Executive Employment Agreement - Halliburton Co. and William E. Bradford


                        EXECUTIVE EMPLOYMENT AGREEMENT


     This Executive Employment Agreement ('Agreement'), including the attached
Exhibits 'A' and 'B', is entered into by and between Halliburton Company, a
Delaware corporation having offices at 3600 Lincoln Plaza, 500 N. Akard Street,
Dallas, Texas 75201-3391 ('Employer'), and William E. Bradford, an individual
currently residing at 3835 Potomac, Dallas, Texas 75205 ('Employee'), to be
effective on the later of the date of execution of this Agreement by the parties
hereto or the effective date of the merger between Halliburton N.C., Inc. and
Dresser Industries, Inc.(the 'Merger') pursuant to the terms of that certain
Agreement and Plan of Merger (the 'Merger Agreement') by and among Employer,
Halliburton N.C., Inc. and Dresser Industries, Inc. ('Dresser') dated February
25, 1998 (the 'Effective Date').

                                  WITNESSETH:

     WHEREAS, Employer is desirous of employing Employee pursuant to the terms
and conditions and for the consideration set forth in this Agreement, and
Employee is desirous of entering the employ of Employer pursuant to such terms
and conditions and for such consideration.

     NOW, THEREFORE, for and in consideration of the mutual promises, covenants,
and obligations contained herein, Employer and Employee agree as follows:

ARTICLE 1:          EMPLOYMENT AND DUTIES

1.1  Employer agrees to employ Employee, and Employee agrees to be employed by
     Employer, beginning as of the Effective Date and continuing until January
     31, 2000 (the 'Term'), subject to the terms and conditions of this
     Agreement.

1.2  Beginning on the Effective Date, Employee shall be employed as Chairman of
     the Board of Directors of Employer.  Employee agrees to serve in the
     assigned position and to perform diligently and to the best of Employee's
     abilities the duties and services appertaining to such position as
     determined by Employer, as well as such additional or different duties and
     services appropriate to such position which Employee from time to time may
     be reasonably directed to perform by Employer.  As of the Effective Date,
     Employee shall be elected as a member of Employer's Board of Directors.
     Employee shall at all times comply with and be subject to such policies and
     procedures as Employer may establish from time to time, including, without
     limitation, the Halliburton Company Code of Business Conduct.

1.3  Employee shall, during the period of Employee's employment by Employer,
     devote Employee's full business time, energy, and best efforts to the
     business and affairs of Employer.  Employee may not engage, directly or
     indirectly, in any other business, investment, or activity that interferes
     with Employee's performance of Employee's duties hereunder, is contrary to
     the interests of Employer, or requires any significant portion of

 
Executive Employment Agreement
William E. Bradford


     Employee's business time.  The foregoing notwithstanding, the parties
     recognize and agree that Employee may engage in passive personal
     investments and other business activities which do not conflict with the
     business and affairs of the Employer or interfere with Employee's
     performance of his duties hereunder.  In that regard, Employee may serve on
     the board of directors of up to three unaffiliated corporations of his
     choice, so long as service on any such board simultaneously with his
     service on Employer's Board of Directors does not constitute a violation of
     federal statutory provisions, or related rules and regulations, pertaining
     to interlocking directorships and the meeting times of such boards of
     directors do not conflict with the meeting times of Employer's Board of
     Directors.  Except as provided in the preceding sentence, Employee may not
     serve on the board of directors of any entity other than the Employer
     during the Term without the approval of the Audit Committee of the
     Employer's Board of Directors in accordance with the Employer's policies
     and procedures regarding such service, which approval will not be
     unreasonably withheld. Employee shall be permitted to retain any
     compensation received for such service on other corporations' boards of
     directors.

1.4  Employee acknowledges and agrees that Employee owes a fiduciary duty of
     loyalty, fidelity and allegiance to act at all times in the best interests
     of the Employer and to do no act which would intentionally injure
     Employer's business, its interests, or its reputation.  It is agreed that
     any direct or indirect interest in, connection with, or benefit from any
     outside activities, particularly commercial activities, which interest
     might in any way adversely affect Employer, or any of its affiliates,
     involves a possible conflict of interest. In keeping with Employee's
     fiduciary duties to Employer, Employee agrees that Employee shall not
     knowingly become involved in a conflict of interest with Employer, or its
     affiliates, or upon discovery thereof, allow such a conflict to continue.
     Moreover, Employee agrees that Employee shall disclose to the Audit
     Committee of the Employer's Board of Directors any facts which might
     involve a possible conflict of interest.

1.5  Effective as of the Effective Date, Employer and Employee shall enter into
     an Indemnification Agreement containing the terms and conditions set forth
     in Exhibit A attached to, and forming a part of, this Agreement.

ARTICLE 2:          COMPENSATION AND BENEFITS

2.1  Employee's base salary during the Term shall be payable at the rate of not
     less than $925,000.00 per annum which shall be paid in accordance with the
     Employer's standard payroll practice for its executives. Employee's base
     salary may be increased from time to time during the Term in a manner
     similar to that used to establish the base salary of other members of the
     Executive Committee of Employer, with the approval of the Compensation
     Committee of Employer's Board of Directors. Such increased base salary
     shall become the minimum base salary under this Agreement and may not be
     decreased during the Term.

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Executive Employment Agreement
William E. Bradford


2.2  Employee shall be entitled to receive the bonus earned under the Dresser
     1998 Executive Incentive Compensation Plan (the 'Dresser EVA Plan') for its
     fiscal year ended October 31, 1998, based upon the actual level of
     attainment of Dresser's established performance targets for the period
     ended October 31, 1998 or, if the actual level of performance cannot be
     determined, a reasonable estimate thereof, provided he remains employed by
     the Employer during the entirety of such period. Such bonus shall be
     payable by Dresser in a single lump sum payment as soon as practicable
     following October 31, 1998. For the period November 1, 1998 through
     December 31, 1998, Employee shall be entitled to a bonus in an amount
     determined as follows: (i) Employee's base salary shall be multiplied by
     the same percentage of base salary as used in the calculation of Employee's
     bonus earned under the Dresser EVA Plan for the period ended October 31,
     1998 and (ii) the product thereof shall be multiplied by two-twelfths
     (2/12).  Beginning January 1, 1999 and for the remainder of the Term,
     Employee shall participate in Employer's Annual Performance Pay Plan, or
     any successor annual incentive plan approved by the Compensation Committee
     of Employer's Board of Directors (the 'CVA Plan'); provided, however, that
     if the bonus amount earned by Employee for any plan year during the Term is
     less than the average of bonus amounts earned by Employee under the Dresser
     EVA Plan or the predecessor annual incentive plan for the fiscal years
     ended October 31, 1997 and 1998 (the 'Average Dresser Bonus'), Employer
     shall pay to Employee an additional cash bonus equal to the difference. For
     plan year 2000, the CVA Plan bonus earned shall be prorated through the
     last day of the Term and the Average Dresser Bonus shall likewise be
     prorated through such period for the purpose of determining whether or not
     an additional bonus is payable.

2.3  During the Term, Employee shall participate in the Halliburton Company 1993
     Stock and Long-Term Incentive Plan, or any successor stock-related plan
     adopted by Employer's Board of Directors, in the same grant cycle for
     awards under such plan as the other members of Employer's Executive
     Committee.

2.4. Employer shall, as of the effective time of the Merger, adopt Dresser's
     Supplemental Executive Retirement Plan, with such amendments thereto as may
     be necessary or appropriate to reflect the Merger and the applicable
     provisions of Section 7.09 of the Merger Agreement, and Employee shall
     continue to participate in such plan in accordance with its terms, as such
     may be revised.

2.5  From and after the Effective Date, Employer shall pay, or reimburse
     Employee, for all ordinary, reasonable and necessary expenses which
     Employee incurs in performing his duties under this Agreement including,
     but not limited to, travel, entertainment, professional dues and
     subscriptions, and all dues, fees and expenses associated with membership
     in various 

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William E. Bradford


     professional, business and civic associations and societies of which
     Employee's participation is in the best interest of Employer.

2.6  While employed by Employer, Employee shall be allowed to participate, on
     the same basis generally as other executive employees of Employer, in all
     general employee benefit plans and programs, including improvements or
     modifications of the same, which on the Effective Date or thereafter are
     made available by Employer to all or substantially all of Employer's
     executive employees.  Such benefits, plans, and programs may include,
     without limitation, medical, health, and dental care, life insurance,
     disability protection, and qualified and non-qualified retirement plans.
     Except as specifically provided herein, nothing in this Agreement is to be
     construed or interpreted to increase or alter in any way the rights,
     participation, coverage, or benefits under such benefit plans or programs
     than provided to executive employees pursuant to the terms and conditions
     of such benefit plans and programs.

2.7  Except for the programs and/or plans provided in Sections 2.1, 2.2 and 2.9
     herein, Employer shall not by reason of this Article 2 be obligated to
     institute, maintain, or refrain from changing, amending, or discontinuing,
     any incentive compensation or employee benefit program or plan, so long as
     such actions are similarly applicable to covered employees generally.

2.8  Employer may withhold from any compensation, benefits, or amounts payable
     under this Agreement all federal, state, city, or other taxes as may be
     required pursuant to any law or governmental regulation or ruling.

2.9  Employer has assumed certain obligations with respect to certain plans and
     programs of Dresser pursuant to Section 7.09 of the Merger Agreement.  With
     respect  to Employee, such plans and programs include the following:


     a.   Exhibit B hereto sets forth the Dresser stock options and tandem
          restricted shares held by Employee as of May 12, 1998. Employer
          acknowledges its obligations to assume the Dresser stock options and
          the Dresser stock plans as, and to the extent provided, under Section
          7.09 of the Merger Agreement and to issue upon exercise of outstanding
          stock options shares of Employer common stock on a one-to-one ratio
          (adjusted pursuant to Section 3.01(a) of the Merger Agreement, if
          applicable) in accordance with the terms of the Dresser stock plans
          and the underlying stock option agreements. As of the Effective Date,
          Employee shall continue to be entitled to all his stock option and
          tandem restricted share rights under outstanding stock options held by
          Employee prior to the Effective Date.

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William E. Bradford


     b.   Employee has 93,374 stock units in Dresser's Deferred Compensation
          Plan, and Employer hereby recognizes its obligation to perform and pay
          out such compensation pursuant to the terms of such plan.

     c.   Employee is a participant in Dresser's Performance Stock Unit Program
          for the four (4) year cycles FY 1994 - 1997 and FY 1996 - 1999.
          Employer hereby recognizes its obligation to pay and perform under
          such plan pursuant to its terms with such reasonable estimates of the
          earnings and equity of Dresser for the latter cycle as may be
          necessitated by the Merger. Employer recognizes that the performance
          target for the FY 1996-1999 cycle of such plan is average Return on
          Equity of 15% or greater.

     d.   Employee is a participant in Dresser's Executive Life Insurance
          Program. Employer acknowledges its obligations to maintain such
          program for the benefit of Employee.

     e.   Employee is a participant in Dresser's Supplemental Executive
          Retirement Plan. Employer hereby acknowledges its obligations under
          Section 2.4 hereof and its obligations under Section 7.09 of the
          Merger Agreement to maintain such plan with respect to Employee with
          the offset under such plan to take into account any employer provided
          retirement benefits under any plans or programs of Employer or any of
          its subsidiaries.

     f.   Employee is a participant in Dresser's Retirement Saving Plan and as
          such  receives 'pension equalizer' contributions under such plan.
          Employer hereby  acknowledges its obligations to Employee to maintain
          such 'pension equalizer' contributions to such plan, the related
          nonqualified savings plan or a successor plan that will provide at
          least the same level of benefits as the 'pension equalizer'
          arrangement after taking into account any retirement benefits provided
          to Employee by any plans or programs of the Employer or any of its
          subsidiaries.

     g.   Employee is eligible for Dresser's Retiree Medical Benefit Plan and
          Employer hereby acknowledges its obligations to maintain such plan for
          the benefit of Employee, except to the extent that any modifications
          thereto are consistent with changes in the medical plans provided by
          Employer and its subsidiaries for similarly situated active employees.

2.10 Employee shall be eligible to participate in the Halliburton Elective
     Deferral Plan of Employer.

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William E. Bradford


ARTICLE 3:          TERMINATION PRIOR TO EXPIRATION OF TERM AND
                    EFFECTS OF SUCH TERMINATION:

3.1  Employee's employment with Employer shall be terminated (i) upon the death
     of Employee, (ii) upon Employee's permanent disability (permanent
     disability being defined as Employee's physical or mental incapacity to
     perform his usual duties as an employee with such condition likely to
     remain continuously and permanently); provided, however, that in the event
     of such permanent disability, Employee's employment and full compensation
     and benefits shall be continued hereunder until the end of the Term, with
     Employee's compensation during such period being reduced by any Employer-
     financed disability benefits, (iii) at any time during the Term by Employer
     upon notice to Employee or by Employee upon sixty (60) days' notice to
     Employer for any or no reason.

3.2  If Employee's employment is terminated by reason of a 'Voluntary
     Termination' (as hereinafter defined), the death of Employee, permanent
     disability of Employee (as defined in Section 3.1) or by the Employer for
     'Cause' (as hereinafter defined), all future compensation to which Employee
     is otherwise entitled and all future benefits for which Employee is
     eligible shall cease and terminate as of the date of termination, except as
     specifically provided in this Section 3.2 and in Section 3.1(ii).
     Employee, or his estate in the case of Employee's death, shall be entitled
     to pro rata base salary through the date of such termination and shall be
     entitled to any individual bonuses or individual incentive compensation not
     yet paid but payable under Employer's plans for years prior to the year of
     Employee's termination of employment, but shall not be entitled to any
     bonus or incentive compensation for the year in which Employee's employment
     is terminated or any other payments or benefits by or on behalf of Employer
     except for those which may be payable pursuant to the terms of Dresser's or
     Employer's employee benefit plans (as hereinafter defined), stock, stock
     option, incentive compensation or deferred compensation plans or the
     applicable agreements underlying such plans.  For purposes of this Section
     3.2, a 'Voluntary Termination' of the employment relationship by Employee
     prior to expiration of the Term shall be a termination of employment in the
     sole discretion of and at the election of Employee, other than (i) a
     termination of Employee's employment because of a material breach by
     Employer of any material provision of this Agreement which remains
     uncorrected for thirty (30) days following written notice of such breach by
     Employee to Employer or (ii) a termination of Employee's employment within
     six (6) months of a material reduction in Employee's rank or responsibility
     with Employer. For purposes of this Section 3.2, the term 'Cause' shall
     mean any of (i) Employee's gross negligence or willful misconduct in the
     performance of the duties and services required of Employee pursuant to
     this Agreement; (ii) Employee's final conviction of a felony; or (iii)
     Employee's material breach of any material provision of this Agreement
     which remains uncorrected for thirty (30) days following written notice to
     Employee by Employer of such breach.

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3.3  If Employee's employment is terminated for any reason other than as
     described in the first sentence of Section 3.2 above during the Term,
     Employee shall nevertheless continue to receive his full compensation (base
     salary and bonus) and benefits under this Agreement for the duration of the
     Term. The amounts paid pursuant to this Section 3.3 to Employee shall be in
     consideration of Employee's continuing obligations hereunder after such
     termination (including, without limitation, Employee's non-competition
     obligations).  Employee shall not be under any duty or obligation to seek
     or accept other employment following a termination of employment pursuant
     to which payments under this Section 3.3 are owing and the amounts due
     Employee pursuant to this Section 3.3 shall not be reduced or suspended if
     Employee accepts subsequent employment or earns any amounts as a
     self-employed individual. If Employee should die while receiving
     compensation and benefits pursuant to this Section 3.3, such compensation
     and benefits shall be prorated through the date of his death and paid to
     his estate, but all future compensation and benefits shall cease and
     terminate as of the date of Employee's death except for those which may be
     payable pursuant to the terms of Dresser's or Employer's employee benefit
     plans (as hereinafter defined), stock, stock option, incentive compensation
     or deferred compensation plans or the applicable agreements underlying such
     plans. Employee's rights under this Section 3.3 are Employee's sole and
     exclusive rights against the Employer or its affiliates and the Employer's
     sole and exclusive liability to Employee under this Agreement, in contract,
     tort or otherwise, for the termination of his employment relationship with
     Employer. Employee covenants not to sue or lodge any claim, demand or cause
     of action against Employer based upon Employee's termination of employment
     for any monies other than those specified in this Section 3.3. If Employee
     breaches this covenant, Employer shall be entitled to recover from Employee
     all sums expended by Employer (including costs and attorneys' fees), in
     connection with such suit, claim, demand or cause of action. Nothing
     contained in this Section 3.3 shall be construed to be a waiver by Employee
     of any benefits accrued for or due Employee under any employee benefit plan
     (as such term is defined in the Employees' Retirement Income Security Act
     of 1974, as amended) or any of the benefits, plans or programs provided for
     in Section 2.09 hereof maintained by Dresser or Employer except that
     Employee shall not be entitled to any severance benefits pursuant to any
     severance plan or program of Employer.

3.4  It is expressly acknowledged and agreed that the decision as to whether
     'Cause' exists for termination of the employment relationship by the
     Employer and whether and as of what date Employee has become permanently
     disabled is delegated to the Board of Directors of Employer for
     determination. If Employee disagrees with the decision reached by Employer,
     the dispute will be limited to whether the Board of Directors of Employer
     reached this decision in good faith.

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Executive Employment Agreement
William E. Bradford


3.5  Termination of the employment relationship does not terminate those
     obligations imposed by this Agreement which are continuing obligations,
     including, without limitation, Employee's obligations under Articles 4
     and 5.

ARTICLE 4:          OWNERSHIP AND PROTECTION OF INTELLECTUAL
                    PROPERTY AND CONFIDENTIAL INFORMATION

4.1  All information, ideas, concepts, improvements, discoveries, and
     inventions, whether patentable or not, which are conceived, made, developed
     or acquired by Employee, individually or in conjunction with others, during
     Employee's employment by Employer (whether during business hours or
     otherwise and whether on Employer's premises or otherwise) which relate to
     Employer's business, products or services (including, without limitation,
     all such information relating to corporate opportunities, research,
     financial and sales data, pricing and trading terms, evaluations, opinions,
     interpretations, acquisition prospects, the identity of customers or their
     requirements, the identity of key contacts within the customer's
     organizations or within the organization of acquisition prospects, or
     marketing and merchandising techniques, prospective names, and marks), and
     all writings or materials of any type embodying any of such items, shall be
     disclosed to Employer and are and shall be the sole and exclusive property
     of Employer.

4.2  Employee acknowledges that the businesses of Employer and its affiliates
     are highly competitive and that their strategies, methods, books, records,
     and documents, their technical information concerning their products,
     equipment, services, and processes, procurement procedures and pricing
     techniques, the names of and other information (such as credit and
     financial data) concerning their customers and business affiliates, all
     comprise confidential business information and trade secrets which are
     valuable, special, and unique assets which Employer, or its affiliates use
     in their business to obtain a competitive advantage over their competitors.
     Employee further acknowledges that protection of such confidential business
     information and trade secrets against unauthorized disclosure and use is of
     critical importance to Employer and its affiliates in maintaining their
     competitive position.  Employee hereby agrees that Employee will not, at
     any time during or after his employment by Employer, make any unauthorized
     disclosure of any confidential business information or trade secrets of
     Employer, or its affiliates, or make any use thereof, except in the
     carrying out of his employment responsibilities hereunder.  The above
     notwithstanding, a disclosure shall not be unauthorized if (i) it is
     required by law or by a court of competent jurisdiction or (ii) it is in
     connection with any judicial or other legal proceeding in which Employee's
     legal rights and obligations as an employee or under this Agreement are at
     issue; provided, however, that Employee shall, to the extent practicable
     and lawful in any such events, give prior notice to Employer of his intent
     to disclose any such confidential business information in such context so
     as to allow Employer an 

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William E. Bradford


     opportunity (which Employee will not oppose) to obtain such protective
     orders or similar relief with respect thereto as it may deem appropriate.

4.3  All written materials, records, and other documents made by, or coming into
     the possession of, Employee during the period of Employee's employment by
     Employer which contain or disclose confidential business information or
     trade secrets of Employer, or its affiliates shall be and remain the
     property of Employer, or its affiliates, as the case may be.  Upon
     termination of Employee's employment by Employer, for any reason, Employee
     promptly shall deliver the same, and all copies thereof, to Employer.

ARTICLE 5:          POST-EMPLOYMENT AND NON-COMPETITION OBLIGATIONS

5.1  As part of the consideration for the compensation and benefits to be paid
     to Employee hereunder, and as an additional incentive for Employer to enter
     into this Agreement, Employer and Employee agree to the non-competition
     provisions of this Article 5. Employee agrees that during the period of
     Employee's non-competition obligations hereunder, Employee will not,
     directly or indirectly for Employee or for others, in any geographic area
     or market where Employer or any of their affiliated companies are
     conducting any business (other than de minimis business operations) as of
     the date of termination of the employment relationship or have during the
     previous twelve (12) months conducted any business (other than de minimis
     business operations):

     (i)    engage in any business directly competitive with any business (other
            than de minimis business operations) conducted by Employer or any of
            Employer's affiliates:

     (ii)   render advice or services to, or otherwise assist, any other person,
            association, or entity who is engaged, directly or indirectly, in
            any business directly competitive with any business (other than de
            minimis business operations) conducted by Employer or any of
            Employer's affiliates; or

     (iii)  induce any employee of Employer or any of its affiliates (other than
            Employee's personal secretary or administrative assistant) to
            terminate his employment with Employer, or its affiliates, or hire
            or assist in the hiring of any such induced employee by any person,
            association, or entity not affiliated with Employer.

     These non-competition obligations shall extend until one (1) year after
     termination of the employment relationship between Employer and Employee.
     The above notwithstanding, nothing in this Section 5.1 shall prohibit
     Employee from engaging in or being employed by 

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     any entity that engages in the provision of management consulting or other
     consulting services to third parties, even where such entity on occasion
     renders advice or services to, or otherwise assists, any other person,
     association, or entity who is engaged, directly or indirectly, in any
     business directly competitive with any business conducted by Employer or
     any of Employer's affiliates, so long as Employee does not personally,
     directly or indirectly (i) participate in rendering such advice, services
     or assistance to any such competing person, association or entity, (ii)
     provide any information or other assistance to any other person employed by
     Employee or by any such consulting entity for use, directly or indirectly,
     in rendering such assistance to any competing person, association or entity
     or (iii) engage in any conduct which would be violative of the provisions
     of Article 4 hereof.

5.2  Employee understands that the foregoing restrictions may limit his ability
     to engage in certain businesses anywhere in the world during the period
     provided for above, but acknowledges that Employee will receive
     sufficiently high remuneration and other benefits under this Agreement to
     justify such restriction.  Employee acknowledges that money damages would
     not be sufficient remedy for any breach of this Article 5 by Employee, and
     agrees that Employer, on its own behalf or on behalf of any of its
     affiliates, shall be entitled to specific performance and injunctive relief
     as remedies for such breach or any threatened breach.  Such remedies shall
     not be deemed the exclusive remedies for a breach of this Article 5, but
     shall be in addition to all remedies available at law or in equity to
     Employer, including, without limitation, the recovery of damages from
     Employee and his agents involved in such breach.

5.3  It is expressly understood and agreed that Employer and Employee consider
     the restrictions contained in this Article 5 to be reasonable and necessary
     to protect the proprietary information and/or goodwill of Employer and its
     affiliates.  Nevertheless, if any of the aforesaid restrictions are found
     by a court having jurisdiction to be unreasonable, or overly broad as to
     geographic area or time, or otherwise unenforceable, the parties intend for
     the restrictions therein set forth to be modified by such courts so as to
     be reasonable and enforceable and, as so modified by the court, to be fully
     enforced.

ARTICLE 6:          MISCELLANEOUS

6.1  For purposes of this Agreement, (i) the terms 'affiliates' or affiliated'
     means an entity who directly, or indirectly through one or more
     intermediaries, controls, is controlled by, or is under common control with
     Employer or in which Employer has a 50% or more equity interest, and (ii)
     any action or omission permitted to be taken or omitted by Employer
     hereunder shall only be taken or omitted by Employer upon the express
     authority of the Board of Directors of Employer or of any Committee of the
     Board to which authority over such matters may have been delegated.

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6.2  For purposes of this Agreement, notices and all other communications
     provided for herein shall be in writing and shall be deemed to have been
     duly given when received by or tendered to Employee or Employer, as
     applicable, by prepaid courier or by United States registered or certified
     mail, return receipt requested, postage prepaid, addressed as follows:

          If to Employer, Halliburton Company at its corporate headquarters to
          the attention of the General Counsel of Halliburton Company.

          If to Employee, to his last known personal residence.

6.3  This Agreement shall be governed in all respects by the laws of the State
     of Texas, without regard to any conflict-of-law rule or principle, unless
     preempted by federal law, in which case federal law shall govern.

6.4  No failure by either party hereto at any time to give notice of any breach
     by the other party of, or to require compliance with, any condition or
     provision of this Agreement shall be deemed a waiver of similar or
     dissimilar provisions or conditions at the same or at any prior or
     subsequent time.

6.5  It is a desire and intent of the parties that the terms, provisions,
     covenants, and remedies contained in this Agreement shall be enforceable to
     the fullest extent permitted by law.  If any such term, provision,
     covenant, or remedy of this Agreement or the application thereof to any
     person, association, or entity or circumstances shall, to any extent, be
     construed to be invalid or unenforceable in whole or in part, then such
     term, provision, covenant, or remedy shall be construed in a manner so as
     to permit its enforceability under the applicable law to the fullest extent
     permitted by law.  In any case, the remaining provisions of this Agreement
     or the application thereof to any person, association, or entity or
     circumstances other than those to which they have been held invalid or
     unenforceable, shall remain in full force and effect.

6.6  This Agreement shall be binding upon and inure to the benefit of Employer
     and any other person, association, or entity which may hereafter acquire or
     succeed to all or substantially all of the business or assets of Employer
     by any means whether direct or indirect, by purchase, merger,
     consolidation, or otherwise.  Employee's rights and obligations under this
     Agreement are personal and such rights, benefits, and obligations of
     Employee shall not be voluntarily or involuntarily assigned, alienated, or
     transferred, whether by operation of law or otherwise, without the prior
     written consent of Employer, other than in the case of death or
     incompetence of Employee.

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6.7  This Agreement replaces and merges any previous agreements and discussions
     pertaining to the subject matter covered herein.  Further, this Agreement
     specifically replaces and terminates that certain Employee Severance
     Agreement between Employee and Dresser dated February 25, 1998.  This
     Agreement constitutes the entire agreement of the parties with regard to
     such subject matter, and contains all of the covenants, promises,
     representations, warranties, and agreements between the parties with
     respect to such subject matter.  Each party to this Agreement acknowledges
     that no representation, inducement, promise, or agreement, oral or written,
     has been made by either party with respect to such subject matter, which is
     not embodied herein, and that no agreement, statement, or promise relating
     to the employment of Employee by Employer that is not contained in this
     Agreement shall be valid or binding.  Any modification of this Agreement
     will be effective only if it is in writing and signed by each party whose
     rights hereunder are affected thereby, provided that any such modification
     must be authorized or approved by the Board of Directors of Employer.

     IN WITNESS WHEREOF, Employer and Employee have duly executed this Agreement
at Dallas, Texas in multiple originals to be effective on the Effective Date.

                                         HALLIBURTON COMPANY


                                         By:
                                            ------------------------------------
                                              Richard B. Cheney
                                              Chairman of the Board and
                                              Chief Executive Officer

                                         EMPLOYEE


                                         By:
                                            ------------------------------------
                                         Name:    William E. Bradford

Date:
     ---------------------------

                                      -12-

 
                                  EXHIBIT A TO
                         EXECUTIVE EMPLOYMENT AGREEMENT
                     BY AND BETWEEN WILLIAM E. BRADFORD AND
                              HALLIBURTON COMPANY



                           INDEMNIFICATION AGREEMENT


     THIS AGREEMENT is made this         day of                      , 1998, by
                                 -------        ---------------------
and between Halliburton Company, a Delaware corporation, (the 'Company') and
William E. Bradford (the 'Indemnitee').

A.   The Indemnitee has been requested to serve, or is presently serving, as a
     Director and/or an officer of the Company.  The Company desires the
     Indemnitee to serve or to continue to serve in such capacity.  The Company
     believes that the Indemnitee's undertaking or continued undertaking of such
     responsibilities is important to the Company and that the protection
     afforded by this Agreement will enhance the Indemnitee's ability to
     discharge such responsibilities under existing circumstances.  The
     Indemnitee is willing, subject to certain conditions including, without
     limitation, the execution and performance of this Agreement by the Company
     and the Company's agreement to provide the Indemnitee at all times the
     broadest and most favorable (to Indemnitee)) indemnification permitted by
     applicable law (whether by legislative action or judicial decision), to
     serve or to continue to serve in that capacity.

B.   In addition to the indemnification to which the Indemnitee is entitled
     under the Restated Certificate of Incorporation of the Company (the
     'Charter') or the By-laws, as amended, of the Company (the 'By-laws'), the
     Company has purchased and currently maintains insurance protecting its
     officers and directors and certain other persons (including the Indemnitee)
     against certain losses arising out of actual or threatened actions, suits
     or proceedings to which such persons may be made or threatened to be made
     parties ('D&O Insurance').

     NOW, THEREFORE, for and in consideration of the premises, the mutual
promises hereinafter set forth, the reliance of the Indemnitee hereon in
continuing to serve the Company in his present capacity and in undertaking to
serve the Company in any additional capacity or capacities, the Company and the
Indemnitee agree as follows:

1.   Indemnification - General.  The Company shall indemnify and advance
     -------------------------
     Expenses (as hereinafter defined) to Indemnitee to the fullest extent, and
     only to the extent, permitted by applicable law in effect on the date
     hereof and to such greater extent as applicable law may thereafter from
     time to time permit.  The rights of Indemnitee provided under the 

                                      A-1

 
Exhibit A
Executive Employment Agreement
William E. Bradford


     preceding sentence shall include, but shall not be limited to, the rights
     set forth in the other Sections of this Agreement.

     Although there can be no assurance as to the continuation or renewal of the
     D&O Insurance or that any such D&O Insurance will provide coverage for
     losses to which the Indemnitee may be exposed, the Company will use
     commercially reasonable efforts, taking into consideration availability of
     D&O Insurance in the marketplace, to continue D&O Insurance in effect at
     current levels for the duration of Indemnitee's service and for six (6)
     years thereafter.

2.   Proceedings Other than Proceedings by or in the Right of the Company.
     --------------------------------------------------------------------
     Indemnitee shall be entitled to the indemnification rights provided in this
     Section 2 if, by reason of his Corporate Status (as hereinafter defined),
     he is, or is threatened to be made, a party to, or otherwise incurs
     Expenses in connection with, any threatened, pending or completed
     Proceeding (as hereinafter defined), other than a Proceeding by or in the
     right of the Company.  Pursuant to this Section 2, Indemnitee shall be
     indemnified against Expenses, judgments, penalties, fines and amounts paid
     in settlement actually and reasonably incurred by him or on his behalf in
     connection with such Proceeding or any claim issue or matter therein, 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 Company, and, with respect to any
     criminal Proceeding, had no reasonable cause to believe his conduct was
     unlawful.

3.   Proceedings by or in the Right of the Company.  Indemnitee shall be
     ---------------------------------------------
     entitled to the indemnification rights provided in this Section 3, if, by
     reason of his Corporate Status, he is, or is threatened to be made, a party
     to, or otherwise incurs Expenses in connection with, any threatened,
     pending or completed Proceeding brought by or in the right of the Company
     to procure a judgment in its favor.  Pursuant to this Section 3, Indemnitee
     shall be indemnified against Expenses actually and reasonably incurred by
     him or on his behalf in connection with such 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 Company. Notwithstanding the forgoing, no
     indemnification against such Expenses shall be made in respect of any
     claim, issue or matter in such Proceeding as to which Indemnitee shall have
     been adjudged to be liable to the Company if applicable law prohibits such
     indemnification; provided, however, that, if applicable law so permits,
     indemnification against Expenses shall nevertheless be made by the Company
     despite such adjudication of liability, if and only to the extent that the
     Court of Chancery of the State of Delaware, or the court in which such
     Proceeding shall have been brought or is pending, shall determine.

                                      A-2

 
Exhibit A
Executive Employment Agreement
William E. Bradford


4.   Indemnification for Expenses of a Party Who is Wholly or Partly Successful.
     --------------------------------------------------------------------------
     Notwithstanding any other provision of this Agreement, to the extent that
     Indemnitee is, by reason of his Corporate Status, a party to and is
     successful, on the merits or otherwise, in any Proceeding, he shall be
     indemnified against all Expenses actually and reasonably incurred by him or
     on his behalf in connection therewith.  If Indemnitee is not wholly
     successful in such Proceeding but is successful on the merits or otherwise,
     as to one or more but less than all claims, issues or matters in such
     Proceeding, the Company shall indemnify Indemnitee against all Expenses
     actually and reasonably incurred by him or on his behalf in connection with
     each successfully resolved claim, issue or matter.  For the purposes of
     this Section 4 and without limitation, the termination of any claim, issue
     or matter in such a Proceeding by dismissal, with or without prejudice,
     shall be deemed to be a successful result as to such claim, issue or
     matter.

5.   Contribution.  In the event that the indemnity contained in Sections 2, 3
     ------------
     or 4 of this Agreement is unavailable or insufficient to hold Indemnitee
     harmless in a Proceeding described therein, then in accordance with the
     non-exclusivity provisions of the Delaware General Corporation Law and the
     Charter and By-laws, and separate from and in addition to, the indemnity
     provided elsewhere herein, the Company shall contribute to Expenses,
     judgments, penalties, fines and amounts paid in settlement actually and
     reasonably incurred by or on behalf of Indemnitee in connection with such
     Proceeding or any claim, issue or matter therein, in such proportion as
     appropriately reflects the relative benefits received by, and fault of, the
     Company on the one hand and Indemnitee on the other in the acts,
     transactions or matters to which the Proceeding relates and other equitable
     considerations.

6.   Procedure for Determination of Entitlement to Indemnification
     -------------------------------------------------------------

     (a)  To obtain indemnification under this Agreement, Indemnitee shall
          submit to the Company a written request, including such documentation
          and information as is reasonably available to Indemnitee and is
          reasonably necessary to determine whether and to what extent
          Indemnitee is entitled to indemnification.  The determination of
          Indemnitee's entitlement to indemnification shall be made not later
          than 90 days after receipt by the Company of the written request for
          indemnification.  The Secretary of the Company shall, promptly upon
          receipt of such a request for indemnification, advise the Board of
          Directors in writing that Indemnitee has requested indemnification.

     (b)  Indemnitee's entitlement to indemnification under any of Sections 2,
          3, 4 and 5 of this Agreement shall be determined in the specific case:
          (i) by the Board of 

                                      A-3

 
Exhibit A
Executive Employment Agreement
William E. Bradford


          Directors by a majority vote of a quorum of the Board consisting of
          Disinterested Directors (as hereinafter defined); (ii) by Independent
          Counsel (as hereinafter defined), in a written opinion if a quorum of
          the Board of Directors consisting of Disinterested Directors is not
          obtainable or, even if obtainable, such quorum of Disinterested
          Directors so directs; or (iii) by the stockholders of the Company. If,
          with regard to Section 5 of this Agreement, such a determination is
          not permitted by law or if a quorum of Disinterested Directors so
          directs, such determination shall be made by the Chancery Court of the
          State of Delaware or the court in which the Proceeding giving rise to
          the claim for indemnification is brought.

     (c)  In the event that the determination of entitlement to indemnification
          is to be made by Independent Counsel pursuant to Section 6(b) of this
          Agreement, the Independent Counsel shall be selected as provided in
          this Section 6(c).  The Independent Counsel shall be selected by the
          Board of Directors, and the Company shall give written notice to
          Indemnitee advising him of the identity of the Independent Counsel so
          selected.  Indemnitee may, within 7 days after receipt of such written
          notice of selection shall have been given, deliver to the Company a
          written objection to such selection.  Such objection may be asserted
          only on the ground that the Independent Counsel so selected does not
          meet the requirements of 'Independent Counsel' as defined in Section
          13 of this Agreement, and the objection shall set forth with
          particularity the factual basis of such assertion.  If such written
          objection is made, the Independent Counsel so selected shall be
          disqualified from acting as such.  If, within 20 days after submission
          by Indemnitee of a written request for indemnification pursuant to
          Section 6(a) of this Agreement, no Independent Counsel shall have been
          selected, or if selected shall have been objected to, in accordance
          with this Section 6(c), either the Company or Indemnitee may petition
          the Court of Chancery of the State of Delaware for the appointment as
          Independent Counsel of a person selected by such court or by such
          other person as such court shall designate, and the person so
          appointed shall act as Independent Counsel under Section 6(b) of this
          Agreement, and the Company shall pay all reasonable fees and expenses
          incident to the procedures of this Section 6(c), regardless of the
          manner in which such Independent Counsel was selected or appointed.

7.   Advancement of Expenses.  The Company shall advance all reasonable Expenses
     -----------------------
     incurred by or on behalf of Indemnitee in connection with any Proceeding
     within 20 days after the receipt by the Company of a statement or
     statements from Indemnitee requesting such advance or advances from time to
     time, whether prior to or after final disposition of such 

                                      A-4

 
Exhibit A
Executive Employment Agreement
William E. Bradford


     Proceeding. Indemnitee shall, and hereby undertakes to, repay any Expenses
     advanced if it shall ultimately be determined that Indemnitee is not
     entitled to be indemnified against such Expenses.

8.   Presumptions and Effect of Certain Proceedings.  The termination of any
     ----------------------------------------------                         
     proceeding described in any of Sections 2, 3 or 4 of this Agreement, or of
     any claim, issue or matter therein, by judgment, order, settlement or
     conviction, or upon a plea of nolo contendere or its equivalent, shall not
                                   ---- ----------                             
     (except as otherwise expressly provided in this Agreement) of itself
     adversely affect the right of Indemnitee to indemnification or create a
     presumption that Indemnitee 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
     Company or, with respect to any criminal Proceeding, that Indemnitee had
     reasonable cause to believe that his conduct was unlawful.

9.   Term of Agreement.  All agreements and obligations of the Company contained
     -----------------                                                          
     herein shall commence as of the time the Indemnitee commenced to serve as a
     director, officer, employee or agent of the Company (or commenced to serve
     at the request of the Company as a director, officer, employee or agent of
     another corporation, partnership, joint venture, trust, employee benefit
     plan or other enterprise) and shall continue for so long as Indemnitee
     shall so serve or shall be, or could become, subject to any possible
     Proceeding in respect of which Indemnitee is granted rights of
     indemnification or advancement of Expenses hereunder.

10.  Notification and Defense of Claim.  Promptly after receipt by Indemnitee of
     ---------------------------------                                          
     notice of the commencement of any Proceeding, Indemnitee will, if a claim
     in respect thereof is to be made against the Company under this Agreement,
     notify the Company of the commencement thereof; but the omission to notify
     the Company will not relieve it from any liability which it may have to
     Indemnitee otherwise than under this Agreement.  With respect to any such
     Proceeding as to which Indemnitee notifies the Company of the commencement
     thereof:

     (a)  The Company will be entitled to participate therein at its own
          expense.

     (b)  Except as otherwise provided below, to the extent that it may wish,
          the Company jointly with any other indemnifying party similarly
          notified will be entitled to assume the defense thereof, with counsel
          satisfactory to Indemnitee.  After notice from the Company to
          Indemnitee of its election so to assume the defense thereof, the
          Company will not be liable to Indemnitee under this Agreement for any
          legal or other Expenses subsequently incurred by Indemnitee in
          connection with the 

                                      A-5

 
Exhibit A
Executive Employment Agreement
William E. Bradford


          defense thereof other than reasonable costs of investigation or as
          otherwise provided below. Indemnitee shall have the right to employ
          its counsel in such Proceeding but the fees and Expenses of such
          counsel incurred after notice from the Company of its assumption of
          the defense thereof shall be at the expense of Indemnitee unless (i)
          the employment of counsel by Indemnitee has been authorized by the
          Company, or (ii) Indemnitee shall have reasonably concluded that there
          may be a conflict of interest between the Company and Indemnitee in
          the conduct of the defense of such Proceeding, or (iii) the Company
          shall not in fact have employed counsel to assume the defense of such
          Proceeding, in each of which cases the fees and Expenses of counsel
          shall be at the expense of the Company. The Company shall not be
          entitled to assume the defense of any Proceeding brought by or on
          behalf of the Company or as to which Indemnitee shall have made the
          conclusion provided for in (ii) above.

     (c)  The Company shall not be liable to indemnify Indemnitee under this
          Agreement for any amounts paid in settlement of any Proceeding or
          claim effected without its written consent.  The Company shall not
          settle any Proceeding or claim in any manner which would impose any
          penalty or limitation on Indemnitee without Indemnitee's written
          consent.  Neither the Company nor Indemnitee will unreasonably
          withhold their consent to any proposed settlement.

11.  Enforcement
     -----------

     (a)  The Company expressly confirms and agrees that it has entered into
          this Agreement and assumed the obligations imposed on it hereby in
          order to induce Indemnitee to serve or continue to serve as a director
          and/or officer of the Company, and acknowledges that Indemnitee is
          relying upon this Agreement in serving or continuing to serve in such
          capacity.

     (b)  In the event Indemnitee is required to bring any action to enforce
          rights or to collect moneys due under this Agreement and is successful
          in such action, the Company shall reimburse Indemnitee for all of
          Indemnitee's reasonable fees and Expenses in bringing and pursuing
          such action.

12.  Non-Exclusivity of Rights.  The rights of indemnification and to receive
     -------------------------                                               
     advancement of Expenses as provided by this Agreement shall not be deemed
     exclusive of any other rights to which Indemnitee may at any time be
     entitled under applicable law, the Charter, the By-laws, any agreement, a
     vote of stockholders or a resolution of directors, or otherwise.

                                      A-6

 
Exhibit A
Executive Employment Agreement
William E. Bradford


13.  Definitions.  For purposes of this Agreement:
     -----------                                  

     (a)  'Corporate Status' describes the status of a person who is or was a
          director, officer, employee, agent or fiduciary of the Company or of
          any other corporation, partnership, joint venture, trust, employee
          benefit plan or other enterprise which such person is or was serving
          at the request of the Company.

     (b)  'Disinterested Director' means a director of the Company who is not
          and was not at any time a party to the Proceeding in respect of which
          indemnification is sought by Indemnitee.

     (c)  'Expenses' shall include all reasonable attorneys' fees, retainers,
          court costs, transcript costs, fees of experts, witness fees, travel
          expenses, duplicating costs, printing and binding costs, telephone
          charges, postage, delivery service fees, and all other disbursements
          or Expenses of the types customarily incurred in connection with
          prosecuting, defending, preparing to prosecute or defend or
          investigating a Proceeding.

     (d)  'Independent Counsel' means a law firm, or a member of a law firm,
          that is experienced in matters of corporation law and neither
          presently is, nor in the past five years has been, retained to
          represent: (i) the Company or Indemnitee in any matter material to
          either such party or (ii) any other party to the Proceeding giving
          rise to a claim for indemnification hereunder.  Notwithstanding the
          foregoing, the term 'Independent Counsel' shall not include any person
          who, under the applicable standards of professional conduct then
          prevailing, would have a conflict of interest in representing either
          the Company or Indemnitee in an action to determine Indemnitee's
          rights under this Agreement.

     (e)  'Proceeding' includes any action, suit, arbitration, alternate dispute
          resolution mechanism, investigation, administrative hearing or any
          other proceeding whether civil, criminal, administrative or
          investigative.

14.  Severability.  Each of the provisions of this Agreement is a separate and
     ------------                                                             
     distinct agreement and independent of the others, so that if any provision
     hereof shall be held to be invalid or unenforceable for any reason, such
     invalidity or unenforceability shall not affect the validity or
     enforceability of the other provisions hereof.

                                      A-7

 
Exhibit A
Executive Employment Agreement
William E. Bradford


15.  Governing Law; Binding Effect; Amendment and Termination.
     -------------------------------------------------------- 

     (a)  THIS AGREEMENT SHALL BE INTERPRETED AND ENFORCED IN ACCORDANCE WITH
          THE LAWS OF THE STATE OF DELAWARE, EXCLUDING ANY CONFLICT-OF-LAW RULE
          OR PRINCIPLE THAT MIGHT REFER TO THE LAWS OF ANOTHER STATE OR COUNTRY.

     (b)  This Agreement shall be binding upon Indemnitee and upon the Company,
          its successors and assigns, and shall inure to the benefit of
          Indemnitee, his heirs, personal representatives and assigns and to the
          benefit of the Company, its successors and assigns.

     (c)  No amendment, modification, termination or cancellation of this
          Agreement shall be effective unless in writing by the parties.

     The parties have executed this Agreement as of the day and year first above
written.



                                    HALLIBURTON COMPANY



                                    By:
                                       -----------------------------------------
                                         Richard B. Cheney
                                         Chief Executive Officer



                                    By:
                                       -----------------------------------------
                                         William E. Bradford
                                         Indemnitee

                                      A-8

 
                                  Exhibit B to
                         Executive Employment Agreement
                     By and Between William E. Bradford and
                              Halliburton Company

                             STOCK OPTION STATEMENT


   Grant    Grant              Options     Options       Option     Expiration       Options
   Date     Type               Granted   Outstanding      Price        Date          Vested
---------------------------------------------------------------------------------------------------------
                                                                       
5/17/1990   NQSO          R      2,138      2,138       $25.15630     5/16/2000       2,138    current

8/28/1995   Restricted           6,445                    $.00000                         0    current
                                                                                      6,445 on 8/28/1998

11/16/1995  NQSO          R     50,000     10,000       $21.75000    11/15/2005      10,000    current

11/16/1995  NQSO          R     50,000     50,000       $23.75000    11/15/2005      50,000    current

11/16/1995  NQSO          R     48,025     48,025       $25.75000    11/15/2005      48,025    current

1/18/1996   NQSO          R     10,744     10,744       $23.87500     1/17/2006      10,744    current

1/18/1996   NQSO          R     10,744     10,744       $25.87500     1/17/2006      10,744    current

1/18/1996   NQSO          R      7,158      7,158       $27.87500     1/17/2006       7,158    current

1/18/1996   ISO           R      3,587      3,587       $27.87500     1/17/2006       3,587    current

1/6/1997    Restricted           1,292                    $.00000                         0    current
                                                                                      1,292 on 1/6/2000

1/6/1997    Restricted             520                    $.00000                         0    current
                                                                                        520 on 1/6/2000

1/6/1997    Restricted             466                    $.00000                         0    current
                                                                                        466 on 1/6/2000

1/16/1997   ISO           R      2,507      2,507       $39.87500     1/15/2007           0    current
                                                                                      2,507 on 1/16/1999

1/16/1997   NQSO          R     11,525     11,525       $35.87500     1/15/2007      11,525    current

1/16/1997   NQSO          R     11,525     11,525       $37.87500     1/15/2007      11,525    current

1/16/1997   NQSO          R      9,018      9,018       $39.87500     1/15/2007           0    current
                                                                                      9,018 on 1/16/1999

1/16/1997   Restricted          30,000                    $.00000                         0    current
                                                                                     30,000 on 11/21/1999

11/20/1997  NQSO          R    331,500    331,500       $38.87500    11/19/2007           0    current


As of 5/12/1998                  Page 1 of 2

 
                                  Exhibit B to
                         Executive Employment Agreement
                     By and Between William E. Bradford and
                              Halliburton Company

                             STOCK OPTION STATEMENT


   Grant    Grant              Options     Options       Option     Expiration       Options
   Date     Type               Granted   Outstanding      Price        Date          Vested
---------------------------------------------------------------------------------------------------------
                                                                       
1/5/1998    Restricted           8,861                    $.00000                         0    current
                                                                                      8,861 on 1/4/2001

1/15/1998   NQSO          R     24,268     24,268       $36.81250    1/14/2008            0    current
                                                                                     24,268 on 7/15/1998

1/15/1998   NQSO          R     24,268     24,268       $38.81250    1/14/2008            0    current
                                                                                     24,268 on 1/15/1999

1/15/1998   ISO           R      2,450      2,450       $40.81250    1/14/2008            0    current
                                                                                      2,450 on 1/15/2000

1/15/1998   NQSO          R     21,818     21,818       $40.81250    1/14/2008            0    current
                                                                                     21,818 on 1/15/2000
---------------------------------------------------------------------------------------------------------

                                 Total Stock Options Exercisable                    165,446
 



As of 5/12/1998                  Page 2 of 2