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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.
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     (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
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shall effect a split of the Common Stock or a dividend payable in Common Stock,
or in the event the outstanding

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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
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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
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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
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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
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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

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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.

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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

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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.

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     (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
                                               ------------------------

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