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. 2)
                               (Final Amendment)

                       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>

*    For purposes of calculating fee only.
**   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: [X]


   2


                             TENDER OFFER STATEMENT

         This is the Final Amendment to the Tender Offer Statement on Schedule
TO relating to the tender offer by AIMCO Properties, L.P., a Delaware limited
partnership, to purchase outstanding units of limited partnership interest of
United Investors Income Properties, a Missouri 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, together constituted the
tender offer.

         At 5:00 p.m. Eastern time on October 2, 2001, the offer expired
pursuant to its terms. A total of 1,613 units, representing approximately 2.62%
of the outstanding units, were validly tendered and not withdrawn pursuant to
the offer. AIMCO Properties, L.P., has accepted for payment all of those units
at a price of $120.40 per unit.
   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: October 5, 2001

                                             AIMCO PROPERTIES, L.P.

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

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