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                                                                     Exhibit 4.2

                       THIRD AMENDMENT TO RIGHTS AGREEMENT

     This Third Amendment to Rights Agreement (this "Amendment") dated May 29,
2002, is by and between EEX Corporation, a Texas corporation ("Company"), as
successor to Lone Star Energy Plant Operations, Inc., and Computershare Investor
Services, LLC ("Rights Agent"), as successor Rights Agent to Harris Trust
Company of New York ("Harris"). This Amendment amends the Rights Agreement,
dated as of September 10, 1996, by and between Company and Harris, as amended by
that certain First Amendment to Rights Agreement dated December 21, 1998, and as
subsequently amended by that certain Second Amendment to Rights Agreement dated
as of May 13, 2002 (as so amended, the "Rights Agreement"). Except as
specifically noted, capitalized terms used but not otherwise defined in this
Amendment have the meanings ascribed in the Rights Agreement.

                                    RECITALS

     A. Company, Newfield Exploration Company ("Parent") and a wholly-owned
subsidiary of Parent ("Merger Sub") plan to enter into an Agreement and Plan of
Merger (the "Merger Agreement"), whereby Parent will acquire Company through the
merger of Merger Sub with and into Company.

     B. Simultaneously with the execution of the Merger Agreement, Parent, David
A. Trice, Terry W. Rathert and each of Warburg Pincus Equity Partners, L.P.,
Warburg, Pincus Netherlands Equity Partners I, C.V., Warburg, Pincus Netherlands
Equity Partners II, C.V., Warburg, Pincus Netherlands Equity Partners III, C.V.,
Thomas M Hamilton, David R. Henderson and Richard S. Langdon (collectively, the
"Shareholders") plan to enter into a Voting Agreement and Irrevocable Proxy (the
"Voting Agreement"), pursuant to which the Shareholders will, among other
things, (i) agree to vote or cause to be voted their respective shares in favor
of the Merger and each of the other transactions contemplated by the Merger
Agreement, (ii) agree to vote or cause to be voted their respective shares
against proposals inconsistent with the Merger and the other transactions
contemplated by the Merger Agreement and (iii) grant to David A. Trice and Terry
W. Rathert irrevocable proxies to vote such Shareholders' shares of common
and/or preferred stock of the Company with respect to such matters.

     C. In connection with the transactions contemplated by the Merger Agreement
and the Voting Agreement, and without giving effect to this Amendment, each of
Parent and Merger Sub may be an "Acquiring Person" under the Rights Agreement.

     D. Pursuant to and in compliance with Section 26 of the Rights Agreement,
the board of directors of Company deems it to be in the best interests of
Company to amend the Rights Agreement in order to, among other things, exclude,
subject to certain conditions, Parent and Merger Sub from the definition of the
term "Acquiring Person" in connection with their entry into the Merger Agreement
and Parent's entry into the Voting Agreement.

     NOW THEREFORE, in consideration of the premises contained herein and for
other good and valuable consideration, the sufficiency of which is hereby
acknowledged, the Rights Agreement is hereby modified, adjusted and amended as
follows:

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                             STATEMENT OF AGREEMENT

1.   Amendment of Section 1. Each of the additions and revisions described below
     ----------------------
are hereby made to the Rights Agreement.

         (a) Section 1 of the Rights Agreement is amended by adding thereto a
new definition immediately after the definition of "Final Expiration Date" and
immediately before the definition of "NASDAQ", which new definition shall read
as follows:

         "Merger Agreement" shall mean the Agreement and Plan of Merger, dated
         as of May 29, 2002, by and among Company, Newfield Exploration Company
         and Newfield Production Company, as the same may be amended from time
         to time.

         (b) Section 1 of the Rights Agreement is amended by adding thereto a
new definition immediately after the definition of "NASDAQ" and immediately
before the definition of "Original Rights", which new definition shall read as
follows:

         "Parent Parties" shall have the meaning given in Section 35.

         (c) Section 1 of the Rights Agreement is amended by adding thereto a
new definition immediately after the definition of "Triggering Event" and
immediately before Section 2 of the Rights Agreement, which new definition shall
read as follows:

         "Voting Agreement" shall mean that certain voting agreement dated as of
         May 29, 2002 by and among Newfield Exploration Company, David A. Trice,
         Terry W. Rathert, Warburg, Pincus Equity Partners, L.P., a Delaware
         limited partnership, Warburg, Pincus Netherlands Equity Partners I,
         C.V., a Dutch limited partnership, Warburg, Pincus Netherlands Equity
         Partners II, C.V., a Dutch limited partnership, Warburg, Pincus
         Netherlands Equity Partners III, C.V., a Dutch limited partnership,
         Thomas M Hamilton, David R. Henderson and Richard S. Langdon.

2.   New Section 35.  The Rights Agreement is amended by adding thereto a new
     --------------
Section 35 which provides as follows:

         Section 35. Exception for Merger and Voting Agreement. Notwithstanding
         anything in this Rights Agreement to the contrary, (a) none of Newfield
         Exploration Company, Newfield Production Company, David A. Trice and
         Terry W. Rathert and none of any of the foregoing Persons' Affiliates
         (together, the "Parent Parties"), either alone or as a group, shall be
         or become an Acquiring Person, and no Stock Acquisition Date or
         Distribution Date shall occur, solely as a result of (i) the execution,
         delivery or performance of the Merger Agreement (or any amendments
         thereto) or the consummation of the transactions contemplated thereby,
         including, without limitation, the Merger (as defined in the Merger
         Agreement), (ii) the execution, delivery or performance of the Voting
         Agreement or any amendments thereto, or the consummation of the
         transactions contemplated thereby, (iii) the announcement of the Merger
         Agreement or the

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         Voting Agreement, or (iv) becoming the Beneficial Owner of shares of
         Common Stock pursuant to the Merger Agreement, the Voting Agreement or
         otherwise as a result of any of the transactions contemplated by the
         Merger Agreement or the Voting Agreement, including, without
         limitation, the Merger. In addition, none of the Parent Parties shall
         be deemed to be the Beneficial Owners (or to have Beneficial Ownership)
         of any Common Stock or Preferred Stock solely as a result of Newfield
         Exploration Company being a party to the Voting Agreement.

3.       Remainder of Agreement Not Affected. The parties hereto acknowledge and
agree that, except as specifically supplemented and amended, changed or modified
hereby, the Rights Agreement shall remain in full force and effect in accordance
with its terms. On or after the date of this Amendment, each reference in the
Rights Agreement to "this Agreement," "hereunder," "hereof," "herein" or words
of like import referring to the Rights Agreement shall mean and be a reference
to the Rights Agreement as amended, and this Amendment shall be deemed to be a
part of the Rights Agreement.

4.       Authority. Each party represents that such party has full power and
Fauthority to enter into this Amendment, and that this Amendment constitutes a
legal, valid and binding obligation of such party, enforceable against such
party in accordance with its terms.

5.       Counterparts.  This Amendment may be executed in one or more
         ------------
counterparts, including facsimile counterparts, each of which will be deemed to
be an original, but all of which together will constitute one and the same
agreement.

6.       Applicable Law.  THIS AMENDMENT (INCLUDING, THE VALIDITY AND
         --------------
ENFORCEABILITY HEREOF) SHALL BE GOVERNED BY, AND CONSTRUED IN ACCORDANCE WITH,
THE LAWS OF THE STATE OF TEXAS, OTHER THAN THE CONFLICT OF LAW RULES THEREOF.

                            [Signature Page Follows]

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         IN WITNESS WHEREOF, the parties hereto have caused this Amendment to be
duly executed and attested, all as of the day and year first above written.

                            EEX CORPORATION


                            By:               /s/ Richard L. Edmonson
                                   -------------------------------------------
                            Name:  Richard L. Edmonson
                            Title: Senior Vice President, General Counsel
                                    and Secretary

                            COMPUTERSHARE INVESTOR SERVICES, LLC


                            By:               /s/ Keith Bradley
                                   -------------------------------------
                            Name:             Keith Bradley
                                   -------------------------------------
                            Title:            Manager - Client Services
                                   -------------------------------------


CERTIFICATION:

         I, Richard L. Edmonson, Senior Vice President, General Counsel and
Secretary of Company, hereby certify that this Amendment complies with Section
26 of the Rights Agreement.

                            By:               /s/ Richard L. Edmonson
                                   -------------------------------------------
                            Name:  Richard L. Edmonson
                            Title: Senior Vice President, General Counsel
                                   and Secretary

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