AMENDMENT NO. 2
                                       TO
                           SECOND AMENDED AND RESTATED
                                CUSTODY AGREEMENT

     Short-Term Investments Co., a Massachusetts business trust ("STIC-Mass"),
on behalf of its Limited Maturity Treasury Portfolio, assigned all of its rights
and obligations under the Second Amended and Restated Custody Agreement dated
June 16, 1987, as amended, between STIC-Mass and The Bank of New York (the
"Custodian"), to AIM Investment Securities Funds, a Delaware statutory trust
(the "Fund"), with respect to its Limited Maturity Treasury Portfolio, now known
as Limited Maturity Treasury Fund, on October 15, 1993.

     Amendment No. 2 (the "Amendment") to that certain Second Amended and
Restated Custody Agreement dated as of June 16, 1987 between the Fund and the
Custodian (hereinafter the "Custody Agreement") is made as of May 31, 2005.

                                   WITNESSETH:

     WHEREAS, the Fund desires to execute an Agreement with JP Morgan Chase
Bank, N.A.;

     NOW, THEREFORE, the Fund and the Custodian hereby amend the Custody
Agreement as follows:

     1. Section 7 of Article XV is hereby renumbered Section 7(a).

     2. A new Section 7(b) is hereby added to Article XV to read in its entirety
as follows:

          "(b) Notwithstanding any other provision in this Agreement, the Fund
     shall appoint JP Morgan Chase Bank, N.A. (the "Bank") by executing the form
     of Agreement attached hereto (the "Agreement"). The Fund agrees that
     notwithstanding any other provision in this Agreement: (1) the Custodian
     shall have no duty to supervise or monitor the Bank under the Agreement,
     nor shall the Custodian have any liability for the acts or omissions of the
     Bank, for its appointment, or for its receiving, holding, or disbursing any
     assets; and (2) without limiting the generality of the foregoing, the Fund
     shall indemnify and hold harmless the Custodian from and against any loss,
     liability, claim, expense or demand incurred by the Custodian relating to
     or arising out of the Agreement or the appointment or actions or omissions
     of the Bank. The provisions of this Section 7(b) shall survive any
     resignation of the Custodian or the terms of this Agreement."


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     IN WITNESS WHEREOF, the parties hereto have caused this Amendment No. 2 to
be executed by their respective officers, thereof to duly authorize as of the
day and year first above written.

                                        AIM INVESTMENT SECURITIES FUNDS


                                        By:  /s/ Sidney Dilgren
                                             -----------------------------------
                                        Name: Sidney Dilgren
                                        Title: Vice President & Fund Treasurer


                                        THE BANK OF NEW YORK


                                        By: /s/ Edward G. McGann
                                            ------------------------------------
                                        Name: Edward G. McGann
                                        Title: Managing Director

Attest:


-------------------------------------
(seal)


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