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                                                                     EXHIBIT 4.1

                           CERTIFICATE OF DESIGNATION

                                       of

                 SERIES A JUNIOR PARTICIPATING PREFERRED STOCK

                                       of

                           CROSS TIMBERS OIL COMPANY

             Pursuant to Section 151 of the General Corporation Law
                            of the State of Delaware

     Cross Timbers Oil Company, a corporation organized and existing under the
General Corporation Law of the State of Delaware, in accordance with the
provisions of Section 103 thereof, DOES HEREBY CERTIFY:

     That pursuant to the authority vested in the Board of Directors in
accordance with the provisions of the Second Restated Certificate of
Incorporation of the said Corporation, the said Board of Directors on August 25,
1998 adopted the following resolution creating a series of 70,000 shares of
Preferred Stock designated as "Series A Junior Participating Preferred Stock":

          RESOLVED, that pursuant to the authority vested in the Board of
     Directors of this Corporation in accordance with the provisions of the
     Second Restated Certificate of Incorporation, a series of Preferred Stock,
     par value $.01 per share, of the Corporation be and hereby is created, and
     that the designation and number of shares thereof and the voting and other
     powers, preferences and relative, participating, optional or other rights
     of the shares of such series and the qualifications, limitations and
     restrictions thereof are as follows:

                 Series A Junior Participating Preferred Stock

     1.   Designation and Amount.  There shall be a series of Preferred Stock
that shall be designated as "Series A Junior Participating Preferred Stock," and
the number of shares constituting such series shall be 70,000.  Such number of
shares may be increased or decreased by resolution of the Board of Directors;
provided, however, that no decrease shall reduce the number of shares of Series
A Junior Participating  Preferred Stock to less than the number of shares then
issued and 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.

     2.   Dividends and Distribution.

          (A)  Subject to the prior and superior rights of the holders of any
shares of any class or series of stock of the Corporation ranking prior and
superior to the shares of Series A Junior
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Participating Preferred Stock with respect to dividends, the holders of shares
of Series A Junior Participating Preferred Stock, in preference to the holders
of shares of any class or series of stock of the Corporation ranking junior to
the Series A Junior Participating Preferred Stock in respect thereof, shall be
entitled to receive, when, as and if declared by the Board of Directors out of
funds legally available for the purpose, quarterly dividends payable in cash on
the 15th day of January, April, July and October, 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 Series A Junior Participating Preferred Stock, in an
amount per share (rounded to the nearest cent) equal to the greater of (a)
$10.00 or (b) the Adjustment Number (as defined below) times the aggregate per
share amount of all cash dividends, and the Adjustment Number 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 or a
subdivision of the outstanding shares of Common Stock (by reclassification or
otherwise), declared on the Common Stock, par value $.01 per share, of the
Corporation (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 Series A
Junior Participating Preferred Stock. The "Adjustment Number" shall initially be
1000. In the event the Corporation shall at any time after September 15, 1998
(i) declare and pay any dividend on Common Stock payable in shares of Common
Stock, (ii) subdivide the outstanding Common Stock or (iii) combine the
outstanding Common Stock into a smaller number of shares, then in each such case
the Adjustment Number in effect immediately prior to such event shall be
adjusted by multiplying such Adjustment 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)  The Corporation shall declare a dividend or distribution on
the Series A Junior Participating Preferred Stock as provided in paragraph (A)
above immediately after it declares a dividend or distribution on the Common
Stock (other than a dividend payable in shares of Common Stock).

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

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determination of holders of shares of Series A Junior Participating Preferred
Stock entitled to receive payment of a dividend or distribution declared
thereon, which record date shall be no more than 60 days prior to the date fixed
for the payment thereof.

       3.   Voting Rights.  The holders of shares of Series A Junior
Participating Preferred Stock shall have the following voting rights:

            (A)  Each share of Series A Junior Participating Preferred Stock
shall entitle the holder thereof to a number of votes equal to the Adjustment
Number on all matters submitted to a vote of the stockholders of the
Corporation.

            (B)  Except as required by law and by Section 10 hereof, holders of
Series A Junior Participating Preferred Stock shall have no special voting
rights and their consent shall not be required (except to the extent they are
entitled to vote with holders of Common Stock as set forth herein) for taking
any corporate action.

            (C)  If, at the time of any annual meeting of stockholders for the
election of directors, the equivalent of six quarterly dividends (whether or not
consecutive) payable on any share or shares of Series A Junior Participating
Preferred Stock are in default, the number of directors constituting the Board
of Directors of the Company shall be increased by two. In addition to voting
together with the holders of Common Stock for the election of other directors of
the Company, the holders of record of the Series A Junior Participating
Preferred Stock, voting separately as a class to the exclusion of the holders of
Common Stock, shall be entitled at said meeting of stockholders (and at each
subsequent annual meeting of stockholders), unless all dividends in arrears on
the Series A Junior Participating Preferred Stock have been paid or declared and
set apart for payment prior thereto, to vote for the election of two directors
of the Company, the holders of any Series A Junior Participating Preferred Stock
being entitled to cast a number of votes per share of Series A Junior
Participating Preferred Stock as is specified in paragraph (A) of this Section
3. Each such additional director shall not be a member of Class I, Class II, or
Class III of the Board of Directors of the Company, but shall serve until the
next annual meeting of stockholders for the election of directors, or until his
successor shall be elected and shall qualify, or until his right to hold such
office terminates pursuant to the provisions of this Section 3(C). Until the
default in payments of all dividends which permitted the election of said
directors shall cease to exist, any director who shall have been so elected
pursuant to the next preceding sentence may be removed at any time, without
cause, only by the affirmative vote of the holders of the shares of Series A
Junior Participating Preferred Stock at the time entitled to cast a majority of
the votes entitled to be cast for the election of any such director at a special
meeting of such holders called for that purpose, and any vacancy thereby created
may be filled by the vote of such holders. If and when such default shall cease
to exist, the holders of the Series A Junior Participating Preferred Stock shall
be divested of the foregoing special voting rights, subject to revesting in the
event of each and every subsequent like default in payments of dividends. Upon
the termination of the foregoing special voting rights, the terms of office of
all persons who may have been elected directors pursuant to said special voting
rights shall forthwith terminate, and the number of directors constituting the
Board of Directors shall be reduced by two. The voting

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rights granted by this Section 3(C) shall be in addition to any other voting
rights granted to the holders of the Series A Junior Participating Preferred
Stock in this Section 3.

     4.   Certain Restrictions.

          (A)  Whenever quarterly dividends or other dividends or distributions
payable on the Series A Junior Participating Preferred Stock as provided in
Section 2 are in arrears, thereafter and until all accrued and unpaid dividends
and distributions, whether or not declared, on shares of Series A Junior
Participating 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 (either as to dividends or upon liquidation, dissolution or
winding up) to the Series A Junior Participating Preferred Stock;

               (ii) declare or pay dividends on or make any other distributions
on any shares of stock ranking on a parity (either as to dividends or upon
liquidation, dissolution or winding up) with the Series A Junior Participating
Preferred Stock, except dividends paid ratably on the Series A Junior
Participating 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 Series A Junior Participating Preferred Stock, or any shares of stock
ranking on a parity with the Series A Junior Participating 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 Series A Junior
Participating Preferred Stock, or to such holders and holders of any such shares
ranking on a parity therewith, 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 4, purchase or otherwise acquire such shares at such time and in
such manner.

          5.  Reacquired Shares. Any shares of Series A Junior Participating
Preferred Stock purchased or otherwise acquired by the Corporation in any manner
whatsoever shall be retired promptly after the acquisition thereof. All such
shares shall upon their retirement become authorized but unissued shares of
Preferred Stock and may be reissued as part of a new series of Preferred

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Stock to be created by resolution or resolutions of the Board of Directors,
subject to any conditions and restrictions on issuance set forth herein.

          6.   Liquidation, Dissolution or Winding Up. (A) Upon any liquidation,
dissolution or winding up of the Corporation, voluntary or otherwise, no
distribution shall be made to the holders of shares of stock ranking junior
(either as to dividends or upon liquidation, dissolution or winding up) to the
Series A Junior Participating Preferred Stock unless, prior thereto, the holders
of shares of Series A Junior Participating Preferred Stock shall have received
an amount per share (the "Series A Liquidation Preference") equal to the greater
of (i) $10.00 plus an amount equal to accrued and unpaid dividends and
distributions thereon, whether or not declared, to the date of such payment, or
(ii) the Adjustment Number times the per share amount of all cash and other
property to be distributed in respect of the Common Stock upon such liquidation,
dissolution or winding up of the Corporation.

               (B)  In the event, however, that there are not sufficient assets
available to permit payment in full of the Series A Liquidation Preference and
the liquidation preferences of all other classes and series of stock of the
Corporation, if any, that rank on a parity with the Series A Junior
Participating Preferred Stock in respect thereof, then the assets available for
such distribution shall be distributed ratably to the holders of the Series A
Junior Participating Preferred Stock and the holders of such parity shares in
proportion to their respective liquidation preferences.

               (C)  Neither the merger or consolidation of the Corporation into
or with another corporation nor the merger or consolidation of any other
corporation into or with the Corporation shall be deemed to be a liquidation,
dissolution or winding up of the Corporation within the meaning of this Section
6.

          7.  Consolidation, Merger, Etc. In case the Corporation shall enter
into any consolidation, merger, combination or other transaction in which the
outstanding shares of Common Stock are exchanged for or changed into other stock
or securities, cash and/or any other property, then in any such case each share
of Series A Junior Participating Preferred Stock shall at the same time be
similarly exchanged or changed in an amount per share equal to the Adjustment
Number times the aggregate amount of stock, securities, cash and/or any other
property (payable in kind), as the case may be, into which or for which each
share of Common Stock is changed or exchanged.

          8.   No Redemption. Shares of Series A Junior Participating Preferred
Stock shall not be subject to redemption by the Company.

          9.   Ranking. The Series A Junior Participating Preferred Stock shall
rank junior to all other series of the Preferred Stock as to the payment of
dividends and as to the distribution of assets upon liquidation, dissolution or
winding up, unless the terms of any such series shall provide otherwise, and
shall rank senior to the Common Stock as to such matters.

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          10.  Amendment.  At any time that any shares of Series A Junior
Participating Preferred Stock are outstanding, 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 Series A Junior
Participating Preferred Stock so as to affect them adversely without the
affirmative vote of the holders of two-thirds of the outstanding shares of
Series A Junior Participating Preferred Stock, voting separately as a class.

          11.  Fractional Shares. Series A Junior Participating Preferred Stock
may be issued in fractions of a share that shall entitle the holder, in
proportion to such holder's fractional shares, to exercise voting rights,
receive dividends, participate in distributions and to have the benefit of all
other rights of holders of Series A Junior Participating Preferred Stock.

          IN WITNESS WHEREOF, the undersigned has executed this Certificate this
25th day of August, 1998.

                                          CROSS TIMBERS OIL COMPANY


                                          By: /s/ BOB R. SIMPSON
                                             ------------------------------
                                             Name: Bob R. Simpson
                                             Title: Chairman of the Board

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