1
                       SECURITIES AND EXCHANGE COMMISSION
                              WASHINGTON, DC 20549

                                 SCHEDULE TO/A

        TENDER OFFER STATEMENT UNDER SECTION 14(d)(1) OR 13(e)(1) OF THE
                         SECURITIES EXCHANGE ACT OF 1934
                               (AMENDMENT NO. 1)

                       United Investors Income Properties
--------------------------------------------------------------------------------
                        (Name of Subject Company (Issuer)

                        AIMCO Properties, L.P. -- Offeror
--------------------------------------------------------------------------------
            (Names of Filing Persons (Identifying Status as Offeror,
                            Issuer or Other Person))

                            Limited Partnership Units
--------------------------------------------------------------------------------
                           (Title of Class Securities)

                                      None
--------------------------------------------------------------------------------
                       (CUSIP Number of Class Securities)

                                 Patrick J. Foye
                            Executive Vice President
                   Apartment Investment And Management Company
                           Colorado Center, Tower Two
                   2000 South Colorado Boulevard, Suite 2-1000
                             Denver, Colorado 80222
                                 (303) 757-8081
--------------------------------------------------------------------------------
           (Name, address, and telephone numbers of person authorized
       to receive notices and communications on behalf of filing persons)

                                    Copy To:

                                Gregory M. Chait
                               Katherine M. Koops
                     Powell, Goldstein, Frazer & Murphy LLP
                   191 Peachtree Street, N.E., Sixteenth Floor
                             Atlanta, Georgia 30303
                                 (404) 572-6600

                            Calculation of Filing Fee

<Table>
<Caption>
-------------------------------------------------------------------------------
Transaction valuation                    Amount of filing fee
-------------------------------------------------------------------------------
                                      
$ 4,920,025.60                           $ 985.00*
-------------------------------------------------------------------------------
</Table>

*    Previously paid.

[ ]  Check the box if any part of the fee is offset as provided by Rule
     0-11(a)(2) and identify the filing with which the offsetting fee was
     previously paid. Identify the previous filing by registration statement
     number, or the Form or Schedule and the date of its filing.

Amount Previously Paid:   $                  Filing Party:

Form or Registration No.:                    Date Filed:


[ ] Check the box if the filing relates solely to preliminary communications
made before the commencement of a tender offer.

Check the appropriate boxes below to designate any transactions to which the
statement relates:

<Table>
<Caption>
                                                         
     [X] third-party tender offer subject to Rule 14d-1     [ ]  going-private transaction subject to Rule 13e-3

     [ ] issuer tender offer subject to Rule 13e-4          [ ]  amendment to Schedule 13D under Rule 13d-2
</Table>

Check the following box if the filing is a final amendment reporting the results
of the tender offer: [ ]


   2


                             TENDER OFFER STATEMENT

      This Amended Tender Offer Statement on Schedule TO/A relates to the tender
offer by AIMCO Properties, L.P., a Delaware limited partnership, to purchase all
of the outstanding units, or such lesser number of units as are properly
tendered, of limited partnership interest of United Investors Income Properties,
a New York limited partnership (the "Partnership"), at a price of $120.40 per
unit, subject to the conditions set forth in the Offer to Purchase dated
September 4, 2001, as supplemented September 24, 2001, and in the related Letter
of Transmittal and Acknowledgment and Agreement, which, as amended and
supplemented from time to time, together constitute the tender offer. Copies of
the Offer to Purchase, Supplement, amended Letter of Transmittal and amended
Acknowledgment and Agreement are filed with this Schedule TO/A as Exhibits 1, 7,
8 and 9, respectively. In addition, because AIMCO Properties, L.P. is an
affiliate of the Partnership, this Schedule TO/A is intended to satisfy the
reporting requirements of Rule 13e-4(c)(1) of the Securities Exchange Act of
1934, as amended.

      The information in Exhibits 1-3, 5(a)-(c), 7, 8 and 9, respectively, is
incorporated in this Schedule TO/A by reference in answer to items 1 through 11
of Schedule TO.

      Neither AIMCO Properties, L.P. nor any of the people or entities listed on
Annex I to the Offer to Purchase has, during the last five years, been convicted
in a criminal proceeding (excluding traffic violations or similar misdemeanors),
or was, during the last five years, a party to any judicial or administrative
proceeding (except for matters that were dismissed without sanction or
settlement) that resulted in a judgment, decree or final order enjoining the
person from future violations of, or prohibiting activities subject to, federal
or state securities laws, or a finding of any violation of federal or state
securities laws.

Item 12. Exhibits.

          * 1     Offer to Purchase, dated September 4, 2001.

          * 2     Letter of Transmittal and related Instructions (included as
                  Annex II to the Offer to Purchase attached as Exhibit (a)(1)).

          * 3     Acknowledgement and Agreement dated September 4, 2001.

          * 4     Letter, dated September 4, 2001, from AIMCO Properties, L.P.
                  to the limited partners of the Partnership.

            5(a)  Credit Agreement (Secured Revolving Credit Facility), dated as
                  of August 16, 1999, among AIMCO Properties, L.P., Bank of
                  America, Bank Boston, N.A., and First Union National Bank.
                  (Exhibit 10.1 to AIMCO's Current Report on Form 8-K, dated
                  August 16, 1999 is incorporated herein by this reference.)

            5(b)  Amended and Restated Credit Agreement, dated as of March 15,
                  2000, among AIMCO Properties, L.P., Bank of America, Bank
                  Boston, N.A., and First Union National Bank. (Exhibit 10.20 to
                  AIMCO Properties, L.P.'s Annual Report on Form 10-K for the
                  year ended December 31, 1999 is incorporated herein by this
                  reference.)

            5(c)  First Amendment to $345,000,000 Amended and Restated Credit
                  Agreement, dated as of April 14, 2000, among AIMCO Properties,
                  L.P., Bank of America, as Administrative Agent, and U.S. Bank
                  National Association, as Lender. (Exhibit 10.4 to AIMCO's
                  Current Report on Form 10-Q for quarter ended March 31, 2000
                  is incorporated herein by this reference.)

            6     Intentionally omitted.

         ** 7     Supplement, dated September 24, 2001, to Offer to Purchase,
                  dated September 4, 2001.

         ** 8     Amended Letter of Transmittal and related Instructions.

         ** 9     Amended Acknowledgement and Agreement, dated September 24,
                  2001.

-----

*  Indicates items filed with the original Schedule TO on September 4, 2001.

** Indicates items filed herewith.

   3




                                    SIGNATURE

               After due inquiry and to the best of my knowledge and belief, I
certify that the information set forth in this statement is true, complete and
correct.

Date: September 24, 2001

                                             AIMCO PROPERTIES, L.P.

                                             By: AIMCO-GP, INC.
                                                 (General Partner)

                                             By: /s/ Patrick J. Foye
                                                 ------------------------------
                                                 Executive Vice President

   4




                                  EXHIBIT INDEX


<Table>
<Caption>
EXHIBIT
NUMBER        DESCRIPTION
-------       -----------
           
 * 1          Offer to Purchase, dated September 4, 2001.

 * 2          Letter of Transmittal and related Instructions (included as
              Annex II to the Offer to Purchase attached as Exhibit (a)(1)).

 * 3          Acknowledgement and Agreement dated September 4, 2001.

 * 4          Letter, dated September 4, 2001, from AIMCO Properties, L.P.
              to the limited partners of the Partnership.

   5(a)       Credit Agreement (Secured Revolving Credit Facility), dated as
              of August 16, 1999, among AIMCO Properties, L.P., Bank of
              America, Bank Boston, N.A., and First Union National Bank.
              (Exhibit 10.1 to AIMCO's Current Report on Form 8-K, dated
              August 16, 1999 is incorporated herein by this reference.)

   5(b)       Amended and Restated Credit Agreement, dated as of March 15,
              2000, among AIMCO Properties, L.P., Bank of America, Bank
              Boston, N.A., and First Union National Bank. (Exhibit 10.20 to
              AIMCO Properties, L.P.'s Annual Report on Form 10-K for the
              year ended December 31, 1999 is incorporated herein by this
              reference.)

   5(c)       First Amendment to $345,000,000 Amended and Restated Credit
              Agreement, dated as of April 14, 2000, among AIMCO Properties,
              L.P., Bank of America, as Administrative Agent, and U.S. Bank
              National Association, as Lender. (Exhibit 10.4 to AIMCO's
              Current Report on Form 10-Q for quarter ended March 31, 2000
              is incorporated herein by this reference.)

   6          Intentionally omitted.

** 7          Supplement, dated September 24, 2001, to Offer to Purchase,
              dated September 4, 2001.

** 8          Amended Letter of Transmittal and related Instructions.

** 9          Amended Acknowledgement and Agreement, dated September 24,
              2001.
</Table>

-----

*  Indicates items filed with the original Schedule TO on September 4, 2001.

** Indicates items filed herewith.