<PAGE>
 
                                                                     EXHIBIT 4.4


                      FIRST AMENDMENT TO RIGHTS AGREEMENT
                         -----------------------------
                                        
     THIS FIRST AMENDMENT TO RIGHTS AGREEMENT (this "Amendment"), dated December
21, 1998, is by and between EEX Corporation, a Texas corporation (the
"Company"), as the successor to Lone Star Energy Plant Operations, Inc.
("LSEPO"), and Harris Trust Company of New York (the "Rights Agent").

                                R E C I T A L S
                                ---------------

     A.  The Company and the Rights Agent are parties to that certain Rights
Agreement (the "Rights Agreement"), dated September 10, 1996.

     B. The Company and the Rights Agent now desire to make certain amendments
to the Rights 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:

     1.  All capitalized terms used in this Amendment and not otherwise defined
herein shall have the meaning ascribed to such terms in the Rights Agreement.

     2.  The following definitions in Section 1 of the Rights Agreement are
amended and restated in their entirety to read as follows:

     "Acquiring Person" shall mean any Person who or which, together with all
Affiliates and Associates of such Person, shall be the Beneficial Owner of
eighteen percent (18%) or more of the shares of Common Stock then outstanding,
but shall not include (i) the Company, (ii) any Subsidiary of the Company, (iii)
any employee benefit plan of the Company or of any Subsidiary of the Company,
(iv) any Person or entity organized, appointed or established by the Company for
or pursuant to the terms of any such plan, (v) any such Person who has reported
or is required to report such ownership (but less than 20%) on Schedule 13G
under the Exchange Act (or any comparable or successor statement) or on Schedule
13D under Exchange Act (or any comparable or successor statement) which Schedule
13D does not state any intention to or reserve the right to control or influence
the management or policies of the Company or engage in any of the actions
specified in Item 4 of such Schedule (other than the disposition of the Common
Stock) and, within 10 Business Days of being requested by the Company to advise
it regarding the same, certifies to the Company that such Person acquired shares
of common Stock in excess of 17.9% inadvertently or without knowledge of the
terms of the Rights and who, together with all Affiliates and Associates,
thereafter does not acquire additional shares of Common Stock while the
Beneficial Owner of eighteen percent (18%) or more of the Common Stock then
outstanding or (vii) any of Warburg, Pincus Equity Partners, L.P., Warburg,
Pincus Netherlands Equity Partners I, C.V., Warburg, Pincus Netherlands Equity
Partners II, C.V., and Warburg, Pincus Netherlands Equity Partners III, C.V.,
and their respective Affiliates.

     3.  The term "Continuing Director" in Section 1 of the Rights Agreement is
deleted in its entirety.


     4.   Section 23(a) is amended and restated in its entirety to read as
follows:
<PAGE>
 
     (a) The Board may, at its option, at any time prior to the earlier of (i)
the close of business on the fifteenth day following the Stock Acquisition date
(or, if the Stock Acquisition Date shall have occurred prior to the Record Date,
the close of business on the fifteenth day following the Record Date), as such
date may be extended from time to time (but in to event more than a year from
the Stock Acquisition Date) by the Board while the Rights are redeemable in
accordance with the terms of this Agreement, or (ii) the Final Expiration Date,
redeem all but not less than all  the them outstanding Rights at a redemption
price of $.01 per Rights, as such amount may be appropriately adjusted to
reflect any stock split, stock dividend or similar transaction occurring after
the date hereof (such redemption price being hereinafter referred to as the
"Redemption Price").

     5.  The parties hereto hereby 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.

     6.  THIS AMENDMENT (INCLUDING, BUT NOT LIMITED TO, 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 LAWS RULES THEREOF.

     7.  This Amendment may be executed in two or more counterparts, and it
shall not be necessary that the signature of all parties hereto be contained on
any one counterpart hereof; each counterpart shall be deemed an original, but
all of which together shall constitute one and the same instrument.

                  [Remainder of Page Intentionally Left Blank]

                                       2
<PAGE>
 
     IN WITNESS HEREOF, the parties hereto have caused this Amendment to be
executed as of the date first written above.


                                    EEX Corporation


                                    /s/ J. T. Leary
                                    -------------------------------------- 
                                    J. T. Leary
                                    Vice President - Finance and Treasurer


                                    Harris Trust Company of New York



                                    By: /s/ Joseph McFadden
                                       ----------------------------------
                                    Name: Joseph McFadden
                                         --------------------------------
                                    Title: Vice President
                                          -------------------------------
                                          

CERTIFICATION:


I, J. T. Leary, Vice President - Finance and Treasurer of the Company, hereby
certify that this Amendment complies with Section 26 of the Rights Agreement.


                                     /s/ J. T. Leary
                                     _____________________________________ 
                                     J. T. Leary

                                        

                                       3