Document:

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                                                                    EXHIBIT 10.9

                             PURE RESOURCES, INC.

                                EQUITY PLAN FOR
                               OUTSIDE DIRECTORS

     Section 1.     Establishment and Purpose.  Pure Resources, Inc., a Delaware
                    -------------------------
corporation (the "Company"), hereby establishes this Pure Resources, Inc. Equity
Plan for Outside Directors (the "Plan").  The purpose of the Plan is to
encourage the highest level of director performance by providing outside
directors of the Company with a more direct interest in the Company's attainment
of its financial goals.

     Section 2.     Certain Definitions.  For purposes of the Plan, the
                    -------------------
following terms shall have the indicated meanings:

     (a) "Annual Retainer" shall have the meaning specified in Section 5(a)
hereof.

     (b) "Board of Directors" means the Board of Directors of the Company.

     (c) "Cash Compensation" shall have the meaning specified in Section 5(a)
hereof.

     (d) "Cash Unit" means the entry in a Deferred Compensation Account of a
fictional deferred compensation unit equal to One Dollar to be used solely for
accounting purposes under this Plan.

     (e) "Common Stock" means the Common Stock, par value $.01 per share, of the
Company, or any stock or other securities of the Company hereafter issued or
issuable in substitution or exchange for the Common Stock.

     (f) "Committee" means the committee appointed by the Board of Directors to
administer the Plan pursuant to Section 3.

     (g) "Deferred Compensation Account" shall have the meaning specified in
Section 6(d) hereof.

     (h) "Director Compensation" shall have the meaning specified in Section 6
hereof.

     (i) "Fair Market Value" of a share of Common Stock means, as of a
particular Trading Date, (i) if shares of Common Stock are listed on a national
securities exchange, the average of the high and low sales prices of Common
Stock on the consolidated transaction reporting system for the principal
national securities exchange on which shares of Common Stock are listed on that
date, or, if there shall have been no such sale so reported on that date, on the
last preceding date on which such a sale was so reported, (ii) if shares of
Common Stock are not so listed but are quoted on the NASDAQ National Market
System, the average of the high and low sales prices of Common Stock reported by
the NASDAQ National Market System on that date, or, if there shall have been no
such sale so reported on that date, on the last preceding date on which such a
sale was so reported, (iii) if the Common Stock is not so listed or quoted, the
average of the high and low sales prices on that date, or, if there are no
quotations available for such date, on the last preceding date on which such
quotations shall be available, as reported by the NASDAQ National Market System,
or, if not
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reported by the NASDAQ National Market System, by the National Quotation Bureau
Incorporated or (iv) if shares of Common Stock are not publicly traded, the
value determined by an independent appraiser appointed by the Company for such
purpose.

     (j) "Interest Equivalent" means the entry in a Deferred Compensation
Account of an interest credit with respect to a Cash Unit, the interest factor
initially being equal to 6.34% per year. Without notice to an Outside Director
or any other person, the Interest Equivalent shall automatically be increased or
decreased, as the case may be, on the first day of each Plan Year, such that the
Interest Equivalent shall then be equal to Company's average cost of funds for
the twelve month period ending on September 30 of such year.

     (k) "Outside Director" means an individual duly elected or chosen as a
director of the Company who is not also an officer or employee of the Company or
any of its affiliates.

     (l) "Plan Quarter" means each of the following three-month periods during a
Plan Year: (i) the period commencing on the first day of the Plan Year and
ending on and including the day prior to the day which is three months after the
first day of the Plan Year, (ii) the period commencing three months after the
first day of the Plan Year and ending on and including the day prior to the day
which is six months after the first day of the Plan Year, (iii) the period
commencing six months after the first day of the Plan Year and ending on and
including the day prior to the day which is nine months after the first day of
the Plan Year, and (iv) the period commencing nine months after the first day of
the Plan Year and ending on and including the day prior to the next following
Plan Year.

     (m) "Plan Year" means each 12-month period commencing on the date of the
annual meeting of the shareholders of the Company and ending on and including
the day prior to the next following annual meeting of the shareholders of the
Company, except that the first Plan Year hereunder shall commence on the date of
consummation of the merger of TRH, Inc. with into Titan Exploration, Inc.
pursuant to the terms of the Agreement and Plan of Merger dated as of December
13, 1999, by and among Union Oil Company of California, the Company, TRH, Inc.,
and Titan Exploration, Inc. and end on and include the day prior to the 2001
annual meeting of the shareholders of the Company.

     (n) "Required Share Amount" means an amount of money constituting 60% of an
Outside Director's Annual Retainer earned by such Outside Director for his
services as a director of the Company for a Plan Year, which amount is payable
in whole shares of Common Stock pursuant to Section 5(c) hereof.

     (o) "Share Award" means an issuance of shares of Common Stock to an Outside
Director pursuant to the provisions of the Plan.

     (p) "Stock Compensation" means the compensation earned by an Outside
Director for his services as a director of the Company which is payable in whole
shares Common Stock pursuant to Section 5(c).

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     (q)  "Stock Unit" means the entry in a Deferred Compensation Account of a
fictional deferred compensation unit equal to one share of Common Stock to be
used solely for accounting purposes under this Plan.

     (r) "Term of Office" means the term of office as a director of the Company
for which the Outside Director has been elected pursuant to and in accordance
with the provisions of the certificate of incorporation and bylaws of the
Company.

     (s) "Trading Day" means any day on which the stock exchange or stock market
referred to in Section 2(e) hereof is open for trading on a regular basis.

     (t) "Voluntary Share Amount" means the amount of Cash Compensation earned
by an Outside Director for a Plan Year which the Outside Director elects to
apply to the purchase of shares of Common Stock pursuant to Section 5(b) hereof.

     Section 3.     Plan Administration.  The Committee shall be responsible for
                    -------------------
the administration of the Plan.  The Committee shall be appointed by and serve
at the pleasure of the Board of Directors and shall be composed solely of at
least three members of the Board of Directors who are not Outside Directors.
The Committee shall have total and exclusive responsibility to control, operate,
manage and administer the Plan in accordance with its terms.  The Committee
shall have all the authority that may be necessary or helpful to enable it to
discharge its responsibilities with respect to the Plan.  Without limiting the
foregoing, the Committee is authorized to interpret the Plan, prescribe, amend,
and rescind rules and regulations relating to the Plan, provide for conditions
and assurances deemed necessary or advisable to protect the interests of the
Company in connection with the operation of the Plan, and make all other
determinations necessary or advisable for the administration of the Plan, but
only to the extent not contrary to the express provisions of the Plan.  No
member of the Board of Directors or the Committee shall be liable for any action
or determination made in good faith with respect to the Plan.  The
determinations, interpretations, and other actions of the Board of Directors and
the Committee pursuant to the provisions of the Plan shall be binding and
conclusive for all purposes and on all persons.

     Section 4.     Stock Subject to the Plan.
                    -------------------------

     (a) Number of Shares.  Two hundred thousand (200,000) shares of Common
         ----------------
Stock are authorized for issuance under the Plan in accordance with the
provisions of the Plan.  Shares of Common Stock that are issued pursuant to the
Plan shall be applied to reduce the maximum number of shares of Common Stock
remaining available for use under the Plan.  The Company shall at all times
during the term of the Plan retain as authorized and unissued Common Stock at
least the number of shares from time to time required under the provisions of
the Plan or otherwise assure itself of its ability to perform its obligations
hereunder.  Shares of Common Stock issued pursuant to the Plan may be shares of
original issuance or treasury shares or a combination of the foregoing, as the
Board of Directors, in its discretion, shall from time to time determine.

     (b) Adjustments Upon Changes in Common Stock.  In the event the Company
         ----------------------------------------
shall effect a split of the Common Stock or a dividend payable in Common Stock,
or in the event the outstanding

                                      -3-
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Common Stock shall be combined into a smaller number of shares, then the maximum
number of shares of Common Stock that may be issued under the Plan shall be
proportionately adjusted by the Board of Directors. In the event of a
reclassification of the Common Stock not covered by the foregoing, or in the
event of a liquidation or reorganization (including a merger, consolidation, or
sale of assets) of the Company, the Board of Directors shall make such
adjustments, if any, as it may deem appropriate in the number and kind of shares
that are authorized for issuance or are issuable pursuant to the Plan to give
effect to such transaction.

     Section 5.     Share Awards Applicable to Retainer.
                    -----------------------------------

     (a) Retainer; Required Share Amount.  The amount of the retainer to be paid
         -------------------------------
to each Outside Director for each Plan Year (the "Annual Retainer") shall be
determined by the Board of Directors from time to time; 40% of the Annual
Retainer shall be the cash component of the retainer, payable as cash
compensation (the "Cash Compensation"), and the other 60% of the Annual Retainer
shall be the equity component of the retainer, payable in whole shares of Common
Stock as the Required Share Amount.  The Cash Compensation for each Plan Year
shall be payable in installments as of the last day of each Plan Quarter in
arrears.  An Outside Director who has served in such capacity for less than an
entire Plan Quarter shall have his Cash Compensation for such Plan Quarter pro-
rated based on his number of days of service as an Outside Director during such
Plan Quarter.  The Required Share Amount for each Plan Year shall be payable in
installments as of the last day of each Plan Quarter in arrears.  An Outside
Director who has served in such capacity for less than the entire Plan Quarter
shall have his Required Share Amount for such Plan Quarter pro-rated based on
his number of days of service as an Outside Director during such Plan Quarter.

     (b) Voluntary Share Amount.  For any Plan Year, an Outside Director may
         ----------------------
elect to have up to 100% of his Cash Compensation earned for such Plan Year
applied to the purchase of shares of Common Stock pursuant to the provisions of
Section 5(c) hereof.  An Outside Director must notify the Company in writing of
such election prior to the first day of the Plan Year for which the election is
made (or prior to such later date as may be approved by the Committee);
provided, however, that a newly elected Outside Director who was not serving as
a director of the Company immediately prior to the time of his election to the
Board of Directors may make such an election prior to the commencement of such
Outside Director's initial Term of Office with respect to Cash Compensation
earned by him in the balance of the Plan Year of his initial election to the
Board of Directors.  Unless otherwise determined by the Committee, a separate
election must be made for each Plan Year.  An election made pursuant to this
Section 5(b) for a Plan Year shall be irrevocable from and after the first day
of such Plan Year; provided, however, that an election made pursuant to this
Section 5(b) during a Plan Year for the remaining portion of such Plan Year
shall be irrevocable from and after the date the election is made.  Such
elections shall be on a form prescribed for this purpose by the Committee.

     (c) Issuance of Shares.  As soon as practicable following the end of each
         ------------------
Plan Quarter, the Company shall issue to (or with respect to) each Outside
Director, effective as of the last day of such Plan Quarter:

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         (i)    a Share Award equal to a number of whole shares of Common Stock
     determined by dividing (x) the Required Share Amount earned by such Outside
     Director for such Plan Quarter by (y) the Fair Market Value of the Common
     Stock on the last Trading Day of such Plan Quarter or, if such Outside
     Director did not serve as an Outside Director during the entire Plan
     Quarter, for that portion of the Plan Quarter during which he served in
     that capacity,

                                      and

         (ii)   a Share Award equal to a number of whole shares of Common Stock
     determined by dividing (x) such Outside Director's Voluntary Share Amount,
     if any, for such Plan Quarter by (y) the Fair Market Value of the Common
     Stock on the last Trading Day of such Plan Quarter or, if such Outside
     Director did not serve as an Outside Director during the entire Plan
     Quarter, for that portion of the Plan Quarter during which he served in
     that capacity.

In the event of the death of an Outside Director during a Plan Quarter, the
Share Award with respect to such Outside Director shall be issued to the
beneficiary of such Outside Director or, if no beneficiary has been designated
by the Outside Director, to the Outside Director's estate.  No fractional shares
of Common Stock shall be issued by the Company pursuant to this subsection 5(c);
cash shall be paid in lieu of factional shares (which amount shall be Cash
Compensation for purposes of the Plan).

     Section 6.     Deferral of Director Compensation.  Outside Directors shall
                    ---------------------------------
have the right to defer the receipt of their Stock Compensation and/or Cash
Compensation (hereinafter "Director Compensation") in accordance with the
following provisions of this Section 6.

     (a) Election to Defer.  An Outside Director may elect to defer the receipt
         -----------------
of all or a portion of his Cash Compensation and/or Stock Compensation for a
Plan Year in accordance with the provisions of this Section 6 by filing a
written election to defer with the Committee.  Such election shall be made on a
form or forms prescribed for this purpose by the Committee.  Such election must
include the following:  (i) the whole percentage of Cash Compensation and/or
Stock Compensation to be deferred; (ii) an irrevocable election of a method of
payment as provided in Section 6(f) hereof; and (iii) a designation of
beneficiary as provided in Section 6(g) hereof.  Except as provided in Section
6(c) hereof, a deferral election shall apply only to Director Compensation to be
earned in the Plan Year next following the Plan Year in which the election is
made.  An election to defer made under this Section 6 shall be irrevocable.  For
purposes of this Section 6, the term "Participant" means an Outside Director who
has elected to defer the receipt of his Director Compensation in accordance with
the provisions of this Section 6.

     (b) Amount of Deferral.  The amount of Director Compensation to be deferred
         ------------------
in any Plan Year shall be designated by the Outside Director as a percentage of
Cash Compensation and/or Stock Compensation in integral multiples of 5%, but
shall not be less than 10%.

     (c) Time of Election.  Except as otherwise determined by the Committee, an
         ----------------
election to defer Director Compensation hereunder must be received by the
Committee prior to the

                                      -5-
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commencement of the Plan Year in which the Director Compensation is earned;
provided, however, that a newly elected Outside Director who was not serving as
a director of the Company immediately prior to the time of his election to the
Board of Directors may make a deferral election prior to the commencement of
such Outside Director's initial Term of Office with respect to Director
Compensation earned by him in the balance of the Plan Year of his initial
election to the Board of Directors. Unless otherwise determined by the
Committee, a separate deferral election must be made for each Plan Year. A
deferral election by an Outside Director with respect to Director Compensation
in a given year will not preclude a different action by the Outside Director
with respect to Director Compensation in subsequent years.

     (d) Deferred Compensation Accounts.  Director Compensation deferred by a
         ------------------------------
Participant pursuant to this Section 6 shall be credited to an account
("Deferred Compensation Account") established by the Company for such
Participant.  Cash Units in an amount equal to the deferred Cash Compensation
shall be credited to the Participant's Deferred Compensation Account at the time
the deferred Cash Compensation would otherwise have been paid had no election to
defer been made.  Stock Units in an amount equal to the deferred Stock
Compensation shall be credited to the Participant's Deferred Compensation
Account at the time the deferred Stock Compensation would otherwise have been
paid had no election to defer been made.  The amounts credited to a
Participant's Deferred Compensation Account in accordance with this Section 6(d)
and the account adjustments made pursuant to Section 6(e) shall represent the
total amount of the Company's liability to the Participant for the payment of
deferred compensation under this Section 6.

     (e) Account Adjustments.
         -------------------

         (i)    As additional deferred compensation for Participants with Cash
     Units credited to their Deferred Compensation Accounts, the Company shall
     credit a Participant's Deferred Compensation Account on a quarterly basis
     with the Interest Equivalent.

         (ii)   If a cash dividend is paid on Common Stock, on the date said
     dividend is paid each Deferred Compensation Account which is then credited
     with Stock Units shall be further credited with the number of Stock Units
     equal to the amount of said dividend per share of Common Stock multiplied
     by the number of Stock Units then credited to such Deferred Compensation
     Account, with the product thereof divided by the Fair Market Value of the
     Common Stock on the date such dividend is paid.  If the Company effects a
     split of its shares of common stock or pays a dividend in the form of
     shares of Common Stock, or if the outstanding shares of Common Stock are
     combined into a smaller number of shares, the number of Stock Units then
     credited to each Deferred Compensation Account shall be increased or
     decreased to reflect proportionately the increase or decrease in the number
     of outstanding shares of Common Stock resulting from such split, dividend
     or combination. In the event of a reclassification of shares of Common
     Stock not covered by the foregoing, or in the event of a liquidation,
     separation or reorganization (including, without limitation, a merger,
     consolidation or sale of assets) involving the Company, the Board of
     Directors of the Company shall make such adjustments, if any, to each
     Deferred Compensation Account then credited with Stock Units as such Board
     of Directors in its absolute discretion may deem appropriate.

                                      -6-
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     (f) Payment of Deferred Compensation.  All payments of a Participant's
         --------------------------------
Deferred Compensation Account shall be made at, or shall commence on, the first
day of the calendar year selected by the Participant in accordance with the
provisions of Section 6(a) hereof and this Section 6(f).  The date on which
payment will commence must be designated by the Outside Director.  The Outside
Director may elect to defer the receipt of his Director Compensation to:  (a)
the first day of any calendar year that is at least one year after the calendar
year in which the Director Compensation is earned; or (b) the first day of the
calendar year following (i) the calendar year in which he retires as a director
of the Company; (ii) the calendar year in which his membership on the Board of
Directors terminates; or (iii) the calendar year of his death.  The benefit
commencement date may not be later than the third calendar year following the
attainment of mandatory retirement age for directors of the Company.  Upon the
death of a Participant prior to the final payment of all amounts credited to his
Deferred Compensation Account, the balance of the Deferred Compensation Account
shall be paid in accordance with the provisions of Section 6(g) hereof
commencing on the first day of the calendar year following the year of death.  A
Participant shall have the option of selecting either a single payment schedule
or a series of annual installments (not exceeding ten), provided such election
is irrevocable and made at the date of deferral.  A Participant shall receive in
cash all Cash Units credited to his Deferred Compensation Account.  When Stock
Units credited to a Deferred Compensation Account maintained by the Company for
a Participant become distributable, such Stock Units shall be canceled and the
Company shall deliver to such Participant a stock certificate evidencing the
Participant's ownership of one share of Common Stock for each Stock Unit so
canceled.  If the amount credited to a Deferred Compensation Account is paid in
installments over a period of years, the provisions of Sections 6(e) shall
continue to apply to the amount credited to such account from time to time.

     (g) Designation of Beneficiary.  Each Participant shall name a beneficiary
         --------------------------
to receive any payments due him at the time of his death, with the right to
change such beneficiary at any time.  In case of a failure to designate a
beneficiary or the death of the designated beneficiary without a designated
successor, then to the surviving spouse of a deceased Participant, or, if there
is no surviving spouse, the children of the Participant in equal shares (the
share of any child who predeceases the Participant to go in equal shares to the
issue of such deceased child), or if there is no surviving spouse, children, or
issue of such children, the estate of the Participant.  No designation of
beneficiary shall be valid unless in writing signed by the Participant, dated
and filed with the Committee.  Upon the Participant's death, any balance in his
Deferred Compensation Account shall be payable to the Participant's beneficiary
under the method elected by the Participant or in such other method as the
Committee may determine in its sole discretion.

     (h) Source of Payments.  The Cash and Stock Units credited and the Deferred
         ------------------
Compensation Accounts maintained under this Plan are fictional devices used
solely for the accounting purposes of this Plan to determine an amount of money
to be paid and a number of shares of Common Stock to be delivered by the Company
to a Participant (or designated beneficiary) pursuant to this Plan, and shall
not be deemed or construed to create a trust fund or security interest of any
kind for or to grant a property interest of any kind to any Participant,
designated beneficiary or estate.  Nothing contained in the Plan and no action
taken pursuant to the Plan shall create or be construed to create a trust of any
kind in favor of a Participant or any other person or a fiduciary relationship
between the Company and a Participant.  Title to the beneficial

                                      -7-
<PAGE>

ownership of any assets, whether cash or investments, that the Company may
designate to pay the amounts credited to Deferred Compensation Accounts shall at
all times remain in the Company, and Participants shall have no property
interest whatsoever in any specific assets of the Company. A Participant's
interest in his Deferred Compensation Account shall be limited to the right to
receive payments pursuant to the terms of the Plan, and such right shall be no
greater than the right of any other unsecured general creditor of the Company.

     Section 7.     Plan Amendment, Modification, and Termination.  The Board of
                    ---------------------------------------------
Directors may at any time suspend, terminate, amend, or modify the Plan;
provided, however, that no amendment or modification of the Plan shall become
effective without the approval of such amendment or modification by the
stockholders of the Company if the Company, on the advice of counsel, determines
that stockholder approval is necessary or desirable.  No suspension,
termination, amendment, or modification of the Plan shall in any manner
adversely affect any Share Award theretofore made under the Plan without the
consent of the recipient of such award.

     Section 8.     Plan Effectiveness.  The Plan shall become effective on the
                    ------------------
date of consummation of the merger of TRH, Inc. with into the Titan Exploration,
Inc. pursuant to the terms of the Agreement and Plan of Merger dated as of
December 13, 1999, by and among Union Oil Company of California, the Company,
TRH, Inc., and Titan Exploration, Inc., provided the Plan is approved by Union
Oil Company of California, the sole shareholder of the Company, prior to such
date.  If the Plan is not so approved, the Plan shall terminate and all actions
hereunder shall be null and void.

     Section 9.     General Provisions.
                    ------------------

     (a) No Continuing Right as Director.  Neither the adoption or operation of
         -------------------------------
the Plan, nor the Plan itself or any document describing or relating to the
Plan, or any part hereof, shall confer upon any Outside Director any right to
continue as a director of the Company or any affiliate of the Company.

     (b) Nonalienation of Benefits.  No Outside Director shall have the right to
         -------------------------
sell, assign, transfer, or otherwise convey or encumber in whole or in part the
right to receive any award or payment under the Plan, except in accordance with
the express provisions hereof.

     (c) Binding Effect.  The obligations of the Company under the Plan shall be
         --------------
binding upon any successor corporation or organization resulting from the
merger, consolidation, or other reorganization of the Company, or upon any
successor corporation or organization succeeding to all or substantially all of
the assets and business of the Company.  The terms and conditions of the Plan
shall be binding upon each Outside Director and any other recipient of shares of
Common Stock hereunder and each such person's heirs, legatees, distributees, and
legal representatives.

     (d) Severability.  If any provision of the Plan or any agreement hereunder
         ------------
is held to be illegal or invalid for any reason, the illegality or invalidity
shall not affect the remaining provisions of the Plan or such agreement, as the
case may be, but such provision shall be fully severable and the Plan or such
agreement, as the case may be, shall be construed and enforced as if the illegal
or invalid provision had never been included herein or therein.

                                      -8-
<PAGE>

     (e) Expenses.  All expenses incident to the administration, protection, or
         --------
termination of the Plan, including, but not limited to, legal and accounting
fees, shall be paid by the Company.

     (f) Notices.  Whenever any notice is required or permitted under the Plan
         -------
or any agreement hereunder, such notice must be in writing and personally
delivered or sent by mail.  Any notice required or permitted to be delivered
hereunder or under an agreement shall be deemed to be delivered on the date on
which it is personally delivered, or on the third business day after it is
deposited in the United States mail, certified or registered, postage prepaid,
addressed to the person who is to receive it at the address that such person has
theretofore specified by written notice delivered in accordance herewith.  The
Company or an Outside Director may change, at any time and from time to time, by
written notice to the other, the address that it or he had theretofore specified
for receiving notices.  Until such address is changed in accordance herewith,
notices hereunder or under an agreement shall be delivered or sent (i) to the
Outside Director at his address as set forth in the records of the Company or
(ii) to the Company at the principal executive offices of the Company clearly
marked "Attention: President".

     (g) No Restriction of Corporate Action.  Nothing contained in the Plan
         ----------------------------------
shall be construed to prevent the Company or any affiliate thereof from taking
any corporate action that is deemed by the Company or such affiliate to be
appropriate or in its best interest, whether or not such action would have an
adverse effect on the Plan or any Share Award made or to be made under the Plan.
No Outside Director or other person shall have any claim against the Company or
any affiliate thereof as a result of such action.

     (h) Governing Law.  The provisions of the Plan shall be governed by and
         -------------
construed in accordance with the laws of the State of Delaware.

     (i) Miscellaneous.  Headings are given to the sections and subsections of
         -------------
the Plan solely as a convenience to facilitate reference.  Such headings shall
not be deemed in any way material or relevant to the construction of the Plan or
any provisions hereof.  The use of the masculine gender shall also include
within its meaning the feminine.  Wherever the context of the Plan dictates, the
use of the singular shall also include within its meaning the plural, and vice
versa.

     IN WITNESS WHEREOF, this Plan has been executed as of this 17th day of
April, 2000, to be effective as provided in Section 8.

                                    PURE RESOURCES, INC.

                                    By  /s/ Phillip Ballard
                                      ---------------------------------
                                         Name:  Phillip Ballard
                                              -------------------------
                                         Title: Vice President
                                               ------------------------

                                      -9-<PAGE>

                                                                   EXHIBIT 10.10

                         REGISTRATION RIGHTS AGREEMENT

     This REGISTRATION RIGHTS AGREEMENT (this "Agreement"), made and entered
into as of May __, 2000, by and between Pure Resources, Inc., a Delaware
corporation (the "Company"), and Jack Hightower, an individual residing in
Midland, Texas ("Owner").

          1.   Background.  On the date hereof, the Company is consummating a
               ----------
merger transaction (the "Merger") pursuant to which shares of common stock of
Titan Exploration, Inc. ("Titan Common Stock") have been converted into the
right to receive shares of the Company's common stock, par value $.01 per share
(the "Company Common Stock").  Immediately prior to the Merger, the Owner was
the holder of ______ shares of Titan Common Stock.  Upon consummation of the
Merger, the Owner now will be the holder of _________ shares of the Company
Common Stock.  Immediately prior to the Merger, the Owner had demand and piggy-
back registration rights covering all of this shares of Titan Common Stock,
pursuant to a Registration Rights Agreement dated as of September 30, 1996.
Although the issuance of shares of the Company Common Stock pursuant to the
Merger has been registered pursuant to the Company's Registration Statement on
Form S-4, the Owner's sale of his Company Common Stock is restricted pursuant to
the provisions of Rule 144 and Rule 145 promulgated under the Securities Act.
The parties hereto desire to enter into this Agreement in order to grant to the
Owner registration rights with respect to the Company Common Stock.

          2.   Registration under Securities Act, etc.
               --------------------------------------

          2.1. Registration on Request.
               -----------------------

     (a)  Concurrently with or from time to time after the date hereof, upon the
written request of one or more holders of Registrable Securities, requesting
that the Company effect the registration under the Securities Act of all or a
portion of such holders' Registrable Securities and specifying the intended
method of disposition thereof and whether or not such requested registration is
to be an underwritten offering, the parties hereto agree as follows:

          (i)  The Company will promptly give written notice of such requested
     registration to all other holders of Registrable Securities, if any;

          (ii) Promptly after providing the notice required by clause (i) of
     this Section 2.1(a), and subject to the limitations set forth in subsection
     (e) of this Section 2.1, the Company will use its best efforts to effect
     the registration under the Securities Act of:

               (A)  the Registrable Securities which the Company has been so
          requested to register by such holders, and

               (B)  all other Registrable Securities which the Company has been
          requested to register by the holders thereof by written request given
          to the Company within 30 days after the giving of such written notice
          by the Company (which request
<PAGE>

          shall specify the intended method of disposition of such Registrable
          Securities), all to the extent requisite to permit the disposition (in
          accordance with the intended methods thereof as aforesaid) of the
          Registrable Securities so to be registered.

     (b)  Registration of Other Securities.  Whenever the Company shall effect a
          --------------------------------
registration pursuant to this Section 2.1 in connection with an underwritten
offering by one or more holders of Registrable Securities, no securities other
than Registrable Securities shall be included among the securities covered by
such registration unless (i) the managing underwriter of such offering shall
have advised each holder of Registrable Securities to be covered by such
registration in writing that the inclusion of such other securities would not
adversely affect such offering or (ii) the holders of all Registrable Securities
to be covered by such registration shall have consented in writing to the
inclusion of such other securities.

     (c)  Registration Statement Form.  Registrations under this Section 2.1
          ---------------------------
shall be on such appropriate registration form of the Commission (i) as shall be
selected by the Company and as shall be reasonably acceptable to the Requisite
Holders, and (ii) as shall permit the disposition of such Registrable Securities
in accordance with the intended method or methods of disposition specified in
their request for such registration.  The Company agrees to include in any such
registration statement all information which holders of Registrable Securities
being registered shall reasonably request.

     (d)  Expenses.  The Company will pay all Registration Expenses in
          --------
connection with any registration requested pursuant to this Section 2.1. Any
Selling Expenses in connection with any registration requested under this
Section 2.1 shall be allocated among all Persons on whose behalf securities of
the Company are included in such registration, on the basis of the respective
amounts of the securities then being registered on their behalf.

     (e)  Limitations on Requested Registrations.  The Company's obligation to
          --------------------------------------
take or continue any action to effect a requested registration under this
Section 2.1 shall be subject to the following:

          (i)  The Company shall not be required to effect more than two
     registrations requested pursuant to this section 2.1; provided that, a
     registration requested pursuant to this Section 2.1 shall not be deemed to
     have been effected (A) unless a registration statement with respect thereto
     has been declared effective for a period of at least 90 days,  (B) if after
     a registration statement has become effective, such registration is
     interfered with by any stop order, injunction or other order or requirement
     of the Commission or other governmental agency or court for any reason, or
     (C) if the conditions to closing specified in the purchase agreement or
     underwriting agreement entered into in connection with such registration
     are not satisfied, other than as a result of the voluntary termination of
     such offering by the Requisite Holders;

                                       2
<PAGE>

          (ii)  The Company shall not be required to effect a registration
     pursuant to this Section 2.1 unless such registration has been requested by
     the holders of Registrable Securities which have an estimated aggregate
     offering price to the public of at least (A) $20,000,000, in the case of
     the first registration effected pursuant to this Section 2.1, and (B)
     $10,000,000 otherwise; and

          (iii) The Company shall not be required to effect a registration
     pursuant to this Section 2.1 during the 180 day period after a registration
     statement shall have been filed and declared effective under the Securities
     Act with respect to an underwritten public offering of any class of the
     Company's equity securities (which shall exclude a registration of
     securities with respect to an employee benefit, retirement or similar
     plan).

          (f)   Selection of Underwriters.  If a requested registration pursuant
                -------------------------
to this Section 2.1 involves an underwritten offering, the underwriter or
underwriters thereof shall be selected by the Company with the approval of the
Requisite Holders.

          (g)   Priority in Requested Registrations.  If a requested
                -----------------------------------
registration pursuant to this Section 2.1 involves an underwritten offering, and
the managing underwriter shall advise the Company in writing (with a copy to
each holder of Registrable Securities requesting registration) that, in its
opinion, the number of securities requested to be included in such registration
exceeds the number which can be sold in such offering within a price range
acceptable to the Requisite Holders, the Company will include in such
registration to the extent of the number which the Company is so advised can be
sold in such offering, Registrable Securities requested to be included in such
registration, pro rata among the holders thereof requesting such registration on
the basis of the percentage of the Registrable Securities of the Company held by
the holders of Registrable Securities which have requested that such Securities
be included. In connection with any registration as to which the provisions of
this clause (g) apply, no securities other than Registrable Securities shall be
covered by such registration.

          2.2. Incidental Registration.
               -----------------------

          (a)  Right to Include Registrable Securities.  If the Company at any
               ---------------------------------------
time proposes to register any of its securities under the Securities Act (other
than (i) in connection with a registration of any employee benefit, retirement
or similar plan, or (ii) with respect to a Rule 145 transaction, or (iii)
pursuant to Section 2.1), whether or not for sale for its own account, it will
each such time give prompt written notice to all holders of Registrable
Securities of its intention to do so and of such holders' rights under this
Section 2.2.  Upon the written request of any such holder made within 30 days
after the receipt of any such notice (which request shall specify the
Registrable Securities intended to be disposed of by such holder and the
intended method of disposition thereof), the Company will use its best efforts
to effect the registration under the Securities Act of all Registrable
Securities which the Company has been so requested to register by the holders
thereof, to the extent requisite to permit the disposition (in accordance with
the intended methods thereof as aforesaid) of the Registrable Securities so to
be registered, provided that if, at any time after giving written notice
               --------

                                       3
<PAGE>

of its intention to register any securities and prior to the effective date of
the registration statement filed in connection with such registration, the
Company shall determine for any reason not to register or to delay registration
of such securities, the Company may, at its election, give written notice of
such determination to each holder of Registrable Securities and, thereupon, (i)
in the case of a determination not to register, shall be relieved of its
obligation to register any Registrable Securities in connection with such
registration (but not from its obligation to pay the Registration Expenses in
connection therewith), without prejudice, however, to the rights of any holder
or holders of Registrable Securities entitled to do so to request that such
registration be effected as a registration under Section 2.1, and (ii) in the
case of a determination to delay registering, shall be permitted to delay
registering any Registrable Securities, for the same period as the delay in
registering such other securities. No registration effected under this Section
2.2 shall be deemed to have been effected pursuant to Section 2.1 or shall
relieve the Company of its obligation to effect any registration upon request
under Section 2.1. The Company will pay all Registration Expenses in connection
with each registration of Registrable Securities requested pursuant to this
Section 2.2 and any Selling Expenses shall be allocated among all Persons on
whose behalf securities of the Company are included in such registration, on the
basis of the respective amounts of the securities then being registered on their
behalf. Notwithstanding the other provisions of this Agreement, (x) no holder of
Registrable Securities, other than Owner, shall have any rights under this
section if such holder holds fewer than 1,000,000 shares of Common Stock that
are Registrable Securities (adjusted for any increase or decrease in the number
of issued shares of Common Stock from a stock split, reverse stock split, stock
dividend, combination or reclassification of the common stock, or any other
increase or decrease in the number of issued shares of Common Stock effected
without consideration by the Company), such holder is not an "affiliate" of the
Company, and such shares may be sold freely by such Holder without restriction
under Rule 144(k) (or any successor provisions) without restriction and (y)
Owner shall have no such rights if he holds less than 250,000 shares of Common
Stock that are Registrable Securities (adjusted for any increase or decrease in
the number of issued shares of Common Stock from a stock split, reverse stock
split, stock dividend, combination or reclassification of the common stock, or
any other increase or decrease in the number of issued shares of Common Stock
effected without consideration by the Company), he is not an affiliate of the
Company, and his Registrable Securities may be sold freely under Rule 144(k) (or
any successor provisions) without restriction.

          (b)  Priority in Incidental Registrations.
               ------------------------------------

          (i)  If (A) a registration pursuant to this Section 2.2 involves an
     underwritten offering of the securities so being registered for sale for
     the account of a stockholder (other than the holders of Registrable
     Securities) exercising a demand registration right pursuant to another
     registration rights agreement to be distributed (on a firm commitment
     basis) by or through one or more underwriters of recognized standing under
     underwriting terms appropriate for such a transaction, and (B) the managing
     underwriter of such underwritten offering informs the Company and the
     holders of Registrable Securities in writing of its belief that the number
     of securities requested to be included in such registration exceeds the
     number that can be sold in (or during the time of) such offering, then the
     Company will include in such registration, to the extent of the number that
     the Company is so advised can be sold in (or during the time of) such
     offering:  first, such securities proposed by the stockholder exercising
     the demand registration right to be sold for its account; second, such
     securities requested to be included pursuant to incidental registration
     rights in such

                                       4
<PAGE>

     registration by the holder or holders, as the case may be, including the
     holders of Registrable Securities, pro rata on the basis of the number of
     such securities so proposed to be sold by all such security holders and so
     requested to be included; and third, such securities proposed by the
     Company to be sold for its own account

          (ii)  If (A) a registration pursuant to this Section 2.2 involves an
     underwritten offering of the securities so being registered for sale for
     the account of the Company, to be distributed (on a firm commitment basis)
     by or through one or more underwriters of recognized standing under
     underwriting terms appropriate for such a transaction, and (B) the managing
     underwriter of such underwritten offering shall inform the Company and the
     holders of Registrable Securities in writing of its belief that the number
     of securities requested to be included in such registration exceeds the
     number that can be sold in (or during the time of) such offering, then the
     Company will include in such registration, to the extent of the number that
     the Company is so advised can be sold in (or during the time of) such
     offering, securities proposed by the Company to be sold for its own
     account, and, such securities requested to be included pursuant to
     incidental registration rights in such registration by the holder or
     holders, as the case may be, including the holders of Registrable
     Securities, pro rata on the basis of the number of such securities so
     proposed to be sold by all such security holders and so requested to be
     included.

          2.3.  Registration Procedures.  If and whenever the Company is
                -----------------------
required to use its best efforts to effect the registration of any Registrable
Securities under the Securities Act as provided in Sections 2.1 and 2.2, the
Company will as expeditiously as possible:

          (i)   prepare and (as soon thereafter as possible or in any event no
     later than 60 days after the end of the period within which requests for
     registration may be given to the Company) file with the Commission the
     requisite registration statement to effect such registration and thereafter
     use its best efforts to cause such registration statement to become
     effective, provided that the Company may discontinue any registration of
                --------
     its securities which are not Registrable Securities (and, under the
     circumstances specified in Section 2.2(a), its securities which are
     Registrable Securities) at any time prior to the effective date of the
     registration statement relating thereto;

          (ii)  prepare and file with the Commission such amendments and
     supplements to such registration statement and the prospectus used in
     connection therewith as may be necessary to keep such registration
     statement effective and to comply with the provisions of the Securities Act
     with respect to the disposition of all securities covered by such
     registration statement until such time as all of such securities have been
     disposed of in accordance with the intended methods of disposition by the
     seller or sellers thereof set forth in such registration statement;

          (iii) furnish to each seller of Registrable Securities covered by
     such registration statement such number of conformed copies of such
     registration statement and of each such

                                       5
<PAGE>

     amendment and supplement thereto (in each case including all exhibits),
     such number of copies of the prospectus contained in such registration
     statement (including each preliminary prospectus and any summary
     prospectus) and any other prospectus filed under Rule 424 under the
     Securities Act, in conformity with the requirements of the Securities Act,
     and such other documents, as such seller may reasonably request;

          (iv) use its best efforts to register or qualify all Registrable
     Securities and other securities covered by such registration statement
     under such other securities or blue sky laws of such jurisdictions as each
     seller thereof shall reasonably request, to keep such registration or
     qualification in effect for so long as such registration statement remains
     in effect, and take any other action which may be reasonably necessary or
     advisable to enable such seller to consummate the disposition in such
     jurisdictions of the securities owned by such seller, except that the
     Company shall not for any such purpose be required to qualify generally to
     do business as a foreign corporation in any jurisdiction wherein it would
     not but for the requirements of this subdivision (iv) be obligated to be so
     qualified or to consent to general service of process in any such
     jurisdiction;

          (v)  use its best efforts to cause all Registrable Securities covered
     by such registration statement to be registered with or approved by such
     other governmental agencies or authorities as may be necessary to enable
     the seller or sellers thereof to consummate the disposition of such
     Registrable Securities;

          (vi) furnish to each seller of Registrable Securities a signed
     counterpart, addressed to such seller (and underwriters, if any) of:

               (A) an opinion of counsel for the Company, dated the effective
          date of such registration statement (and, if such registration
          includes an underwritten public offering, dated the date of the
          closing under the underwriting agreement), reasonably satisfactory in
          form and substance to such seller, and

               (B) a "comfort" letter, dated the effective date of such
          registration statement (and, if such registration includes an
          underwritten public offering, dated the date of the closing under the
          underwriting agreement), signed by the independent public accountants
          who have certified the Company's financial statements included in such
          registration statement,

     covering substantially the same matters with respect to such registration
     statement (and the prospectus included therein) and, in the case of the
     accountants' letter, with respect to events subsequent to the date of such
     financial statements, as are customarily covered in opinions of issuer's
     counsel and in accountants' letters delivered to the underwriters in
     underwritten public offerings of securities and, in the case of the
     accountants' letter, such other financial matters, and, in the case of the
     legal opinion, such other legal matters, as such seller may reasonably
     request;

                                       6
<PAGE>

          (vii)  notify each seller of Registrable Securities covered by such
     registration statement, at any time when a prospectus relating thereto is
     required to be delivered under the Securities Act, upon discovery that, or
     upon the happening of any event as a result of which, the prospectus
     included in such registration statement, as then in effect, includes an
     untrue statement of a material fact or omits to state any material fact
     required to be stated therein or necessary to make the statements therein
     not misleading in the light of the circumstances under which they were
     made, and at the request of any such seller promptly prepare and furnish to
     such seller a reasonable number of copies of a supplement to or an
     amendment of such prospectus as may be necessary so that, as thereafter
     delivered to the purchasers of such securities, such prospectus shall not
     include an untrue statement of a material fact or omit to state a material
     fact required to be stated therein or necessary to make the statements
     therein not misleading in the light of the circumstances under which they
     were made;

          (viii) otherwise use its best efforts to comply with all applicable
     rules and regulations of the Commission, and make available to its security
     holders, as soon as reasonably practicable, an earnings statement covering
     the period of at least twelve months, but not more than eighteen months,
     beginning with the first full calendar month after the effective date of
     such registration statement, which earnings statement shall satisfy the
     provisions of Section 11(a) of the Securities Act, and will furnish to each
     such seller at least five business days prior to the filing thereof a copy
     of any amendment or supplement to such registration statement or prospectus
     and shall not file any thereof to which any such seller shall have
     reasonably objected on the grounds that such amendment or supplement does
     not comply in all material respects with the requirements of the Securities
     Act or of the rules or regulations thereunder;

          (ix)   provide and cause to be maintained a transfer agent and
     registrar for all Registrable Securities covered by such registration
     statement from and after a date not later than the effective date of such
     registration statement;

          (x)    use its best efforts to list all Registrable Securities covered
     by such registration statement on any securities exchange on which any of
     the Registrable Securities is then listed; and

          (xi)   enter into such agreements and take such other actions as the
     Requisite Holders shall reasonably request in order to expedite or
     facilitate the disposition of such Registrable Securities.

The Company may require each seller of Registrable Securities as to which any
registration is being effected to furnish the Company such information regarding
such seller and the distribution of such securities as the Company may from time
to time reasonably request in writing.

                                       7
<PAGE>

     Each holder of Registrable Securities agrees by acquisition of such
Registrable Securities that upon receipt of any notice from the Company of the
happening of any event of the kind described in the subdivision (vii) of this
Section 2.3, such holder will forthwith discontinue such holder's disposition of
Registrable Securities pursuant to the registration statement relating to such
Registrable Securities until such holder's receipt of the copies of the
supplemented or amended prospectus contemplated by subdivision (vii) of this
Section 2.3 and, if so directed by the Company, will deliver to the Company (at
the Company's expense) all copies, other than permanent file copies, then in
such holder's possession of the prospectus relating to such Registrable
Securities current at the time of receipt of such notice.

     2.4  Underwritten Offerings.
          ----------------------

          (a)  Requested Underwritten Offerings.  If requested by the
               --------------------------------
underwriters for any underwritten offering by holders of Registrable Securities
pursuant to a registration requested under Section 2.1, the Company will enter
into an underwriting agreement with such underwriters for such offering, such
agreement to be satisfactory in substance and form to each such holder and the
underwriters and to contain such representations and warranties by the Company
and such other terms as are generally prevailing in agreements of this type,
including, without limitation, indemnities to the effect and to the extent
provided in Section 2.7. The holders of Registrable Securities to be distributed
by such underwriters shall be parties to such underwriting agreement and may, at
their option, require that any or all of the representations and warranties by,
and the other agreements on the part of, the Company to and for the benefit of
such underwriters shall also be made to and for the benefit of such holders of
Registrable Securities and that any or all of the conditions precedent to the
obligations of such underwriters under such underwriting agreement be conditions
precedent to the obligations of such holders of Registrable Securities. Any such
holder of Registrable Securities shall not be required to make any
representations or warranties to or agreements with the Company or the
underwriters other than representations, warranties or agreements regarding such
holder, such holder's Registrable Securities and such holder's intended method
of distribution and any other representation required by law.

          (b)  Incidental Underwritten Offerings.  If the Company at any time
               ---------------------------------
proposes to register any of its securities under the Securities Act as
contemplated by Section 2.2 and such securities are to be distributed by or
through one or more underwriters, the Company will, if requested by any holder
of Registrable Securities as provided in Section 2.2 and subject to the
provisions of Section 2.2(b), arrange for such underwriters to include all the
Registrable Securities to be offered and sold by such holder among the
securities to be distributed by such underwriters. The holders of Registrable
Securities to be distributed by such underwriters shall be parties to the
underwriting agreement between the Company and such underwriters and may, at
their option, require that any or all of the representations and warranties by,
and the other agreements on the part of, the Company to and for the benefit of
such underwriters shall also be made to and for the benefit of such holders of
Registrable Securities and that any or all of the conditions precedent to the
obligations of such underwriters under such underwriting agreement be conditions
precedent to the obligations of such holders of Registrable Securities.  Any
such holder of Registrable Securities shall

                                       8
<PAGE>

not be required to made any representations or warranties to or agreements with
the Company or the underwriters other than representations, warranties or
agreements regarding such holder, such holder's Registrable Securities and such
holder's intended method of distribution and any other representation required
by law.

          2.5. Preparation; Reasonable Investigation.  In connection with the
               -------------------------------------
preparation and filing of each registration statement under the Securities Act
pursuant to this Agreement, the Company will give the holders of Registrable
Securities registered under such registration statement, and their  counsel and
accountants, the opportunity to participate in the preparation of such
registration statement, each prospectus included therein or filed with the
Commission, and each amendment thereof or supplement thereto, and will give each
of them such access to its books and records and such opportunities to discuss
the business of the Company with its officers and the independent public
accountants who have certified its financial statements as shall be necessary,
in the opinion of such holders' counsel, to conduct a reasonable investigation
within the meaning of the Securities Act.

          2.6. Additional Rights of Owners.  If any registration statement
               ---------------------------
prepared under this Agreement refers to Owner by name or otherwise as the holder
of any securities of the Company, then Owner shall have the right to require (x)
the insertion therein of language, in form and substance satisfactory to Owner,
to the effect that the holding by Owner of such securities does not necessarily
make Owner a "controlling person" of the Company within the meaning of the
Securities Act and is not to be construed as a recommendation by Owner of the
investment quality of the Company's debt or equity securities covered thereby
and that such holding does not imply that Owner will assist in meeting any
future financial requirements of the Company, or (y) in the event that such
reference to Owner by name or otherwise is not required by the Securities Act or
any rules and regulations promulgated thereunder, the deletion of the reference
to Owner.

          2.7. Indemnification.
               ---------------

          (a)  Indemnification by the Company.  In the event of any registration
               ------------------------------
of any securities of the Company under the Securities Act, the Company will, and
hereby does, in the case of any registration statement filed pursuant to Section
2.1 or 2.2, indemnify and hold harmless the seller of any Registrable Securities
covered by such registration statement, its directors and officers, each other
Person who participates in the offering or sale of such securities and each
other Person, if any, who controls such seller within the meaning of the
Securities Act against any losses, claims, damages or liabilities, joint or
several, to which such seller or any such director or officer or controlling
person may become subject under the Securities Act or otherwise, insofar as such
losses, claims, damages or liabilities (or actions or proceedings, whether
commenced or threatened, in respect thereof) arise out of or are based upon any
untrue statement or alleged untrue statement of any material fact contained in
any registration statement under which such securities were registered under the
Securities Act, any preliminary prospectus, final prospectus or summary
prospectus contained therein, or any amendment or supplement thereto, or any
omission or alleged omission to state therein a material fact required to be
stated therein or necessary to make the statements

                                       9
<PAGE>

therein not misleading, and the Company will reimburse such seller and each such
director, officer, and controlling person for any legal or any other expenses
reasonably incurred by them in connection with investigating or defending any
such loss, claim, liability, action or proceeding; provided that the Company
                                                   --------
shall not be liable in any such case to the extent that any such loss, claim,
damage, liability (or action or proceeding in respect thereof) or expense arises
out of or is based upon an untrue statement or alleged untrue statement or
omission or alleged omission made in such registration statement, any such
preliminary prospectus, final prospectus, summary prospectus, amendment or
supplement in reliance upon and in conformity with written information furnished
to the Company through an instrument duly executed by such seller specifically
stating that it is for use in the preparation thereof and, provided further that
                                                           --------
the Company shall not be liable to any Person who participates as an
underwriter, in the offering or sale of Registrable Securities or any other
Person, if any, who controls such underwriter within the meaning of the
Securities Act, in any such case to the extent that any such loss, claim,
damage, liability (or action or proceeding in respect thereof) or expense arises
out of such Person's failure to send or give a copy of the final prospectus, as
the same may be then supplemented or amended, to the Person asserting an untrue
statement or alleged untrue statement or omission or alleged omission at or
prior to the written confirmation of the sale of Registrable Securities to such
Person if such statement or omission was corrected in such final prospectus.
Such indemnity shall remain in full force and effect regardless of any
investigation made by or on behalf of such seller or any such director, officer,
underwriter or controlling person and shall survive the transfer of such
securities by such seller.

          (b)  Indemnification by the Sellers.  The Company may require, as a
               ------------------------------
condition to including any Registrable Securities in any registration statement
filed pursuant to Section 2.3, that the Company shall have received an
undertaking satisfactory to it from the prospective seller of such securities,
to indemnify and hold harmless (in the same manner and to the same extent as set
forth in subdivision (a) of this Section 2.7) the Company, each director of the
Company, each officer of the Company and each other Person, if any, who controls
the Company within the meaning of the Securities Act, with respect to any
statement or alleged statement in or omission or alleged omission from such
registration statement, any preliminary prospectus, final prospectus or summary
prospectus contained therein, or any amendment or supplement thereto, if such
statement or alleged statement or omission or alleged omission was made in
reliance upon and in conformity with written information furnished to the
Company through an instrument duly executed by such seller specifically stating
that it is for use in the preparation of such registration statement,
preliminary prospectus, final prospectus, summary prospectus, amendment or
supplement.  Such indemnity shall remain in full force and effect, regardless of
any investigation made by or on behalf of the Company or any such director,
officer or controlling Person and shall survive the transfer of such securities
by such seller.

          (c)  Notices of Claims, etc.  Promptly after receipt by an indemnified
               ----------------------
party of notice of the commencement of any action or proceeding involving a
claim referred to in the preceding subdivisions of this Section 2.7, such
indemnified party will, if a claim in respect thereof is to be made against an
indemnifying party, give written notice to the latter of the commencement of
such action, provided that the failure of any indemnified party to give notice
             --------
as provided herein

                                       10
<PAGE>

shall not relieve the indemnifying party of its obligations under the preceding
subdivisions of this Section 2.7, except to the extent that the indemnifying
party is actually prejudiced by such failure to give notice. In case any such
action is brought against an indemnified party, unless in such indemnified
party's reasonable judgment a conflict of interest between such indemnified and
indemnifying parties may exist in respect of such claim, the indemnifying party
shall be entitled to participate in and to assume the defense thereof, jointly
with any other indemnifying party similarly notified to the extent that it may
wish, with counsel reasonably satisfactory to such indemnified party, and after
notice from the indemnifying party to such indemnified party of its election so
to assume the defense thereof, the indemnifying party shall not be liable to
such indemnified party for any legal or other expenses subsequently incurred by
the latter in connection with the defense thereof other than reasonable costs of
investigation. No indemnifying party shall, without the consent of the
indemnified party, consent to entry of any judgment or enter into any settlement
which does not include as an unconditional term thereof the giving by the
claimant or plaintiff to such indemnified party of a release from all liability
in respect to such claim or litigation.

          (d)  Other Indemnification.  Indemnification similar to that specified
               ---------------------
in the preceding subdivisions of this Section 2.7 (with appropriate
modifications) shall be given by the Company and each seller of Registrable
Securities with respect to any required registration or other qualification of
securities under any Federal or state law or regulation of any governmental
authority other than the Securities Act.

          (e)  Indemnification Payments.  The indemnification required by this
               ------------------------
Section 2.7 shall be made by periodic payments of the amount thereof during the
course of the investigation or defense, as and when bills are received or
expense, loss, damage or liability is incurred.

          2.8. Adjustments Affecting Registrable Securities.  The Company will
               --------------------------------------------
not effect or permit to occur any combination or subdivision of Registrable
Securities which would adversely affect the ability of the holders of
Registrable Securities to include such Registrable Securities in any
registration of its securities contemplated by this Section 2, or the
marketability of such Registrable Securities under any such registration.

          3.   Definitions.  As used herein, unless the context otherwise
               -----------
requires, the following terms have the following respective meanings:

          Commission:  The Securities and Exchange Commission or any other
          ----------
          Federal agency at the time administering the Securities Act.

          Company:  As defined in the introductory paragraph of this Agreement.
          -------
          For purposes of this Agreement, all references to the Company shall be
          deemed to include any successor entity or transferee.

          Exchange Act:  The Securities Exchange Act of 1934, or any similar
          ------------
          Federal statute, and the rules and regulations of the Commission
          thereunder, all as the same shall be

                                       11
<PAGE>

          in effect at the time. Reference to a particular section of the
          Securities Exchange Act of 1934 shall include a reference to the
          comparable section, if any, of any such similar Federal statute.

          Majority Holders:  At any time, the holder or holders of more than 50%
          ----------------
          (by number of shares) of all Registrable Securities then outstanding.

          Person:  A corporation, an association, a partnership, a business, an
          ------
          individual, a governmental or political subdivision thereof or a
          governmental agency.

          Registrable Securities:  any Company Common Stock owned by Owner that
          ----------------------
          Owner has acquired from the Company in the Merger or pursuant to
          exercise of stock options and rights under benefit plans or otherwise,
          and any securities issued or issuable with respect to any such Company
          Common Stock by way of distribution or in connection with any
          reorganization, recapitalization, merger, consolidation or otherwise.
          As to any particular Registrable Securities, once issued such
          securities shall cease to be Registrable Securities when (a) a
          registration statement with respect to the sale of such securities
          shall have become effective under the Securities Act and such
          securities shall have been disposed of in accordance with such
          registration statement, (b) they shall have been distributed to the
          public pursuant to Rule 144 or Rule 144A (or any successor provision)
          under the Securities Act, (c) they shall have been otherwise
          transferred, new certificates for them not bearing a legend
          restricting further transfer shall have been delivered by the Company
          and subsequent disposition of them shall not require registration or
          qualification of them under the Securities Act or any similar state
          law then in force, or (d) they shall have ceased to be outstanding.

          Registration Expenses:  All expenses incident to the Company's
          ---------------------
          performance of or compliance with Section 2.1, including, without
          limitation, all registration, filing and National Association of
          Securities Dealers fees, all fees and expenses of complying with
          securities or blue sky laws, all word processing, duplicating and
          printing expenses, messenger and delivery expenses, the fees and
          disbursements of counsel for the Company and of its independent public
          accountants, including the expenses of any special audits or "cold
          comfort" letters required by or incident to such performance and
          compliance, the fees and disbursements incurred by the holders of
          Registrable Securities to be registered (including the fees and
          disbursements of not more than one special counsel to the holders of
          such Registrable Securities), premiums and other costs of policies of
          insurance against liabilities arising out of the public offering of
          the Registrable Securities being registered and any fees and
          disbursements of underwriters customarily paid by issuers or sellers
          of securities, but excluding Selling Expenses, if any, provided that,
          in any case where Registration Expenses are not to be borne by the
          Company, such expenses shall not include salaries of Company personnel
          or general overhead expenses of the Company, auditing fees, premiums
          or other expenses relating to liability insurance required by

                                       12
<PAGE>

          underwriters of the Company or other expenses for the preparation of
          financial statements or other data normally prepared by the Company in
          the ordinary course of its business or which the Company would have
          incurred in any event.

          Requisite Holders:  With respect to any registration of Registrable
          -----------------
          Securities pursuant to Section 2.1, any holder or holders of more than
          50% (by number of shares) of the Registrable Securities to be so
          registered.

          Securities Act:  The Securities Act of 1933, or any similar Federal
          --------------
          statute, and the rules and regulations of the Commission thereunder,
          all as of the same shall be in effect at the time.  References to a
          particular section of the Securities Act of 1933 shall include a
          reference to the comparable section, if any, of any such similar
          Federal Statute.

          Selling Expenses: underwriting discounts and commissions and stock
          ----------------
          transfer taxes relating to securities registered by the Company.

          4.   Rule 144 and Rule 144A:  If the Company shall have filed a
               ----------------------
registration statement pursuant to the requirements of Section 12 of the
Exchange Act or a registration statement pursuant to the requirements of the
Securities Act, the Company will file the reports required to be filed by it
under the Securities Act and the Exchange Act and the rules and regulations
adopted by the Commission thereunder (or, if the Company is not required to file
such reports, will, upon the request of any holder of Registrable Securities,
make publicly available other information) and will take such further action as
any holder of Registrable Securities may reasonably request, all to the extent
required from time to time to enable such holder to sell Registrable Securities
without registration under the Securities Act within the limitation of the
exemptions provided by (a) Rule 144 under the Securities Act, as such Rule may
be amended from time to time or (b) any similar rule or regulation hereafter
adopted by the Commission.  Upon the request of any holder of Registrable
Securities, the Company will deliver to such holder a written statement as to
whether it has complied with such requirements.  After any sale of Registrable
Securities pursuant to this Section 4, the Company will, to the extent allowed
by law, cause any restrictive legends to be removed and any transfer
restrictions to be rescinded with respect to such Registrable Securities.   In
order to permit the holders of Registrable Securities to sell the same, if they
so desire, pursuant to Rule 144A promulgated by the Commission (or any successor
to such rule), the Company will comply with all rules and regulations of the
Commission applicable in connection with use of Rule 144A (or any successor
thereto).  Prospective transferees of Registrable Securities that are Qualified
Institutional Buyers (as defined in Rule 144A) which would be purchasing such
Registrable Securities in reliance upon Rule 144A may request from the Company
information regarding the business, operations and assets of the Company.
Within five business days of any such request, the Company shall deliver to any
such prospective transferee copies of annual audited and quarterly unaudited
financial statements of the Company and such other information as may be
required to be supplied by the Company for it to comply with Rule 144A.

                                       13
<PAGE>

          5.   Amendments and Waivers.  This Agreement may be amended and the
               ----------------------
Company may take any action herein prohibited or omit to perform any act herein
required to be performed by it, only if the Company shall have obtained the
written consent to such amendment, action or omission to act, of the Majority
Holders; provided, however, that no amendment to this Agreement that would
adversely affect the rights of a party hereto may be made without the prior
written consent of such party, with the exception that temporary waivers and
suspensions of the rights of all of the Owners pursuant to customary terms at
the request of the managing underwriter in connection with any underwritten
offering of the Company's securities, may be authorized by consent of the
Majority Holders.  Each holder of any Registrable Securities at the time or
thereafter outstanding shall be bound by any consent authorized by this Section
5, whether or not such Registrable Securities shall have been marked to indicate
such consent.

          6.   Nominees for Beneficial Owners.  In the event that any
               ------------------------------
Registrable Securities are held by a nominee for the beneficial owner thereof,
the beneficial owner thereof may, at its election, be treated as the holder of
such Registrable Securities for purposes of any request or other action by any
holder or holders of Registrable Securities pursuant to this Agreement or any
determination of any number or percentage of shares of Registrable Securities
held by any holder or holders of Registrable Securities contemplated by this
Agreement.  If the beneficial owner of any Registrable Securities so elects, the
Company may require assurances reasonably satisfactory to it of such owner's
beneficial ownership of such Registrable Securities.

          7.   Notices.  All communications provided for hereunder shall be sent
               -------
by first-class mail and (a) if addressed to a party other than the Company,
addressed to such party at the address set forth opposite such parties name on
the execution page hereof, or (b) if addressed to the Company, at 500 West
Texas, Suite 500, Midland, Texas 79701 or at such other address, or to the
attention of such other officer, as the Company shall have furnished to each
holder of Registrable Securities at the time outstanding; provided, however,
                                                                    -------
that any such communication to the Company may also, at the option of any of the
parties hereunder, be either delivered to the Company at its address set forth
above or to any officer of the Company.

          8.   Assignment.  Subject to the following sentence, this Agreement
               ----------
shall be binding upon and inure to the benefit of and be enforceable by the
parties hereto and their respective successors and assigns.  In addition, and
whether or not any express assignment shall have been made, the provisions of
this Agreement which are for the benefit of the parties hereto other than the
Company shall also be for the benefit of and enforceable by (subject to the
provisions respecting the minimum numbers or percentages of shares of
Registrable Securities required in order to be entitled to certain rights, or
take certain actions, contained herein) any subsequent holder of any Registrable
Securities, and only such a subsequent holder, who owns at least 1,000,000
shares of Common Stock that are Registrable Securities (adjusted for any
increase or decrease in the number of issued shares of Common Stock from a stock
split, reverse stock split, stock dividend, combination or reclassification of
the common stock, or any other increase or decrease in the number of issued
shares of Common Stock effected without consideration by the Company) and who is
(a) a direct assign or successor of Owner or (b) the direct assign or successor
of (i) a member of Owner's immediate family, (ii) Owner's estate, (iii) a trust
or private foundation created by Owner, (iv) a partnership or

                                       14
<PAGE>

limited liability company, of which a substantial part of the equity is owned by
members of Owner's family or trusts for the benefit of his family, or (v) is
otherwise an affiliate of Owner.

          9.   Termination.  This Agreement shall terminate when no Registrable
               -----------
Securities remain outstanding.

          10.  Descriptive Headings.  The descriptive headings of the several
               --------------------
sections and paragraphs of this Agreement are inserted for reference only and
shall not limit or otherwise affect the meaning hereof.

          11.  Specific Performance.  The parties hereto recognize and agree
               --------------------
that money damages may be insufficient to compensate the holders of any
Registrable Securities for breaches by the Company of the terms hereof and,
consequently, that the equitable remedy of specific performance of the terms
hereof will be available in the event of any such breach.

          12.  Governing Law.  This Agreement shall be construed and enforced in
               -------------
accordance with, and the rights of the parties shall be governed by, the laws of
the State of Texas.

          13.  Counterparts.  This Agreement may be executed simultaneously in
               ------------
any number of counterparts, each of which shall be deemed an original, but all
such counterparts shall together constitute one and the same instrument.

          IN WITNESS WHEREOF, the parties have caused this Agreement to be
executed and delivered by their respective officers thereunto duly authorized as
of the date first above written.

                                           COMPANY:

                                           PURE RESOURCES, INC.

                                           By:____________________________
                                           Name:__________________________
                                           Title:_________________________

                                           OWNER:

Address:__________________________         _______________________________
                                           JACK HIGHTOWER

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