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.

         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  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:

                  (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 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.

         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