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                                                                  Exhibit 10.50



                         Ritchie Capital Management, LLC
                             2100 Enterprise Avenue
                             Geneva, Illinois 60134


                                  June 29, 2004


Genaissance Pharmaceuticals, Inc.
Five Science Park
New Haven, Connecticut 06511

Attn: Kevin Rakin

         Re:  LIMITATIONS ON CONVERSIONS

Dear Mr. Rakin:

         Reference is made to that certain Securities Purchase Agreement, dated
as of October 29, 2003, by and between Genaissance Pharmaceuticals, Inc. (the
"COMPANY") and RAM Trading, Ltd. (the "SECURITIES PURCHASE AGREEMENT"), the
Registration Rights Agreement, dated as of October 29, 2003, by and between the
Company and RAM Trading, Ltd. (the "REGISTRATION RIGHTS AGREEMENT"), the
Certificate of Designations, Preferences and Rights of the Series A Preferred
Stock of the Company (the "CERTIFICATE OF DESIGNATIONS") and the warrants (the
"WARRANTS") to purchase shares of the Company's Series A Preferred Stock issued
pursuant to the Securities Purchase Agreement (the Securities Purchase
Agreement, the Registration Rights Agreement, the Warrants and the Certificate
of Designations, collectively the "TRANSACTION DOCUMENTS"). Unless otherwise
defined herein, capitalized terms have the meanings set forth in the Certificate
of Designations.

         This letter agreement shall confirm our agreement to certain
restrictions concerning the conversion of shares of the Company's Series A
Preferred Stock by RAM Trading, Ltd. ("BUYER") as set forth below.

         For good and valuable consideration, the receipt and sufficiency of
which are hereby acknowledged, the Company and Buyer agree and confirm the
following matters:

         Notwithstanding anything in the Transaction Documents to the contrary,
         in no event shall the Company effect any conversion of, and no Buyer
         shall have the right to convert any shares of Series A Preferred Stock
         (the "PREFERRED SHARES") into shares of Common to the extent that,
         after giving effect to such conversion such Buyer (together with such
         Buyer's affiliates), through the conversion of Preferred Shares or
         otherwise, would beneficially own in excess of 9.99% of the number of
         shares of Common outstanding immediately after giving effect to such
         conversion. For purposes of the foregoing sentence, the number of
         shares of Common beneficially owned by Buyer and its affiliates shall
         include the number of shares of Common issuable upon conversion of the
         Preferred Shares with respect to which the determination of such
         sentence is being made, but shall


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         exclude the number of shares of Common which would be issuable upon (i)
         conversion of the remaining unconverted Preferred Shares beneficially
         owned by Buyer and its affiliates and (ii) conversion or exercise of
         the unconverted or unexercised portion of any other securities of the
         Company beneficially owned by Buyer and its affiliates subject to a
         limitation on conversion analogous to the limitation contained in this
         paragraph. Except as set forth in the preceding sentence, for purposes
         of this paragraph beneficial ownership shall be calculated in
         accordance with Section 13(d) of the Securities Exchange Act of 1934,
         as amended. For purposes of this paragraph, in determining the number
         of outstanding shares of Common, Buyer may rely on the number of
         outstanding shares of Common as reflected in (1) the Company's most
         recent Form 10-Q or Form 10-K, as the case may be, (2) a more recent
         public announcement by the Company or (3) any other notice by the
         Company or its transfer agent setting forth the number of shares of
         Common outstanding. For any reason at any time, upon the written or
         oral request of any Buyer, the Company shall within two (2) Business
         Days confirm orally and in writing to Buyer the number of shares Common
         then outstanding. Each delivery of a notice of election to convert
         shares pursuant to Section 5(a) of the Certificate of Designations will
         constitute a representation by the Buyer that it has evaluated the
         limitation set forth in this paragraph and determined that issuance of
         the full number of shares of Common Stock requested in such conversion
         notice is permitted under this paragraph. In any case, the number of
         outstanding shares of Common shall be determined after giving effect to
         the conversion or exercise of Securities of the Company, including the
         Preferred Shares, by Buyer or its affiliates since the date as of which
         such number of outstanding shares of Common was reported.


                             -----------------------


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         This letter agreement is effective June 29, 2004 and shall be binding
upon the parties and their respective transferees, successors and assigns.


         If the terms of this letter are acceptable to you, please sign below
where indicated.

                                       Very truly yours,

                                       RAM TRADING, LTD.

                                       By:  Ritchie Capital Management, LLC
                                       Its: Investment Manager


                                       By: /s/ JAMES R. PARK
                                           ------------------------------------
                                           James R. Park
                                           Its: Vice President



Agreed and Accepted this 29th day of June, 2004.

GENAISSANCE PHARMACEUTICALS, INC.


By: /s/ KEVIN RAKIN
   --------------------------------------------
   Name:  Kevin Rakin
   Title: President and Chief Executive Officer