning directly the assets of its more than 50 percent owned
subsidiaries.

          14.  Halliburton, the Distributed Subsidiaries and HDI will each pay
their own expenses, if any, incurred in connection with the Spinoffs.

          15.  To the best of the knowledge of the management of Halliburton,
there is no plan or intention on the part of any of the shareholders of
Halliburton to sell, exchange or otherwise dispose of a number of shares of
Holdco Common Stock to be received in the Halliburton Merger that would reduce
the Halliburton shareholders' ownership of Holdco Common Stock to a number of
shares having a value, as of the Effective Time, of less than 50 percent of the
value of all Halliburton Common Stock outstanding immediately prior to the
Effective Time.

          16.  Halliburton has no plan or intention to issue additional shares
of its stock that would result in HDI's owning less than 80 percent of the
outstanding stock of Halliburton.


          In addition to the facts and representations set forth above, our
opinion is conditioned upon our understanding that the transactions will be
carried out as described herein and that there are no other agreements,
arrangements, or understandings between any of Halliburton, the Distributed
Subsidiaries, or HDI other than those described or referenced herein.
<PAGE>
 
Halliburton Company
Page 10
December 4, 1996

                               LAW AND ANALYSIS
 
THE HOLDING COMPANY RESTRUCTURING UNDER SECTION 368(A)(1)(B)

          Section 368(a)(1)(B) of the Code defines a "reorganization" to include
the acquisition by one corporation, solely for all or part of the voting stock
of a corporation which is in control of such acquiring corporation, of stock of
another corporation, if immediately after the acquisition, the acquiring
corporation is in control of such other corporation.

          Section 368(b) of the Code provides that the term "a party to a
reorganization" includes both corporations, in the case of a reorganization
resulting from the acquisition by one corporation of stock or properties of
another, and that in the case of a reorganization in which the acquisition
consideration is the stock of a corporation which controls the acquiring
corporation, also includes the controlling corporation.  Section 368(c) provides
that the term "control" means the ownership of stock possessing at least 80
percent of the total combined voting power of all classes of stock entitled to
vote and at least 80 percent of the total number of shares of all other classes
of stock of the corporation.

          Treas. Reg. (S) 1.368-1(b) provides that requisite to a reorganization
under the Code are a continuity of the business enterprise under the modified
corporate form and a continuity of interest therein on the part of those persons
who, directly or indirectly, were the owners of the enterprise prior to the
reorganization.

          Treas. Reg. (S) 1.368-1(d) provides that continuity of business
enterprise requires that the acquiring corporation either (i) continue the
historic business of the acquired corporation or (ii) use a significant portion
of the acquired corporation's historic business assets in a business, and that
the continuity of business enterprise requirement is satisfied if the acquiring
corporation continues the acquired corporation's historic business.

          Section 354(a)(1) of the Code provides that no gain or loss shall be
recognized if stock or securities in a corporation a party to a reorganization
are, in pursuance of the plan of reorganization, exchanged solely for stock or
securities in such corporation or in another corporation a party to the
reorganization.

          Section 358(a)(1) of the Code provides that in the case of an exchange
to which section 354 applies, the basis of the property permitted to be received
under such section without the recognition of gain or loss shall be the same as
that of the property exchanged.

          Section 1223(1) of the Code provides in part that in determining the
period for which the taxpayer has held property received in an exchange, there
shall be included the period for which he held the property exchanged if the
property has, for the purpose of determining gain or loss from a sale or
exchange, the same basis in whole or in part in his hands as the property
exchanged and the 
<PAGE>
 
Halliburton Company
Page 11
December 4, 1996

property exchanged at the time of such exchange was a capital asset as defined 
in section 1221 of the Code.

          Section 361(a) of the Code provides that no gain or loss shall be
recognized to a corporation if such corporation is a party to a reorganization
and exchanges property, in pursuance of the plan of reorganization, solely for
stock or securities in another corporation a party to the reorganization.

          Section 362 of the Code provides that the acquiring corporation's
basis of property acquired in a reorganization equals the basis of such property
in the hand of the transferor immediately prior to the reorganization.  Treas.
Reg. (S) 1.1502-31, however, provides that where a corporation acquires stock of
a "common parent" in a reorganization that constitutes a "group structure
change," the acquiring corporation's basis in the stock of the acquired
corporation is determined by reference to the "net asset basis" of the common
parent rather than under section 362.  A "group structure change" is defined in
Treas. Reg. (S) 1.1502-33(f)(1) to include a transaction such as the Halliburton
Merger where a new corporation succeeds another corporation as the common parent
of a consolidated group.

THE SPINOFFS DISTRIBUTIONS UNDER SECTION 355

          Section 355(a)(1) of the Code provides that if (i) a distributing
corporation distributes to a shareholder stock of a corporation which it
controls immediately before the distribution; (ii) as part of the distribution,
the distributing corporation distributes an amount of stock in the controlled
corporation constituting "control" within the meaning of section 368(c) of the
Code; (iii) the requirements of section 355(b) of the Code, relating to active
businesses, are satisfied; and (iv) the transaction was not used principally as
a device for the distribution of the earnings and profits of the distributing
corporation, the controlled corporation or both, then no gain or loss shall be
recognized to (and no amount shall be includible in the income of) such
shareholder on the receipt of such stock.  Section 355(a)(2) of the Code
provides that section 355(a)(1) shall be applied without regard to whether or
not the distribution is pro rata with respect to all of the shareholders of the
distributing corporation and whether or not the shareholders surrender stock in
the distributing corporation.  In addition to the foregoing statutory
requirements, the transaction must be carried out for one or more valid
corporate business purposes and must meet continuity of interest requirements
generally applicable to tax-free reorganizations.  See Treas. Reg. (S) 1.355-
2(b) and (c).

          Section 358(a)(1) of the Code provides that in the case of an exchange
to which section 355 applies, the basis of the property permitted to be received
under section 355 without the recognition of gain or loss shall be the same as
that of the property exchanged.  Section 358(c) provides that for this purpose a
distribution to which section 355 applies shall be treated as an exchange and
the stock of the distributing corporation shall be treated as surrendered and
received back in the exchange.  Section 358(b) provides that the basis of the
property exchanged shall be 
<PAGE>
 
Halliburton Company
Page 12
December 4, 1996

allocated among the property permitted to be received without the recognition of
gain or loss and the stock of the distributing corporation which is retained.
Treas. Reg. (S) 1.358-2(a)(2) provides that such allocation shall be made in
proportion to the fair market value of each.

          Section 1223(1) of the Code provides in part that in determining the
period for which the taxpayer has held property received in an exchange, there
shall be included the period for which he held the property exchanged if the
property has, for the purpose of determining gain or loss from a sale or
exchange, the same basis in whole or in part in his hands as the property
exchanged and the property exchanged at the time of such exchange was a capital
asset as defined in section 1221 of the Code.

          Active Business Requirement

          Section 355(b)(1)(A) of the Code provides that section 355(a) shall
apply to the distribution of stock of a controlled corporation only if the
distributing corporation and the controlled corporation are engaged immediately
after the distribution in the active conduct of a trade or business.  Section
355(b)(2) of the Code provides, in part, that a corporation is treated as
engaged in the active conduct of a trade or business if (i) that corporation is
engaged in the active conduct of a trade or business, (ii) such trade or
business has been actively conducted throughout the five-year period ending on
the date of the distribution, (iii) such trade or business was not acquired
within such five-year period in a transaction in which gain or loss was
recognized in whole or in part, and (iv) control of a corporation which was
conducting such trade or business was not acquired by any distributee
corporation directly (or through one or more corporations) within such five-year
period in a transaction in which gain or loss was recognized in whole or in
part.

          Under section 355(b)(2), a corporation will be treated as engaged in
the active conduct of a trade or business only if that corporation is itself
engaged in the active conduct of a trade or business,/3/ or substantially all of
its assets consist of stock or securities of a corporation or corporations
controlled by it (immediately after the distribution) each of which is so
engaged. Treas. Reg. (S) 1.355-3(b)(1).  The Service has interpreted the phrase
"substantially all" as requiring that 90 percent of the fair market value of the
gross assets of a corporation following a spinoff consist of stock and
securities in controlled corporations engaged in active businesses.  See Section
3.04 of Rev. Proc. 77-37, 1977-2 C.B. 568 and Section 4.03(4) of Rev. Proc. 86-
41, 1986-2 C.B. 716.  In Rev. Rul. 74-382, 1974-2 C.B. 120, the Service ruled
that a holding company satisfied theactive trade or business requirement where
its sole asset was all of the stock of a subsidiary 

- --------------
          /3/ For purposes of issuing advance rulings, the Internal Revenue
Service (the "Service") has indicated that at least 5 percent of a distributing
corporation's gross assets must be used in directly conducting an active trade
or business for the distributing corporation itself to satisfy the active
business requirement of section 355(b). Rev. Proc. 96-43, 1996-35 I.R.B. 6.
<PAGE>
 
Halliburton Company
Page 13
December 4, 1996

holding company that conducted no trade or business but that held as its sole
asset all of the stock of several subsidiaries that each conducted an active
trade or business.

          Under section 355(b)(2)(B), a trade or business that is relied upon to
meet the requirements of section 355(b) must have been actively conducted
throughout the five year period ending on the date of distribution.  Treas. Reg.
(S) 1.355-3(b)(3).  Further, the fact that a trade or business underwent change
during the five year period preceding the distribution (e.g., by the addition of
new or the dropping of old products, changes in production capacity, and the
like) shall be disregarded, provided that the changes are not of such a
character as to constitute the acquisition of a new or different business.  In
particular, if a corporation engaged in the active conduct of one trade or
business during the five year period purchases or creates another trade or
business in the same line of business, then the acquisition or creation of that
other business is ordinarily treated as an expansion of the original business,
all of which is treated as having been actively conducted during the five year
period.  Treas. Reg. (S) 1.355-3(b)(3)(ii).

          Treas. Reg. (S) 1.355-3(b)(2) provides that a corporation shall be
treated as engaged in a trade or business immediately after the distribution if
a specific group of activities is being carried on by the corporation for the
purpose of earning income or profit, and the activities included in such group
include every operation that forms a part of, or a step in, the process of
earning income or profit.  Such group of activities ordinarily must include the
collection of income and the payment of expenses.

          Section 355(b)(2)(D) provides that a corporation shall be treated as
engaged in an active conduct of a trade or business if, among other things, the
corporation conducting such trade or business was not acquired by the
distributing corporation within the five year period ending on the date of
distribution or was so acquired within such period, but was acquired only by
reason of a transaction in which gain or loss was not recognized in whole or in
part.

          Device Restriction

          Treas. Reg. (S) 1.355-2(d)(1) provides that the determination of
whether a transaction is used principally as a device for the distribution of
earnings and profits is to be made from all of the facts and circumstances,
including but not limited to, the presence of certain device factors and
nondevice factors.  Treas. Reg. (S) 1.355-2(d)(3)(ii) provides that a corporate
business purpose for the transaction is evidence that the transaction is not
being used principally as a device.  An assessment of the strength of the
corporate business purpose is based on all of the facts and circumstances,
including, but not limited to, factors such as:  (i) the importance of achieving
the purpose to the success of the business, (ii) the extent to which the
transaction is prompted by a person not having a proprietary interest in either
corporation, or by other factors beyond the control of the distributing 
corporation, and (iii) the immediacy of the conditions prompting the 
transaction.
<PAGE>
 
Halliburton Company
Page 14
December 4, 1996

          Business Purpose

          A transaction must be carried out for one or more valid corporate
business purposes in order to meet the requirements of section 355.  Treas. Reg.
(S) 1.355-2(b)(2) states that a corporate business purpose is a real and
substantial non-Federal tax purpose germane to the business of the distributing
corporation, the controlled corporation, or the affiliated group (defined by
reference to section 1504(a) of the Code) to which the distributing corporation
belongs.

          In Rev. Rul. 76-187, 1976-1 C.B. 97, the Service ruled that the
business purpose requirement was satisfied when a parent corporation distributed
the stock of its wholly-owned subsidiary to a newly formed holding company to
substantially reduce the amount of state and local taxes paid by the parent.
Similarly, in Priv. Ltr. Rul. 9011044 (Dec. 20, 1994),/4/ a spinoff of a
controlled corporation in order to break the nexus with certain states, thus
avoiding sales and use tax obligations, was found to be a valid business
purpose.

          For advance ruling purposes, the Service in Rev. Proc. 96-30, 1996-19
I.R.B. 8, has indicated that a distribution to achieve significant cost savings
(i.e., lower insurance rates, lower borrowing costs, less employees) is a valid
business purpose.  Rev. Proc. 96-30 defines "significant cost savings" as
projection period cost savings equal to at least 1 percent of the base period
net income of a distributing corporation's affiliated group.  In other words,
the Service for advanced ruling purposes will compare the total expected cost
savings that are to result from a distribution to the total net consolidated
financial income of a distributing corporation's affiliated group for a three
year period preceding the distribution.  Although the 1 percent test is only a
guideline and not a safe harbor, a taxpayer can generally have confidence that
the cost savings rationale is a good business purpose if anticipated savings are
expected to exceed the 1 percent level.  In addition, where the distribution is
intended to significantly enhance the protection of one or more businesses from
the risks of another business, the Service in Rev. Proc. 96-30 has found such
risk reduction to be a valid business purpose.

          Continuity of Interest Requirement

          Treas. Reg. (S) 1.355-2(c)(1) provides that section 355 will apply to
a transaction only if one or more persons who, directly or indirectly, were the
owners of the enterprise prior to the distribution or exchange own, in the
aggregate, an amount of stock establishing a continuity of interest in each of
the modified corporate forms in which the enterprise is conducted after the

- --------------
          /4/ It is recognized that private rulings are without precedential
value pursuant to section 6110(j)(3). However, they do indicate the position the
Service has taken in similar situations.

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Halliburton Company
Page 15
December 4, 1996

separation. The regulations indicate that the retention of a 50 percent interest
in each of the distributing corporation and the controlled corporation is
sufficient to satisfy this requirement./5/



                                  CONCLUSIONS

          Based upon the facts, representations, law and analysis set forth
above, in our opinion:

          1.  The Halliburton Merger will constitute a reorganization within the
meaning of section 368(a)(1)(B) of the Code, and Halliburton, Merger Sub, and
Holdco will each be a party to the reorganization within the meaning of section
368(b) of the Code.

          2.  No gain or loss will be recognized by Halliburton, Merger Sub or
Holdco for federal income tax purposes by reason of the Holding Company
Reorganization.  Section 361(a) of the Code.

          3.  No gain or loss will be recognized by the holders of Halliburton
Common Stock upon the receipt of shares of Holdco Common Stock pursuant to the
Holding Company Reorganization. Section 354(a)(1) of the Code.

          4.  The basis of the shares of Holdco Common Stock treated as received
by a holder of Halliburton Common Stock will be the same as the basis of the
shares of Halliburton Common Stock treated as exchanged therefor.  Section
358(a)(1) of the Code.

          5.  The holding period of the shares of Holdco Common Stock treated as
received by a holder of Halliburton Common Stock would include the holding
period of the shares of Halliburton Common Stock treated as exchanged therefor,
provided the Halliburton Common Stock is held as a capital asset at the time of
the Holding Company Reorganization.  Section 1223(1) of the Code.

          6.  The basis of the Halliburton stock in the hands of HDI will be
determined by reference to the "net asset basis" of Halliburton immediately
prior to the Holding Company Reorganization under the principles of Treas. Reg.
(S) 1.1502-31.

          7.  No gain or loss will be recognized to Halliburton upon the
distribution of all of the stock of the Distributed Subsidiaries.  Sections
355(c) and 361(c)(1) of the Code.

          8.  No gain or loss will be recognized to (and no amount will be
includible in the income of) HDI upon the receipt of the stock of the
Distributed Subsidiaries.  Section 355(a)(1) of the Code.

- ---------------------
          /5/  See Treas. Reg. (S) 1.355-2(c)(2), Ex. (2).
<PAGE>
 
Halliburton Company
Page 16
December 4, 1996

          9.  The basis of the Halliburton stock and the stock of the
Distributed Subsidiaries in the hands of HDI following the Spinoffs will be the
same as the basis of the Halliburton stock held immediately before the Spinoffs,
allocated in proportion to the respective fair market values of such stock at
the time of the Spinoffs.  Sections 358(a)(1) and 358(b)(2) of the Code and
Treas. Reg. (S) 1.358-2(a)(2).

          10.  The holding period of the stock of the Distributed Subsidiaries
received by HDI in the Spinoffs will include the holding period of HDI for the
Halliburton stock, provided the Halliburton stock is held as a capital asset at
the time of the Spinoffs.  Section 1223(1) of the Code.

          We express no opinion as to the tax treatment of the transactions
contemplated by the Holding Company Reorganization and the Spinoffs under the
provisions of any other sections of the Code or the regulations under the Code
that also may be applicable thereto or to the tax treatment of any conditions
existing at the time of, or effects resulting from, the transactions
contemplated by the Spinoffs that are not specifically addressed in the
foregoing opinion.

          This opinion is given to you by us solely for your use and is not to
be quoted or otherwise referred to or furnished to any governmental agency
(other than the Service in connection with an examination of the transactions
contemplated by the Holding Company Reorganization and the Spinoffs) or to other
persons without our prior written consent.


                                 Very truly yours,



                                 VINSON & ELKINS L.L.P.

<PAGE>
 
                                                                    EXHIBIT 21.1
 
                   HALLIBURTON COMPANY LIST OF SUBSIDIARIES
<TABLE>
<CAPTION>  

                                                                         COUNTRY OF
COMPANY NAME                                                             INCORPORATION
<S>                                                                      <C> 
2W Underwater Contractors Ltd   U.K.
Aberdeen Cargo Handling Services Limited                                 U.K.
Al-Rushaid Taylor Diving Ltd                                             Saudi Arabia
Amsito Oilwell Services (Malaysia) Sdn Bhd                               Malaysia
Asia Energy Services Sdn. Bhd                                            Malaysia
Asian Marine Contractors Limited                                         Mauritius
Associated Underwriters, Inc                                             U.S.
Atomic Weapons Establishment PLC                                         
Automation Technology International, Inc                                 U.S
Avalon Financial Services, Ltd                                           Cayman Is.
Azteca Transportation Services, Inc                                      U.S.
B&R - G5 Industrial Services (Proprietary) Limited                       South Africa
B&R Washington, Inc                                                      U.S.
Breswater Marine Contracting BV                                          Netherlands
Brown & Root (Asia Pacific) Pte Ltd                                      Singapore
Brown & Root (Gulf) EC                                                   Bahrain
Brown & Root (Labaun) Sendirian Berhad                                   Malaysia
Brown & Root (Malaysia) Sdn Bhd                                          Malaysia
Brown & Root (Overseas) Limited                                          U.K.
Brown & Root (Services) Limited                                          U.K.
Brown & Root (Thailand) Limited                                          Thailand
Brown & Root A/S                                                         Norway
Brown & Root and Associates Ireland Limited                              Ireland
Brown & Root AOC, Limited                                                U.K.
Brown & Root, Booz-Allen Limited                                         U.K.
Brown & Root Braun Canada Inc                                            Canada
Brown & Root Braun Ingenieros de Venezuela SA                            Venezuela
Brown & Root Building Company                                            U.S.
Brown & Root Cayman Holdings, Inc.                                       Cayman Is.
Brown & Root Condor SPA                                                  Algeria
Brown & Root Construction (Overseas) Limited                             U.K.
Brown & Root Constructores Petroleros de Ven. CA                         Venezuela
Brown & Root Corporate Services, Inc                                     U.S.
Brown & Root de Mexico SA de CV                                          Mexico
Brown & Root do Brasil Servico Maritimos Ltda                            Brazil
Brown & Root Ealing Technical Services Limited                           England
Brown & Root Energy Services (India) Private Limited                     India
Brown & Root Energy Services A/S                                         Norway
Brown & Root Engenharia e Construcoes Ltda                               Brazil
Brown & Root Engineering Sdn Bhd                                         Malaysia
Brown & Root Espanola, SA                                                Spain
Brown & Root Far East Engineers Pte Ltd                                  U.S.
Brown & Root Genesis Engineering Company                                 U.S.
Brown & Root Highlands Fabricators Limited                               U.K.
Brown & Root Holdings, Inc                                               U.S.
Brown & Root, Inc                                                        U.S.
</TABLE> 
<PAGE>
 
<TABLE> 
                                                                         COUNTRY OF
COMPANY NAME                                                             INCORPORATION
<S>                                                                      <C> 
Brown & Root Industrial Services, Inc                                    U.S.
Brown & Root Industrial Services Philippines Inc.                        Phillippines
Brown & Root Ingenieros Petroleros de Venezuela CA                       Venezuela
Brown & Root International (Eastern), Inc                                Panama
Brown & Root International, Inc (Delaware)                               U.S.
Brown & Root International, Inc (Panama)                                 Panama
Brown & Root Limited                                                     U.K.
Brown & Root Maintenance, Inc                                            Panama
Brown & Root Malta Limited                                               Malta
Brown & Root Management Ltd                                              Canada
Brown & Root McDermott Fabricators Limited (Class A)                     U.K.
Brown & Root Mid East LLC                                                Oman
Brown & Root NA Limited                                                  Br. Virgin Islands
Brown & Root Nigeria Limited                                             Nigeria
Brown & Root Offshore NV                                                 Netherlands Antilles
Brown & Root Projects Limited                                            U.K.
Brown & Root Property, Inc.                                              Delaware
Brown & Root Pty Limited (Australia)                                     Australia
Brown & Root Saudi Limited Co.                                           Saudi Arabia
Brown & Root Services Corporation                                        U.S.
Brown & Root Servicios Industriales, Inc                                 Panama
Brown & Root Skoda                                                       Czechoslovakia
Brown & Root Technical Services, Inc                                     U.S.
Brown & Root Technology (No.2) Limited                                   U.K.
Brown & Root Technology Limited                                          U.K.
Brown & Root Toll Road Investment Partners, Inc                          U.S.
CAEX Services, Inc.                                                      U.S.
Centend Limited                                                          U.K.
CF Braun & Co of Canada Ltd                                              Canada
CF Braun Engineering Corporation                                         U.S
CF Braun Inc                                                             U.S.
Chemtronics, Inc                                                         U.S.
China Brown & Root Marine Engineering and Construction Company Ltd       China
CNOOC - Otis Well Completion Services Ltd.                               China
COESK - Taylor Diving Company                                            China
Compania Geosource De Mexico, S.A. de C.V.                               Mexico
Constructora Indolatina, SA de CV                                        Mexico
Constructores de Venezuela Brown & Root, Inc CA                          Venezuela
Corporacion Mexicana de Mantenimiento Integral SA de CV                  Mexico
Cyril Lea & Associates Limited                                           U.K.
Dawson AOC Pty Ltd                                                       Australia
Dawson Engineering Pty Ltd                                               Australia
Dawson Group Pty Ltd                                                     Australia
Dawson Industries Ltd                                                    Australia
Devonport Management Limited (Class B Shares)                            U.K.   
Devonport Royal Dockyard Pension Trustees Limited                        U.K.
Devonport Royal Dockyard PLC                                             U.K.
Dorhold Limited                                                          U.K.
Drilling Information Satellite Company                                   U.S.
</TABLE> 

                                       2
<PAGE>
 
<TABLE> 
                                                                         COUNTRY OF
COMPANY NAME                                                             INCORPORATION
<S>                                                                      <C> 
EMC Nederland BV                                                         Netherlands
Enertech Computing Corporation                                           U.S.
Enertech Engineering and Research Co.                                    U.S.
ETI Acquisition Corp                                                     U.S.
European Marine Contractors Limited                                      U.K.
Far East Oilwell Services Sdn Bhd                                        Malaysia
Fargo Engineering Company                                                U.S.
G&H Management Company                                                   U.S.
Gearhart (United Kingdom) Limited                                        U.K.
Gearhart Geodata Holdings Ltd                                            U.K.
Gearhart Well Evaluation Limited                                         U.K.
Gearhart Wireline Holdings Limited                                       U.K.
Geographix, Inc. (Colorado)                                              U.S.
Geophysical Service Europe Co Ltd                                        Hungary
Geophysical Service Intercontinental Limited                             Canada
Geosource EPIG Services Company Limited                                  Sudan
Geosource International (Nederland) BV                                   Netherlands
Geosource Service Corporation                                            U.S.
Geosource UK Limited                                                     U.K.
Global Arabian Company for Engineering and Construction
  Projects Ltd (Saudi Arabia)                                            Saudi Arabia
Global Drilling Services, Inc                                            Panama
GO Turkey SA                                                             Is. of Nevis
Green Sea AS                                                             Norway
Green Sea Operations AS                                                  Norway
Greystone Communities, Inc                                               U.S.
Halliburton (Proprietary) Limited                                        South Africa
Halliburton Affiliates Corporation                                       Delaware
Halliburton Argentina SA                                                 Argentina            
Halliburton Arkhangelsk, Ltd                                             Russia
Halliburton Australia Pty Ltd                                            Australia
Halliburton BV                                                           Netherlands
Halliburton Canada Inc                                                   Canada
Halliburton Cementacao Ltda                                              Brazil
Halliburton CICS Inc                                                     Cayman Islands
Halliburton Company Austria GmbH                                         Austria
Halliburton Company Germany GmbH                                         Germany
Halliburton Consulting Services Nigeria Limited                          Nigeria
Halliburton de Mexico, SA de CV                                          Mexico
Halliburton del Amazonas S.A.                                            Peru
Halliburton del Peru SA                                                  Peru
Halliburton Delaware, Inc.                                               Delaware
Halliburton Energy Services Asia, Inc                                    U. S.
Halliburton Energy Services, Inc.                                        Delaware
Halliburton Energy Services Limited                                      U.K.
Halliburton Energy Services Nigeria Limited                              Nigeria
Halliburton Equipment Company SAE                                        Egypt
Halliburton Espanola SA                                                  Spain
Halliburton Geodata (Overseas) Limited                                   U.K.
</TABLE> 

                                       3
<PAGE>
 
<TABLE> 
                                                                         COUNTRY OF
COMPANY NAME                                                             INCORPORATION
<S>                                                                      <C> 
Halliburton Geodata Limited                                              U.K.
Halliburton Geophysical Services (Cayman) Ltd                            Cayman Islands
Halliburton Geophysical Services (Int'l) Ltd                             Canada
Halliburton Geophysical Services (M) Sdn Bhd                             Malaysia
Halliburton Geophysical Services de Mexico, SA de CV                     Mexico
Halliburton Global, Ltd                                                  Cayman Islands
Halliburton Holdings, Inc                                                U.S.
Halliburton Holdings Limited                                             U.K.
Halliburton International GmbH                                           Austria
Halliburton International, Inc (Del)                                     U.S.
Halliburton Italiana SpA                                                 Italy
Halliburton Kazakhstan Oilfield Services, Ltd                            Kazakhstan
Halliburton Latin America SA                                             Panama
Halliburton Limited                                                      U.K.
Halliburton Logging Services (France) SARL                               France
Halliburton Logging Services (M) Sdn Bhd                                 Malaysia
Halliburton Logging Services (UK) Limited                                U.K.
Halliburton Manufacturing (Singapore) Pte Ltd                            Singapore
Halliburton Manufacturing and Services Limited                           U.K.
Halliburton Multinational, Inc                                           U.S.
Halliburton Nigeria Limited                                              Nigeria
Halliburton Norway, Inc.                                                 U.S.
Halliburton NUS Corporation                                              U.S.
Halliburton NUS Environmental Limited                                    U.K.
Halliburton Offshore Services, Inc                                       U.S.
Halliburton Oil Field Services, Ltd                                      Russia
Halliburton Oilfield Services India Limited                              India
Halliburton Overseas Limited                                             Cayman Islands
Halliburton Products & Services Limited                                  Cayman Islands
Halliburton Real Estate Services, Inc                                    U.S.
Halliburton SAS                                                          France
Halliburton Services (Malaysia) Sdn Bhd                                  Malaysia
Halliburton Servicios (Chile) Ltda                                       Chile
Halliburton Servicos Ltda                                                Brazil
Halliburton Singapore Pte Ltd                                            Singapore
Halliburton Tesel Ltd                                                    U.K.
Halliburton Trinidad, Limited                                            Trinidad
Halliburton West Africa Ltd                                              U.S.
Halliburton Worldwide Limited                                            Cayman Islands
Halliburton-Atyrau Oil & Gas Services                                    Kazakhstan
Halliburton-GERS Ltd.                                                    Russian Federation
Halliburton-Imco (Cameroon) SARL                                         Cameroon
Halliburton-Imco (Gabon) SARL                                            Gabon
Hart Howard Humphreys                                                    Zimbabwe
HBR Energy, Inc.                                                         Delaware
HGS Enterprises Inc                                                      Panama
HGS Limited                                                              U.K.
HLS (Int'l) Holdings, Inc                                                U.S.
HLS (Middle East) Holdings, Inc                                          U.S.
</TABLE> 

                                       4
<PAGE>
 
<TABLE> 
                                                                         COUNTRY OF
COMPANY NAME                                                             INCORPORATION
<S>                                                                      <C> 
HLS (West Africa) Holdings, Inc                                          U.S.
HLS India Limited                                                        India
HLS Nigeria Limited                                                      Nigeria
HLS-Namtvedt A/S                                                         Norway
HLS-Namtvedt Holdings A/S                                                Norway
Houston Executive Air Service, Inc                                       U.S.
Howard Humphreys (Kenya) Limited                                         Kenya
Howard Humphreys (Tanzania) Limited                                      Tanzania
Howard Humphreys (Uganda) Limited                                        Uganda
Howard Humphreys (Zimbabwe) Limited                                      Wales
Howard Humphreys & Partners Limited                                      U.K.
Howard Humphreys and Sons                                                U.K.
Howard Humphreys Group Limited                                           U.K.
Howard Humphreys Limited                                                 U.K.
Howard Humphreys Project Management (Hong Kong) Limited                  Hong Kong
Howard Humphreys Project Management Limited                              U.K.
Hua Mei-Halliburton Petroleum Technical Service Company Ltd              China
Hunting - Brae Limited                                                   U.K.
IMCO Services (UK) Limited                                               England
Integrated Documatics Limited                                            U.K.
International Administrative Services, Ltd.                              Cayman Islands
IPEM Developments Limited                                                U.K.
Japan NUS Company, Ltd                                                   Japan
Jet Research Center, Inc                                                 U.S.
Kestrel Subseas Systems Limited                                          U.K.
Landmark America Latina, SA (Delaware)                                   U.S.
Landmark America Latina, SA (Panama)                                     Panama
Landmark/CAEX, Inc. (Delaware)                                           U.S.
Landmark de Mexico, SA de CV                                             Mexico
Landmark EAME, Ltd                                                       United Kingdom
Landmark Finance Corporation                                             U.S.
Landmark Graphics (Malaysia) Sdn Bhd                                     Malaysia
Landmark Graphics (Nigeria) Ltd                                          Nigeria
Landmark Graphics Argentina SA                                           Argentina
Landmark Graphics Canada, Inc. (Alberta)                                 Canada
Landmark Graphics Colombia SA                                            Colombia
Landmark Graphics Corporation                                            U.S.
Landmark Graphics do Brasil Ltda.                                        Brazil
Landmark Graphics Europe/Africa, Inc.                                    U.S.
Landmark Graphics International, Inc.                                    U.S.
Landmark Graphics Venezuela CA                                           Venezuela
Landmark/ITA, Ltd (Alberta)                                              Canada
Landmark Sales Corporation                                               Barbados
Laurel Financial Services BV                                             Netherlands
Liaohe Halliburton Flow Measurement Company                              People's Rep. China
LMK Land Company                                                         U.S.
Logging Analysis, Inc                                                    U.S.
M-I Drilling Fluids Company, LLC                                         U.S.
Management Logistics, Inc.                                               Delaware
</TABLE> 

                                       5
<PAGE>
 
<TABLE> 
                                                                         COUNTRY OF
COMPANY NAME                                                             INCORPORATION
<S>                                                                      <C> 
Manteniven, SA                                                           Venezuela
Manufacturas Halliburton de Mexico, SA de CV                             Mexico
Manufacturas Halliburton de Venezuela SA                                 Venezuela
Marend Limited                                                           Scotland
Martec-Engenharia e Obras Ltda                                           Brazil
Mashhor Brown & Root Offshore Services Sdn Bhd                           Brunei
Mashhor Well Services Sdn Bhd                                            Brunei
MGI Associates, Inc.                                                     U.S.
Mid-Valley, Inc                                                          U.S.
MIHC, Inc                                                                U.S.
Monenco Offshore Limited                                                 Canada
Moroccan Engineers & Constructors                                        Morocco
Munro Engineering Intl Pte Ltd                                           Singapore
Munro Garrett (Asia Pacific) Pty Ltd                                     Australia
Munro Garrett International, Inc.                                        U.S.
Munro Garrett International Limited                                      Scotland
Newco Engineering Limited                                                Uganda
NIS Ingenieurgesellschaft mbH                                            Germany
Oilfield Marine, Inc                                                     U.S.
Oilfield Telecommunications, Inc                                         U.S.
Otis Energy Services of Japan, Ltd                                       U.S.
Otis Engineering Italiana, Srl                                           Italy
Otis Mexicana, SA                                                        Mexico
Otis of Nigeria Limited                                                  Nigeria
Otis Pressure Control, Limited                                           U.K.
Overseas Administration Services, Ltd                                    Cayman Islands
Overseas Marine Leasing Company                                          U.S.
P.T. Brown & Root Indonesia                                              Indonesia
P.T.  Gema Sembrown                                                      Indonesia
P.T. Landmark Concurrent Solusi Indonesia                                Indonesia
Plantation Land Company, Inc (South Carolina)                            U.S.
Professional Group Consultants Limited                                   Hong Kong
Professional Resources Ltd                                               Bermuda
PT Halliburton Drilling Systems Indonesia                                Indonesia
PT Halliburton Indonesia                                                 Indonesia
PT Halliburton Logging Services Indonesia                                Indonesia
PT M-I, Indonesia                                                        Indonesia
PT Udemco Otis Indonesia                                                 Indonesia
Quimicas Do Brasil Ltda                                                  Brazil
Rezayat Brown & Root Saudi Company Limited                               Saudi Arabia
Rockwater (North Sea) Limited                                            U.K.
Rockwater AS                                                             Norway
Rockwater BV                                                             Netherlands
Rockwater CV                                                             Netherlands
Rockwater Holdings Limited                                               U.K.
Rockwater, Inc                                                           U.S.
Rockwater J/V                                                            Netherlands
Rockwater Limited                                                        U.K.
Rockwater Offshore Contractors 2 BV                                      Netherlands
</TABLE> 

                                       6
<PAGE>
 
<TABLE> 
                                                                         COUNTRY OF
COMPANY NAME                                                             INCORPORATION
<S>                                                                      <C> 
Rockwater Offshore Contractors BV                                        Netherlands
Rockwater Offshore Contractors Pty Limited                               Australia
Rockwater Underwater Services Limited                                    Hong Kong
Sabre Manning Services Limited                                           Channel Islands
SBR Offshore Limited                                                     Canada
Seabase Limited                                                          Canada
Seaforth Engineering Limited                                             U.K.
Seaforth Kinergetics Limited                                             Scotland
Seaforth Logistics Limited                                               U.K.
Seaforth Marine Services Limited                                         U.K.
Seaforth Maritime (Holdings) Limited                                     U.K.
Seaforth Maritime Limited                                                U.K.
Seaforth Workforce Limited                                               U.K.
Sembrown Equipment Pte Ltd                                               Singapore
Service Employees International, Inc                                     Cayman Islands
Servicios Geofisicos "GSI" Ltda                                          Brazil
Servicios Halliburton de Venezuela, SA                                   U.S.
Servicios Tecnicos Brown & Root, SA                                      Panama
Shapadu Rockwater Sdn Bhd                                                Malaysia
Siam Brown and Root Limited                                              Thailand
Sierra Geophysics (UK) Limited                                           U.K.
Sociedade Brasileira de Engenharia e Construcoes Ltda                    Brazil
Stratamodel (Barbados)                                                   Barbados
Stratamodel Limited (England)                                            United Kingdom
Taylor Diving (South East Asia) Pte Ltd                                  Singapore
Taylor International Diving Company, Inc                                 U.S.
Tech Logic, Inc. (Washington)                                            U.S.
Tesel Holdings Limited                                                   U.K.
Texas Fastrac, Inc                                                       U.S.
The Arab Geophysical Exploration Services Company                        Libya
Tri-Can Perforators Limited                                              Trinidad
Tristan Services Limited                                                 U.K.
Ucamar Shipping & Transportation Company (Cayman) Limited                Cayman Islands
Universal Energy Services Aktrengesellschaft                             Liechtenstein
Vann Systems UK Limited                                                  U.K.
Walbridge Brown & Root International LLC                                 Cayman Is.
Walbridge Brown & Root International LLC - Delaware                      Delaware
WCML Development Company Limited                                         U.K.
Wharton Williams Taylor Emirates                                         United Arab Emirates
</TABLE> 

                                       7


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