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

                                  SUPPLEMENT TO
                         EXECUTIVE EMPLOYMENT AGREEMENT



         This Supplement dated as of December 2, 1999 ('Supplement')  amends and
supplements   that   certain   Executive   Employment   Agreement,   as  amended
('Agreement')  entered into by and between Halliburton Company  ('Employer') and
William E. Bradford ('Employee') effective as of September 29, 1998. Capitalized
terms used herein but not defined  shall have the  meanings  ascribed to them in
the Agreement.

         1.   Section 1.1 of the Agreement is amended to read in its entirety as
follows:

                  '1.1 The term of the  Agreement  is from  the  Effective  Date
                  through February 29, 2000 (the 'Term'), on which date Employee
                  shall retire as an employee of Employer.'

         2.   Section 1.2 of the Agreement is hereby amended and supplemented by
adding the following language to the end thereof:

                  'On January 31, 2000,  Employee  shall  voluntarily  resign as
                  Chairman of the Board of Employer,  as a member of  Employer's
                  Board  of  Directors  and  from all  other  positions,  posts,
                  offices and  assignments  with  Employer or any of  Employer's
                  affiliates,  including, but not limited to, Employee's service
                  as a member of the  Executive  Committee  of Employer and as a
                  Trustee of the Halliburton Foundation, Inc.'

         3.   Section 2.2 of  the Agreement  is hereby  amended by  deleting the
last sentence and inserting the following language in lieu thereof:

                  'For plan year 2000,  the bonus  payable to Employee  shall be
                  equal to the Average  Dresser Bonus prorated  through  January
                  31, 2000. Such bonus amount shall be paid to Employee prior to
                  December 31, 2000.'

         4.   The Agreement is hereby supplemented by the  following  additional
terms and provisions:

                  Beginning  March 1, 2000 and continuing  through  February 28,
                  2005, and expressly  contingent  upon  Employee's not being in
                  breach  of  his  obligations  under  Articles  4 and 5 of  the
                  Agreement, Employee shall be entitled to:

                           (i)      Office  space  and   part-time   secretarial
                                    support as mutually  agreed by Employer  and
                                    Employee.

                           (ii)     Office furnishings and equipment  (including
                                    computer   equipment   for   access  to  the
                                    Company's network).

                                     10-12


                                                                 Exhibit 10.12

                                  SUPPLEMENT TO
                         EXECUTIVE EMPLOYMENT AGREEMENT
                                  (continued)


         5.   Except as amended or  supplemented  hereby,  the  Agreement  shall
continue in full force and effect.

         IN WITNESS  WHEREOF,  Employee and  Employer  have duly  executed  this
Supplement in multiple originals as of the date first above written.

                            HALLIBURTON COMPANY



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




                            EMPLOYEE



                            /s/ William E. Bradford
                            --------------------------------
                                William E. Bradford


                                     10-12