<PAGE>

This Warrant and the rights represented hereby shall not be transferable at any
time unless (i) a registration statement under the Securities Act of 1933, as
amended, shall be in effect with respect to this Warrant or the Shares issuable
hereunder at such time, or (ii) the transfer is made in compliance with the
provisions of Section 5.

Number:  *1*                                                    1,200,000 Shares
                                                                 of Common Stock
                                       WARRANT
                                  TO PURCHASE SHARES
                                          OF
                                TIPPERARY CORPORATION

     This certifies that, for value received, Slough Estates USA Inc., a
Delaware corporation, or its registered assigns, is entitled to purchase from
TIPPERARY CORPORATION, a Texas corporation (the "Company"), One Million Two
Hundred Thousand (1,200,000) Shares, as defined below, at the price of Two
Dollars and no/100 ($2.00) per Share (as defined in Section 3) at any time, or
in part from time to time on or after December 23, 2001.  This Warrant shall
expire, if not exercised prior thereto, on December 23, 2009.  The provisions
as to adjustment of the initial exercise price set forth above and the number of
Shares to be issued upon the occurrence of certain events (the Provisions as to
Adjustment) are more fully set forth in Annex I hereto, all of which is
incorporated herein by reference.  (Hereinafter, the initial exercise price set
forth above in this paragraph for the purchase of Shares upon the exercise of
this Warrant, as adjusted pursuant to the Provisions as to Adjustment, is
referred to as the "Exercise Price").  This Warrant is subject to the following
provisions, terms and conditions:

     1.   Exercise of Warrant.

     (a)  The rights represented by this Warrant may be exercised by the holder
hereof, in whole or in part, (but not as to a fractional Share), by the
surrender of this Warrant at the Company's principal office located in Denver,
Colorado (or such other office or agency of the Company as the Company may
designate by notice in writing to the holder hereof at the address of such
holder appearing on the books of the Company at anytime within the period above
named) and delivery of a completed subscription form in the form attached to
this Warrant as Exhibit A, and upon payment to the Company of the Exercise Price
for such Shares; provided, however, that any partial exercise of this Warrant
shall be for at least 100,000 Shares, except that the final, partial exercise of
this Warrant may be for less than 100,000 Shares.

     (b)  Payment of the Exercise Price shall be made in same day funds or by
wire transfer to such account as the Company may designate.

     (c)  The Company agrees that any Shares so purchased by the exercise of
this Warrant shall be deemed to be issued to the holder hereof or its nominee as
the record owner of such Shares as of the close of business on the date on which
this Warrant shall have been surrendered, the completed subscription form
delivered, and payment made for such Shares as aforesaid.

     (d)  Stock certificates evidencing Shares so purchased shall be delivered
to the holder hereof or its nominee as promptly as practicable, after the rights
represented by this Warrant shall have been so exercised.  If this Warrant shall
have been exercised only in part, and unless this Warrant has expired, a new
Warrant representing the number of Shares with respect to which this Warrant
shall not then have been exercised shall also be delivered to the holder hereof
within such time.  Notwithstanding the foregoing, however, the Company shall not
be required to deliver any stock certificate evidencing Shares upon exercise of
this Warrant except in accordance with the provisions, and subject to the
limitations, of Section 5.  The Company will pay all expenses and charges
payable in connection with the preparation, execution and delivery of stock
certificates and any new Warrants.


<PAGE>

     2.   Certain Covenants of the Company.  The Company covenants and agrees as
follows:

     (a)  All Shares which may be issued upon the exercise of the rights
represented by this Warrant (all such Shares, whether previously issued or
subject to issuance upon the exercise of this Warrant, are from time to time
referred to herein as "Warrant Shares") will, upon issuance, be duly authorized
and issued, fully paid and nonassessable and free from all taxes, liens and
charges with respect to the issuance thereof.

     (b)  During the period within which the rights represented by this Warrant
may be exercised, the Company will at all times have authorized and reserved
free of preemptive or other rights for the exclusive purpose of issuance upon
exercise of the purchase rights evidenced by this Warrant, a sufficient number
of Shares to provide for the exercise of rights represented by this Warrant.

     (c)  The Company will not, by amendment or restatement of its Articles of
Incorporation or through any reorganization, transfer of assets, consolidation,
merger, issuance or sale of securities or otherwise, avoid or take any action
which would have the effect of avoiding the performance of any of the terms to
be performed hereunder by the Company, but will at all times in good faith carry
out all of the provisions of this Warrant and take all such action as may be
necessary or appropriate to protect the rights of the holder hereof against
dilution or other impairment and, in particular, will not permit the par value
of any Share to be or become greater than the then effective Exercise Price.

     3.   Definition of Shares.  As used herein, the term "Shares" shall mean
and include shares of the Common Stock, par value $.02 per share, of the
Company as are constituted and exist on the date hereof, and shall also include
any other class of the capital stock of the Company hereafter authorized which
shall neither be limited to a fixed sum or percentage of par value in respect to
the rights of the holders thereof to receive dividends and to participate in the
distribution of assets upon the voluntary or involuntary liquidation,
dissolution or winding up of the Company, nor be subject at any time to
redemption by the Company; provided that the Shares receivable upon exercise of
this Warrant shall include only Shares of the type as are constituted and exist
on the date hereof or Shares resulting from any reclassification of the Shares
as provided for in paragraph (C) of the Provisions as to Adjustment.

     4.   No Rights or Liabilities as a Shareholder.  This Warrant shall not
entitle the holder hereof as such to any rights whatsoever, including, without
limitation, voting rights, as a holder of Shares of the Company.  No provisions
hereof, in the absence of affirmative action by the holder hereof to purchase
Shares, and no mere enumeration herein of the rights or privileges of such
holder, shall give rise to any liability of such holder as a holder of Shares of
the Company, regardless of who may assert such liability.

     5.   Restrictions on Transfer.

     (a)  This Warrant shall not be exercisable by a transferee hereof and/or
transferable and the Warrant Shares shall not be transferable except upon the
conditions specified in this Section 5, which conditions are intended, among
other things, to ensure compliance with the provisions of the Securities Act of
1933, as amended, and the rules and regulations of the Securities and Exchange
Commission (the "Commission") thereunder (collectively the "Securities Act"), in
respect of the exercise and/or transfer of this Warrant and/or transfer of such
Warrant Shares.

     (b)  This Warrant and the Warrant Shares shall not be transferable (except
for a transfer of this Warrant or the Warrant Shares in an offering registered
under the Securities Act, including, without limitation, a transfer in a
registered offering effected pursuant to Section 6, and any subsequent transfer)
unless, prior to any transfer, the holder hereof shall have received from its
transferee reasonable assurances that such person is aware that this Warrant and
the Warrant Shares have not been registered under the Securities Act and that
such person is acquiring this Warrant or the Warrant Shares for investment only
and not with the view to the disposition or public offering thereof (unless in
an offering registered under the Securities Act or exempt therefrom), and that
such person is aware that the stock certificates evidencing

                                        -2-

<PAGE>

the Warrant Shares shall bear a legend restricting transfer and disposition
thereof in accordance with the Securities Act unless, in the opinion of counsel
to the Company, such legend may be omitted.  In the event of any transfer of
this Warrant (other than a transfer in an offering registered under the
Securities Act, including, without limitations a transfer in a registered
offering effected pursuant to Section 6, and any subsequent transfer), the
holder hereof shall provide an opinion of counsel, who shall be reasonably
satisfactory to the Company, that an exemption from the registration
requirements of the Securities Act is available.

     (c)  Any permitted subsequent holder of this Warrant shall be subject to
all the terms and conditions herein, and shall acknowledge, in writing, upon
receipt of this Warrant, his or her acceptance of the terms and conditions
herein.

     (d)  To facilitate sales by a holder of this Warrant or Warrant Shares in
transactions qualifying under Rule 144 promulgated by the Commission under the
Securities Act, if available, the Company agrees to satisfy the current public
information requirements of said Rule 144, for as long as the Shares remain
registered under the Securities Exchange Act of 1934, as amended, and the rules
and regulations of the Commission thereunder (collectively the "Exchange Act"),
and to provide said holder upon request with such other information as such
holder may require for compliance with the provisions of said Rule 144.

     6.   Registration Under Securities Act.

     (a)  If the Company at any time proposes to register any issuance of its
securities under the Securities Act (other than a registration on Form S-8 in
connection with an employee stock purchase or option plan or on Form S-4 in
connection with mergers, acquisitions or exchange offerings), the Company will
at such time give prompt written notice to the holder hereof and to the holders
of all other Warrant Shares issuable from any outstanding Warrants (such holders
are hereinafter referred to as the "Prospective Sellers") of its intention to do
so.  Upon the written request of a Prospective Seller, given within 30 days
after receipt of any such notice (which request shall state the intended method
of disposition of the Warrant Shares to be transferred by such Prospective
Seller), the Company shall use its best efforts to cause all Warrant Shares, the
holders of which (or of the Warrants to which the same are related), shall have
so requested registration of the transfer thereof, to be registered under the
Securities Act, all to the extent requisite to permit the sale or other dis
position (in accordance with the intended method thereof as aforesaid) by the
Prospective Sellers of such Warrant Shares.  The rights granted pursuant to this
Section 6(a) shall not be effective with respect to the Prospective Seller in
the case of an underwritten public offering of securities of the Company by the
Company unless each Prospective Seller agrees to the terms and conditions,
including underwriting discounts and allowances, specified by the managing
underwriter of such offering with respect to such Warrant Shares.  The Company
shall have the right to reduce the number of Warrant Shares of the Prospective
Sellers to be included in a registration statement pursuant to the exercise of
the rights granted by this Section 6(a) if, and to the extent, that the managing
underwriter of such offering is of the good faith opinion, supported by written
reasons therefor that the inclusion of such Warrant Shares would materially,
adversely affect the marketing of the securities of the Company to be offered;
provided, that any such reduction of the number of Warrant Shares the transfer
of which is to be registered on behalf of the Prospective Sellers shall be made
on the basis of a pro rata reduction of all Warrant Shares of all Prospective
Sellers.

     (b)  If and whenever the Company is required by the provisions of this
Section 6 to use its best efforts to effect the registration of any transfer of
Warrant Shares under the Securities Act, the Company will, as expeditiously as
possible,

          (i)  prepare and file with the Commission a registration statement
               with respect to such transfer and use its best efforts to cause
               such registration statement to become and remain effective, but
               not for any period longer than nine months;

                                        -3-

<PAGE>

          (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 transfer of
               all securities covered by such registration statement, including,
               without limitation, taking all necessary actions whenever the
               Prospective Sellers of the Warrant Shares covered by such
               registration statement shall desire to dispose of the same;

         (iii) furnish to each Prospective Seller such number of copies of a
               prospectus, including a preliminary prospectus, in conformity
               with the requirements of the Securities Act, and such other
               documents, as such Prospective Seller may reasonably request in
               order to facilitate the disposition of the Warrant Shares owned
               by such Prospective Seller and covered by such registration
               statement;

          (iv) use its best efforts to register or qualify the securities
               covered by such registration statement under such other
               securities or blue sky laws of such jurisdictions as each
               Prospective Seller shall request, and use its best efforts to do
               any and all other acts and things which may be reasonably
               necessary to enable such Prospective Seller to consummate the
               disposition in such jurisdiction of the Warrant Shares owned by
               such Prospective Seller and covered by such registration
               statement; provided that, notwithstanding the foregoing, the
               Company shall not be required to register in any jurisdiction as
               a broker or dealer of securities or to grant its consent to
               service of process in any such jurisdiction solely on account of
               such intended disposition by such Prospective Seller;

          (v)  furnish to the Prospective Sellers whose intended dispositions
               are registered a signed copy of an opinion of counsel for the
               Company, in form and substance acceptable to such Prospective
               Sellers, to the effect that: (A) a registration statement
               covering such dispositions of Warrant Shares has been filed with
               the Commission under the Securities Act and has been made
               effective by order of the Commission, (B) such registration
               statement and the prospectus contained therein and any amendments
               or supplements thereto comply as to form in all material respects
               with the requirements of the Securities Act, and nothing has come
               to such counsel's attention which would cause him to believe that
               the registration statement or such prospectus, amendment or
               supplement, at the time such registration statement or amendment
               became effective or such supplement was filed with the
               Commission, contained any untrue statement of a material fact or
               omitted to state a material fact required to be stated therein or
               necessary to make the statements therein (in the case of such
               prospectus, amendment or supplement, in the light of the
               circumstances under which they were made) not misleading
               (provided that such counsel need not render any opinion with
               respect to the financial statements and other financial,
               engineering and statistical data included therein), and (C) to
               the best of such counsel's knowledge, no stop order has been
               issued by the Commission suspending the effectiveness of such
               registration statement and no proceedings for the issuance of
               such a stop order are threatened or contemplated;

          (vi) furnish to the Prospective Sellers whose intended dispositions
               are required a blue sky survey in the form and of the substance
               customarily prepared by counsel for the Company and accepted by
               sellers of securities in similar offerings, discussing and
               describing the application provisions of the securities or blue
               sky laws of each state or jurisdiction in which the Company shall
               be required, pursuant to Section 6(b)(iv), to register or quality
               such intended dispositions of such Warrant Shares, or, in the
               event counsel for the underwriters in such offering shall be
               preparing a blue sky

                                        -4-

<PAGE>

               survey, cause such counsel to furnish such survey to, and to
               allow reliance thereon by, such Prospective Sellers;

         (vii) otherwise use its best efforts to comply with all applicable
               rules and regulations of the Commission under the Securities Act
               and the Exchange Act, insofar as they relate to such registration
               and such registration statement; and

        (viii) use its best efforts to list such Warrant Shares on any
               securities exchange on which any securities of the Company are
               then listed or to admit such Warrant Shares for trading in any
               national market system in which any securities of the Company are
               then admitted for trading, if the listing or admission of such
               securities is then permitted under the rules of such exchange or
               system.

     (c)  With respect to the registration by the Company of transfers of
Warrant Shares under the Securities Act pursuant to Section 6(a), the Company
shall pay all expenses incurred by it in complying with this Section 6
(including, without limitation, all registration and filing fees, printing
expenses, blue sky fees and expenses, costs and expenses of audits, and
reasonable fees and disbursements of counsel for the Company and special counsel
designated by Prospective Sellers owning a majority of the Warrant Shares
covered by such registration, but specifically excluding any underwriting
discounts and allowances that are allocable to the Warrant Shares being sold by,
and which shall be paid by, the Prospective Sellers; provided, however,
that if any registration statement filed with the Commission by the Company
under Section 6(b) shall not be declared effective by the Commission, such
attempted registration shall not constitute a registration under this Section
6(c).

     (d)  It shall be a condition precedent to the obligations of the Company to
take any action pursuant to this Section 6 that each Prospective Seller, the
transfer of whose Warrant Shares is registered or to be registered under each
such registration, shall furnish to the Company such written information
regarding the securities held by such Prospective Seller as the Company shall
reasonably request and as shall be required in connection with the action to be
taken by the Company.

     (e)  (i)  in the event of any registration of any transfer of Warrant
Shares under the Securities Act pursuant to this Section 6, the Company will
indemnify and hold harmless each Prospective Seller of such securities, each of
its officers, directors and partners, and each other person, if any, who
controls such Prospective Seller within the meaning of the Securities Act, and
each underwriter, if any, who participates in the offering of such securities,
against any losses, claims, damages or liabilities (or actions in respect
thereof, joint or several, to which each Prospective Seller, officer, director
or partner, controlling person or underwriter may become subject under the
Securities Act or otherwise, insofar as such losses, claims, damages or
liabilities (or actions in respect thereof arise out of or are based upon any
untrue statement or alleged untrue statement of any material fact contained, on
the effective date thereof, in any registration statement under which such
transfer of securities was registered under the Securities Act, any preliminary
prospectus or final prospectus contained therein, or any amendment or supplement
thereto, or arise out of or are based upon the omission or alleged omission to
state therein a material fact required to be stated therein or necessary to make
the statements therein not misleading, or any violation by the Company of the
Securities Act, and will reimburse such Prospective Seller and each of its
officers, directors and partners, and each such controlling person or
underwriter, for any legal or any other expenses reasonably incurred by such
Prospective Seller or its officers, directors and partners or controlling
persons or by each such underwriter, in connection with investigating or
defending any such loss, claim, damage, liability or action; provided, however,
that the Company will not be liable in any such case to the extent that any such
loss, claim, damage or liability arises out of or is based upon an untrue
statement or alleged untrue statement or omission or alleged omission made in
such registration statement, preliminary prospectus or prospectus or such
amendment or supplement in reliance upon and in conformity with written
information furnished to the Company through an instrument duly executed by such
Prospective Seller specifically for use in the preparation thereof.  In the
event of any registration by the Company or any transfer of securities under
the

                                        -5-

<PAGE>

Securities Act pursuant to this Section 6, each Prospective Seller of Warrant
Shares covered by such registration will indemnify and hold harmless the
Company, each other person, if any, who controls the Company within the meaning
of the Securities Act and each officer and director of the Company and the other
Prospective Sellers to the same extent that the Company agrees to indemnity it,
but only with respect to the written information relating to such Prospective
Seller furnished to the Company by such Prospective Seller aforesaid.

     (ii) Each indemnified party shall, as promptly as practicable upon receipt
of notice of the commencement of any action against such indemnified party or
its officers, directors or partners, or any controlling person of such
indemnified party, in respect of which indemnity may be sought from an
indemnifying party on account of the indemnity agreement contained in Section
6(e)(i), notify the indemnifying party in writing of the commencement thereof.
The omission of such indemnified party to so notify the indemnifying party of
any such action shall not relieve the indemnifying party from any liability
which it may have on account of the indemnity agreement contained in Section
6(e)(i) to the extent that the failure to receive such notice within a
reasonable period of time shall not have caused harm, loss or damage to the
indemnifying party, provided that, conversely, if such failure to receive notice
shall have caused any harm, loss or damage to the indemnifying party, such
failure shall constitute a defense to any liability which such indemnifying
party may have on account of such agreement to the extent of the harm, loss or
damage so caused.  In case any such action shall be brought against any
indemnified party, its officers, directors and partners, or any such controlling
person, and such indemnified party shall notify the indemnifying party of the
commencement thereof, the indemnifying party shall be entitled to participate in
(and, to the extent that the indemnifying party shall wish, to direct) the
defense thereof at the indemnifying party's own expense, in which event the
defense shall be conducted by recognized counsel chosen by the indemnifying
party and approved by the indemnified party (whose approval shall not
unreasonably be withheld) and the indemnified party may participate in such
defense at its own expense (unless it is advised by counsel that actual or
potential differing interests or defenses exist or may exist, in which case such
expenses shall be paid by the indemnifying party, provided that the indemnifying
party shall not be required to pay the expenses for more than one counsel for
all such indemnified parties).

     7.   Transfer; Ownership.  Subject to Section 5, this Warrant and all
rights hereunder are transferable, in whole or in part, at the office or agency
of the Company referred to in Section 1 by the holder hereof in person or by a
duly authorized attorney, upon surrender of this Warrant, with an assignment,
acceptable to the Company, duly completed, at which time a new Warrant shall be
made and delivered by the Company, of the same tenor as this Warrant but
registered in the name of the transferee.  The holder of this Warrant, by taking
or holding the same, consents and agrees that this Warrant, when endorsed in
blank, shall be deemed negotiable, and that the holder hereof, when this Warrant
shall have been so endorsed, may be treated by the Company and all other persons
dealing with this Warrant as the absolute owner hereof for any purpose and as
the person entitled to exercise the rights represented by this Warrant and to
transfer this Warrant on the books of the Company, any notice to the contrary
notwithstanding; but until such transfer on such books, the Company may treat
the registered holder hereof as the owner hereof for all purposes.  Any
transfer of this Warrant shall be made in compliance with the Securities Act and
any applicable state securities or blue sky laws.

     8.   Exchange and Replacement.  Subject to Section 7, this Warrant is
exchangeable, upon the surrender hereof by the holder hereof at the office or
agency of the Company referred to in Section 1, for new Warrants of like tenor
and date representing in the aggregate the right to purchase the number of
Shares which may be purchased hereunder, each of such new Warrants to represent
the right to purchase such number of Shares as shall be designated by said
holder hereof at the time of such surrender.  Upon receipt by the Company at the
office or agency referred to in Section 1 of evidence reasonably satisfactory to
it of the loss, theft or destruction of this Warrant and of indemnity or
security reasonably satisfactory to it (provided that the written indemnity of
the holder hereof shall be deemed reasonably satisfactory to the Company for
such purposes), the Company will deliver a new Warrant of like tenor and date in
replacement of this Warrant.  This Warrant shall be promptly canceled by the
Company upon the surrender hereof in

                                        -6-

<PAGE>

connection with any transfer, exchange or replacement.  The Company will pay all
expenses and charges payable in connection with the preparation, execution and
delivery of Warrants pursuant to Section 7 and this Section 8.

     9.   Notices.  Any notice or other document required or permitted to be
given or delivered to the holder hereof shall be delivered at, or sent by
certified or registered mail to, Slough Estates USA Inc., 33 West Monroe Street,
Suite 2000, Chicago, Illinois 60603, or to such other address as shall have been
furnished to the Company in writing by the holder hereof.  Any notice or other
document required or permitted to be given or delivered to the Company shall be
delivered at, or sent by certified or registered mail to, 633 Seventeenth, Suite
1550, Denver, Colorado 80202, or to such other address as shall have been
furnished in writing to the holder hereof by the Company.  Any notice so
addressed and mailed by registered or certified mail or otherwise delivered,
shall be deemed to be given when actually received by the addressee.

     10.  GOVERNING LAW. THIS WARRANT SHALL BE GOVERNED BY, AND CONSTRUED AND
ENFORCED IN ACCORDANCE WITH, THE LAWS OF THE STATE OF TEXAS.

     11.  Miscellaneous.  This Warrant will be binding upon any partnership or
corporation succeeding to the Company by consolidation or acquisition of all or
substantially all of the Company's assets, and upon any successor or assign of
the holder hereto.  This Warrant and any provision hereof may be changed,
waived, discharged or terminated only by an instrument in writing signed by the
party (or any predecessor in interest thereof) against whom enforcement of the
same is sought.  The headings in this Warrant are for purposes of reference only
and shall not affect the meaning or construction of any of the provisions
hereof.

     IN WITNESS WHEREOF, Tipperary Corporation has caused this Warrant to be
signed by its duly authorized officers, under its corporate seal, to be dated
December 23, 1999.

                              TIPPERARY CORPORATION

                              By:/s/ David L. Bradshaw
                                 --------------------------------------------
                                 David L. Bradshaw, President and
                                 Chief Executive Officer

                                        -7-

<PAGE>

                                                                         Annex I

                                TIPPERARY CORPORATION

                            PROVISIONS AS TO ADJUSTMENT OF
                         EXERCISE PRICE AND NUMBER OF SHARES
                       ISSUED UPON OCCURRENCE OF CERTAIN EVENTS

     The Exercise Price and the number of Shares issuable upon the exercise of
the annexed Warrant to purchase shares of TIPPERARY CORPORATION, a Texas
corporation (herein and in this Warrant referred to as the "Company"), shall be
subject to adjustment from time to time as hereinafter provided; however, that
in no event shall the Exercise Price be increased to a price greater than Two
Dollars and no/100 ($2.00) per Share, except as provided by paragraph (C)
hereof.  Upon each adjustment of the Exercise Price, the holder of this Warrant
shall thereafter be entitled to purchase, at the Exercise Price resulting from
such adjustment, the number of Shares obtained by multiplying the number of
Shares purchasable pursuant hereto immediately prior to such adjustment by a
fraction, the numerator of which is the Exercise Price in effect immediately
prior to such adjustment and the denominator of which is the Exercise Price
resulting from such adjustment.  In making the adjustments to the Exercise Price
and the number of Shares issuable upon the exercise of this Warrant, the
following provisions shall be applicable:

     (A)  If and whenever the Company shall issue or sell any Shares for
consideration per Share at less than the Market Price (as hereinafter defined)
of such Shares on the date of such issue or sale, then forthwith upon such issue
or sale the Exercise Price in effect immediately prior thereto shall be adjusted
to an amount (calculated to the nearest cent) determined by dividing (i) an
amount equal to the sum of (a) the number of Shares outstanding immediately
prior to such issue or sale multiplied by the Exercise Price in effect
immediately prior to such issue or sale, and (b) the consideration, if any,
received by the Company upon such issue or sale by (ii) the total number of
Shares outstanding immediately after such issue or sale; provided, however, that
no adjustment shall be made hereunder by reason of:

     (i)  the grant of this Warrant or the issuance of Shares upon the exercise
          of this Warrant or any other warrant of the Company (except for a
          warrant issued after the date hereof the exercise price of which is
          less than the Market Price on the date of issuance of such warrant);
          or

     (ii) the grant by the Company of options to purchase Shares in connection
          with any purchase or option plan for the benefit of employees of the
          Company, or any affiliates or subsidiaries thereof.

No adjustment of the Exercise Price shall be required to be made by the Company
and no notice hereunder must be given if the amount of any required adjustment
is less than 5% of the Exercise Price.  In such case any such adjustment shall
be carried forward and shall be made (and notice thereof shall be given
hereunder) at the time of and together with the next subsequent adjustment
which, together with any adjustment so carried forward, shall amount to not less
than 5% of the Exercise Price.

     (B)  For the purposes of paragraph (A), the following provisions (i)
through (vi), inclusive, shall also be applicable:

     (i)  If, at the time Shares are issued and sold upon the conversion or
          exchange of Convertible Securities or upon the exercise of rights or
          options previously granted by the Company, the price per Share for
          which such Shares are issued (determined by dividing (a) the total
          amount, if any, received by the Company as consideration for such
          Convertible Securities or for the granting of such rights or options,
          plus the aggregate amount of additional consideration paid to the
          Company upon the conversion or exchange of such Convertible Securities
          (which, if so provided in such Convertible Securities, shall be deemed
          to be equal

                                   Annex - Page 1

<PAGE>

          to the outstanding principal amount of the indebtedness represented by
          such Convertible Securities) or upon the exercise of such rights or
          options, by (b) the total number of Shares issued upon the conversion
          or exchange of such Convertible Securities or upon the exercise of
          such rights or options) shall be less than the Exercise Price in
          effect immediately prior to such issue, sale or exercise, then the
          adjustments provided for by the first paragraph of this Annex I and
          paragraph (A) shall be made.  In making the adjustment of the Exercise
          Price provided for by paragraph (A), the amount described in clause
          (a) of this paragraph (B)(i) shall be considered the consideration
          received by the Company upon the issue or sale of the Shares for
          purposes of clause (i)(b) of paragraph (A).

     (ii) In case at any time any Shares or Convertible Securities or any rights
          or options to purchase any Shares or Convertible Securities shall be
          issued or sold for cash, the consideration received therefor shall be
          deemed to be the amount received by the Company therefor without
          deduction therefrom of any expenses incurred or any underwriting
          commissions or concessions paid or allowed by the Company in
          connection therewith.  In case any Shares or Convertible Securities or
          any rights or options to purchase any Shares or Convertible Securities
          shall be issued or sold, in whole or in part, for consideration other
          than cash, the amount of the consideration other than cash received by
          the Company in exchange for the issue or sale of such Convertible
          Securities shall be deemed to be the fair value of such consideration
          as determined in good faith by the board of directors of the Company,
          without deduction therefrom of any expenses incurred or any
          underwriting commissions or concessions paid or allowed by the Company
          in connection therewith; provided that if the holder or holders of at
          least 66-2/3% of the Warrant Shares purchasable under this Warrant
          shall request in writing, the value of such consideration shall be
          determined by an independent expert selected by such holders, the
          costs and expenses of which shall be borne by the Company, and, if the
          value of such consideration as so determined is less than the value
          determined by the board of directors of the Company, the lesser value
          shall be utilized in calculating the consideration per Share received
          by the Company for purposes of making the adjustment provided by
          paragraph (A).  In the event of any merger or consolidation of the
          Company in which the Company is not the surviving corporation or in
          the event of any sale of all or substantially all of the assets of the
          Company for stock or other securities of any corporation, the Company
          shall be deemed to have issued a number of Shares for stock or
          securities of such other corporation computed on the basis of the
          actual exchange ratio on which the transaction was predicated and for
          consideration that is equal to the fair market value on the date of
          such transaction of such stock or securities of the other corporation,
          and if any such calculation results in adjustment of the Exercise
          Price, the determination of the number of Shares issuable upon
          exercise of this Warrant immediately prior to such merger,
          consolidation or sale, for purposes of paragraph (A), shall be made
          after giving effect to such adjustment of the Exercise Price.

    (iii) The number of Shares outstanding at any given time shall not include
          Shares that have been redeemed by the Company and not canceled, if
          any, and that are thus owned or held by or for the account of the
          Company, and the disposition of any such Shares shall be considered an
          issue or sale of Shares for purposes of paragraph (A).

     (iv) "Market Price" shall mean the lower of (a) the average closing sales
          prices of Shares recorded on the principal national securities
          exchange on which the Shares are listed or in a national market system
          for securities in which the Shares are admitted to trading or (b) the
          average of the closing bid and asked prices of Shares reported in the
          domestic over-the-counter market, for the 20 trading days immediately
          prior to the day as of which the Market Price is being determined.  If
          the Shares are not listed on any national securities exchange or
          admitted for trading in any national market system or traded in the
          domestic over-the-counter market, the Market Price shall be the
          higher of (y) the book value of the Shares as

                                   Annex - Page 2

<PAGE>

          determined by a firm of independent public accountants of recognized
          standing selected by the board of directors of the Company as of the
          last day of any month ending within 60 days preceding the date as of
          which the determination is to be made or (z) the fair market value of
          the Shares determined in good faith by the board of directors of the
          Company, provided that if the holder or holders of at least 66-2/3% of
          the Warrant Shares purchasable under the Warrant shall request in
          writing, the fair market value of the Shares shall be determined by an
          independent investment banking firm or other independent expert
          selected by such holders and reasonably satisfactory to the Company,
          the costs and expenses of which shall be born by the Company, which
          determination shall be as of a date which is within 15 days of the
          date as of which the determination is to be made.

     (v)  Anything herein to the contrary notwithstanding, in case the Company
          shall issue any Shares in connection with the acquisition by the
          Company of the stock or assets of any other corporation or the merger
          of any other corporation into the Company under circumstances where,
          on the date of the issuance of such Shares, the consideration received
          for such Shares is less than the Market Price of the Shares, but on
          the date the number of Shares was determined, the consideration
          received for such Shares would not have been less than the Market
          Price thereof, such Shares shall not be deemed to have been issued for
          less than the Market Price, provided that the date the number of
          shares was determined is not greater than ten days prior to the date
          of issuance of such shares.

     (vi) Anything in clause (ii) of this paragraph (B) to the contrary
          notwithstanding, in the case of an acquisition where all or part of
          the purchase price is payable in Shares or Convertible Securities but
          is stated as a dollar amount, where the Company upon making the
          acquisition pays only part of a maximum dollar purchase price which is
          payable in Shares or Convertible Securities and where the balance of
          such purchase price is deferred or is contingently payable under a
          formula related to earnings over a period of time, (a) the
          consideration received for any Shares or Convertible Securities
          delivered at the time of the acquisition shall be deemed to be such
          part of the total consideration as the portion of the dollar purchase
          price then paid in Shares or Convertible Securities bears to the total
          maximum dollar purchase price payable in Shares or Convertible
          Securities and (b) in connection with each issuance of additional
          Shares or Convertible Securities pursuant to the terms of the
          agreement relating to such acquisition, the consideration received
          shall be deemed to be such part of the total consideration as the
          portion of the dollar purchase price then and theretofore paid in
          Shares or Convertible Shares bears to the total maximum dollar
          purchase price payable in Shares or Convertible Securities multiplied
          by a fraction the numerator of which shall be the number of Shares (or
          in the case of Convertible Securities other than capital stock of the
          Company, the aggregate principal amount of such Convertible
          Securities) then issued and the denominator of which shall be the
          total number of shares (or in the case of Convertible Securities other
          than capital stock of the Company, the aggregate principal amount of
          such Convertible Securities) then and theretofore issued under such
          acquisition agreement.  In the event only a part of the purchase price
          for an acquisition is paid in Shares or Convertible Securities in the
          manner referred to in this clause (vi), the term "total consideration"
          as used in this clause (vi) shall mean that part of the aggregate
          consideration as is fairly allocable to the purchase price paid in
          Shares or Convertible Securities in the manner referred to in this
          clause (vi), as determined by the board of directors of the Company.

     (C)  In the case at any time the Company shall subdivide its outstanding
Shares into a greater number of Shares, then from and after the record date for
such subdivision the Exercise Price in effect immediately prior to such
subdivision shall be proportionately reduced and the number of Shares
purchasable upon the exercise of this Warrant shall be correspondingly
increased, and, conversely, in case the outstanding Shares shall be combined
into a smaller number of Shares, then from and after the record

                                   Annex - Page 3

<PAGE>

date for such combination the Exercise Price in effect immediately prior to such
combination shall be proportionately increased and the number of Shares
purchasable upon the exercise of this Warrant shall be correspondingly
decreased.

     (D)  If any capital reorganization or reclassification of the capital stock
of the Company, or consolidation or merger of the Company with another
corporation, or sale of all or substantially all of its assets to another
corporation, shall be effected in such a way that holders of Shares (or any
other securities of the Company then issuable upon the exercise of this Warrant)
shall be entitled to receive stock, securities or assets with respect to or in
exchange for Shares (or such other securities) then, as a condition of such
reorganization, reclassification, consolidation, merger or sale, lawful and
adequate provision shall be made whereby the holder hereof shall thereafter have
the right to purchase and receive upon the basis and upon the terms and
conditions specified in this Warrant and in lieu of the Shares (or other
securities) of the Company immediately theretofore purchasable and receivable
upon the exercise of the rights represented hereby, such shares of stock,
securities or assets as may be issued or payable with respect to or in exchange
for a number of outstanding Shares (or other securities) equal to the number of
Shares (or other securities) immediately theretofore so purchasable and
receivable had such reorganization, reclassification, consolidation, merger or
sale not taken place, and in any such case appropriate provision shall be made
with respect to the rights and interests of the holder of this Warrant to the
end that the provisions hereof (including, without limitation, provisions for
adjustment of the Exercise Price and of the number of Shares (or other
securities) purchasable upon the exercise of this Warrant and for the
registration thereof as provided in Section 6 of this Warrant) shall thereafter
be applicable, as nearly as may be, in relation to any shares of stock,
securities or assets thereafter deliverable upon the exercise hereof (including
an immediate adjustment, by reason of such consolidation, merger or sale, of the
Exercise Price to the value of the Shares (or other securities) reflected by the
terms of such consolidation, merger or sale if the value so reflected is less
than the Exercise Price in effect immediately prior to such consolidation,
merger or sale).  In the event of a consolidation or merger of the Company with
or into another corporation as a result of which a greater or lesser number of
securities of the surviving corporation are issuable to holders of Shares in
respect of the number of Shares outstanding immediately prior to such
consolidation or merger, then the Exercise Price in effect immediately prior to
such consolidation or merger shall be adjusted in the same manner as though
there were a subdivision or combination of the outstanding Shares.  The Company
shall not effect any such consolidation, merger or sale, unless prior to or
simultaneously with the consummation thereof the surviving or successor
corporation (if other than  the Company) resulting from such consolidation or
merger of the corporation purchasing such assets shall assume, by written
instrument executed and mailed to the registered holder hereof at the last
address of such holder appearing on the books of the Company, the obligation to
deliver to such holder such Shares of stock, securities or assets as, in
accordance with the foregoing provisions, such holder may be entitled to
purchase, and containing the express assumption of such surviving or successor
corporation of the due performance of every provision of this Warrant to be
performed by the Company and of all liabilities and obligations of the Company
hereunder.

     (E)  In case at any time the Company shall pay any dividend on or make any
other distribution with respect to Shares (or any other securities of the
Company then issuable upon the exercise of the Warrant) that is payable in
Shares, Convertible Securities, any other securities of the Company or other
stock, securities or assets, other than cash, then thereafter, and in lieu of
any adjustment of the Exercise Price and the number of Shares issuable upon the
exercise of this Warrant, the holder of this Warrant, upon any exercise of the
rights represented hereby, shall be entitled to receive the number of Shares (or
other securities) being purchased upon such exercise and, in addition to and
without further payment, the Shares, Convertible Securities, other Securities of
the Company or other stock, securities or assets which the holder of this
Warrant would have received by way of such distributions, as if continuously
since the date of the Warrant (or, if this Warrant shall have been issued
pursuant to Section 7 of this Warrant, the date of the predecessor Warrant to
which this Warrant relates), such holder had been the record holder of the
number of Shares (or other securities) then being purchased upon the exercise
hereof and had retained all such Shares, Convertible Securities, other
securities of the Company or other stock, securities or assets distributable
with respect to such Shares (or other securities) then being purchased upon the
exercise hereof

                                   Annex - Page 4

<PAGE>

and, furthermore, all cash, stock, securities or assets payable as dividends or
distributions with respect to the foregoing distributable securities or assets
and originating directly or indirectly therefrom.  The Company shall reserve and
retain in escrow from any such dividend or distribution of Shares, Convertible
Securities, other securities of the Company or other stock, securities or
assets, and from any such dividends or distributions with respect thereto and
originating directly or indirectly therefrom, such Shares, Convertible
Securities, other securities of the Company and other stock, securities, assets
and cash as shall be necessary to fulfill its obligations to the holder hereof
pursuant to this paragraph (E).

     (F)  If at any time conditions arise by reason of action taken by the
Company, which in the good faith opinion of the board of directors of the
Company, are not adequately covered by the provisions of this Annex I, and which
might materially adversely affect the rights of the holder of this Warrant, the
Company shall appoint a firm of independent public accountants of recognized
standing (which may be the regular accountants or auditors of the Company),
which shall give their opinion as to the adjustments, if any, in the Exercise
Price and the number of Shares purchasable upon the exercise of this Warrant, or
other change in the rights of the holder hereof, on a basis consistent with the
other provisions of this Annex I, necessary to preserve without diminution the
rights of the holder hereof.  Upon receipt of such opinion, the Company shall
forthwith make the adjustments described herein.

     (G)(i)    Within two (2) days of any adjustment of the Exercise Price or
               change in the number of Shares purchasable upon the exercise of
               this Warrant made pursuant to the above paragraphs (A)  through
               (F) or any change in the rights of the holder of this Warrant by
               reason of the occurrence of events described such paragraphs, the
               Company shall give written notice by certified or registered mail
               to the registered holder of this Warrant at the address of such
               holder as shown on the books of the Company, which notice shall
               describe the event requiring such adjustments, the Exercise Price
               resulting from such adjustment, the increase or decrease in the
               number of Shares purchasable upon the exercise of this Warrant,
               and any other change in the rights of such holder, and set forth
               in reasonable detail the method of calculation of such
               adjustments and the facts upon which such calculations are based.
               Within three (3) days of receipt from the holder hereof of a
               written request therefor (which request shall not be made more
               than once each calendar quarter), the Company shall give written
               notice by certified or registered mail to such holder at its
               address as shown on the books of the Company of the Exercise
               Price in effect as of the date of receipt of such written
               request, and the number of Shares purchasable or the number or
               amount of other shares of stock, securities or assets receivable
               as of such date, and set forth in reasonable detail the method of
               calculation of such numbers.

          (ii) Upon each adjustment of the Exercise Price and each change in the
               number of Shares purchasable upon the exercise of this Warrant,
               and change in the rights of the holder of this Warrant by reason
               of the occurrence of other events herein set forth, then and in
               each case, upon written request of the holder of this Warrant
               (which request shall be made not more often than once each
               calendar year), the Company will at its expense promptly obtain
               an opinion of independent public accountants reasonably
               satisfactory to each holder stating the then effective Exercise
               Price and the number of Shares then purchasable, or specifying
               the other shares of stock, securities or assets and the amount
               thereof then receivable, and setting forth in reasonable detail
               the method of calculation of such numbers and the facts upon
               which such calculations are based.  The Company will promptly
               mail a copy of such opinion to the registered holder hereof.

     (H)  In case at any time:

     (i)  The Company shall pay any dividend payable in capital stock on its
          outstanding Shares or make any distribution (other than regular cash
          dividends) to the holders of Shares;

                                   Annex - Page 5

<PAGE>

     (ii) The Company shall offer for subscription pro rata to the holders of
          Shares any additional capital stock or other rights;

    (iii) There shall be authorized any capital reorganization or
          reclassification of the capital stock of the Company, or consolidation
          or merger of the Company with, or sale of all or substantially all of
          its assets to, another corporation; or

     (iv) There shall be authorized or commence a voluntary or involuntary
          dissolution, liquidation or winding up of the Company,

then, in one or more of said cases, the Company shall given written notice by
certified or registered mail to the holder of this Warrant at the address of
such holder as shown on the books of the Company on the date on which (1) the
books of the Company shall close or a record shall be taken for such dividend,
distribution, or subscription rights, or (2) such reorganization,
reclassification, consolidation, merger, sale, dissolution, liquidation or
winding up shall take place or be voted upon by the shareholders of the Company,
as the case may be.  Such notice shall also specify the date as of which the
holders of record of Shares shall participate in such dividend, distribution or
subscription rights, or shall be entitled to exchange their Shares for
securities or other property deliverable upon such reorganization,
reclassification, consolidation, merger, sale, dissolution, liquidation or
winding up, as the case may be.  Such written notice shall be given at least
thirty (30) days prior to the action in question and no less than thirty (30)
days prior to the record date or the date on which the Company's books are
closed in respect thereto.

                                   Annex - Page 6

<PAGE>

EXHIBIT A

                                  SUBSCRIPTION FORM

                       To be Executed by the Registered Holder
                      Desiring to Exercise the Within Warrant of
                                TIPPERARY CORPORATION

     The undersigned registered holder hereby exercises the right to purchase
____________ Shares (not less than 100,000 Shares, except for the final exercise
of this Warrant, which may be for a lesser number of Shares) covered by the
within Warrant according to the conditions thereof, and herewith makes payment
of the Exercise Price of such Shares, $___________.

     Name of Registered Holder:_______________________________________________

               Address of Registered Holder:________________________________

                                         _________________________________

               Registered Holder's Tax I.D. No.:_________________


               Name of Nominee  (if applicable):______________________________

               Address of Nominee:________________________________

                                _________________________________

                    Nominee's Tax I.D. No.:______________________


               Signature of
               Registered Holder:__________________________________________

               Title of Signing Officer
               or Agent (if any):_____________________________________


Dated: __________________, 19_____.