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                                                                     EXHIBIT 4.6


                       THIRD AMENDMENT TO RIGHTS AGREEMENT


         This Third Amendment to Rights Agreement (this "Third Amendment") made
as of the 19th day of August, 1998, between Coho Energy, Inc., a Texas
corporation (the "Company"), and Chase Manhattan Bank (the "Rights Agent").


                              W i t n e s s e t h:

         WHEREAS, the Company and the Rights Agent (or its predecessor) entered
into that certain Rights Agreement dated September 12, 1994 (the "Rights
Agreement"), which sets forth the terms and conditions pursuant to which holders
of Rights (as defined in the Rights Agreement) would be able to exercise them
for shares of Common Stock of the Company; and

         WHEREAS, in connection with the execution and performance of the Stock
Purchase Agreement dated August 19, 1998, by and among the Company and HM4 COHO,
L.P., a Texas limited partnership (the "Purchaser"), the Company has agreed to
sell, and the Purchaser has agreed to purchase, shares of Common Stock of the
Company (the "Shares"), and

         WHEREAS, upon purchase of the Shares, the Purchaser would become an
Acquiring Person as defined in the Rights Agreement; and

         WHEREAS, the Company and the Rights Agent desire to amend the Rights
Agreement so that the purchase of the Shares by the Purchaser would not
constitute the Purchaser an Acquiring Person;

         NOW, THEREFORE, for and in consideration of the mutual covenants and
agreements hereinafter set forth, the parties hereto agree that the Rights
Agreement shall be amended as set forth below:

         1. The first sentence of Section 1(a) of the Rights Agreement shall be
amended to read as follows in its entirety:

         "`Acquiring Person'" shall mean any Person (as such term is hereinafter
         defined) who or which, together with all Affiliates and Associates (as
         such terms are hereinafter defined) of such Person, shall be the
         Beneficial Owner (as such term is hereinafter defined) of 20% or more
         of the Common Shares then outstanding, but shall not include (i) the
         Company, (ii) any Subsidiary (as such term is hereinafter defined) of
         the Company, (iii) any employee benefit plan of the Company or of any
         Subsidiary of the Company, or any entity holding Common Shares for or
         pursuant to the terms of any such plan or (iv) HM4 COHO, L.P.

         2. Except as amended hereby, the Rights Agreement shall remain in full
force and effect and this Third Amendment shall be subject to the terms thereof.



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


Attest:                                  COHO ENERGY, INC.



By    /s/ Anne Marie O'Gorman            By    /s/ Jeffrey Clarke 
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Attest:                                  CHASE MANHATTAN BANK



By    /s/ Thomas F. Uurno                By    /s/                       
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