SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, DC  20549

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

                                 SCHEDULE 13D
                                (RULE 13D-101)

                INFORMATION TO BE INCLUDED IN STATEMENTS FILED
               PURSUANT TO RULE 13D-1(A) AND AMENDMENTS THERETO
                        FILED PURSUANT TO RULE 13D-2(A)

                            (Amendment No.1)/1/
                                             -   

                             RENTERS CHOICE, INC.
- --------------------------------------------------------------------------------
                               (Name of Issuer)

                                 COMMON STOCK
- --------------------------------------------------------------------------------
                        (Title of Class of Securities)

                                   760114108
- --------------------------------------------------------------------------------
                                (CUSIP Number)

                            John F. Hartigan, Esq.
                          Morgan, Lewis & Bockius LLP
                            300 South Grand Avenue
                      Los Angeles, California 90071-3132
                                (213) 612-2500
- --------------------------------------------------------------------------------
                 (Name, Address and Telephone Number of Person
               Authorized to Receive Notices and Communications)

                                August 18, 1998
- --------------------------------------------------------------------------------
            (Date of Event Which Requires Filing of This Statement)

     If the filing person has previously filed a statement on Schedule 13G to
report the acquisition which is the subject of this Schedule 13D, and is filing
this schedule because of Rule 13d-1(e), 13d-1(f) or 13d-1(g), check the
following box [_].

     NOTE:  Schedules filed in paper format shall include a signed original and
five copies of the schedule, including all exhibits. See Rule 13d-7(b) for other
parties to whom copies are to be sent.

     /1/ The remainder of this cover page shall be filled out for a reporting
      -  
person's initial filing on this form with respect to the subject class of
securities, and for any subsequent amendment containing information which would
alter disclosures provided in a prior cover page.

     The information required on the remainder of this cover page shall not be
deemed to be "filed" for the purpose of Section 18 of the Securities Exchange
Act of 1934 or otherwise subject to the liabilities of that section of the Act
but shall be subject to all other provisions of the Act (however, see the
Notes).

                               Page 1 of 8 Pages

 
                                 SCHEDULE 13D
- -----------------------                                  ---------------------
  CUSIP NO. 760114108                                      PAGE 2 OF 8 PAGES
- -----------------------                                  ---------------------
 
- ------------------------------------------------------------------------------
      NAME OF REPORTING PERSON
 1    S.S. I.R.S. IDENTIFICATION NOS. OF ABOVE PERSONS (ENTITIES ONLY)
                          
              Apollo Investment Fund IV, L.P.
- ------------------------------------------------------------------------------
      CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*
 2                                                              (a) [_]
                                                                (b) [x]
- ------------------------------------------------------------------------------
      SEC USE ONLY
 3
 
- ------------------------------------------------------------------------------
      SOURCE OF FUNDS*
 4    
              OO
- ------------------------------------------------------------------------------
      CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED PURSUANT 
      TO ITEMS 2(d) or 2(e) [_]
 5    
- ------------------------------------------------------------------------------
      CITIZENSHIP OR PLACE OF ORGANIZATION
 6    
              Delaware
- ------------------------------------------------------------------------------
                          SOLE VOTING POWER
                     7     
     NUMBER OF            
                                 8,493,610 shares of Common Stock
      SHARES       -----------------------------------------------------------
                          SHARED VOTING POWER
   BENEFICIALLY      8    
                                 
     OWNED BY                    357,974 shares of Common Stock
                   -----------------------------------------------------------
       EACH               SOLE DISPOSITIVE POWER
                     9     
    REPORTING             
                                 8,493,610 shares of Common Stock
      PERSON       -----------------------------------------------------------
                          SHARED DISPOSITIVE POWER
       WITH          10   
                                 357,974 shares of Common Stock
- ------------------------------------------------------------------------------
      AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON
11    
      
              8,851,584 shares of Common Stock
- ------------------------------------------------------------------------------
      CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES CERTAIN SHARES*
12                  
      [x]
- ------------------------------------------------------------------------------
      PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)
13    
              26.9%
- ------------------------------------------------------------------------------
      TYPE OF REPORTING PERSON*
14
              PN
- ------------------------------------------------------------------------------
                     *SEE INSTRUCTIONS BEFORE FILLING OUT!
         INCLUDE BOTH SIDES OF THE COVER PAGE, RESPONSES TO ITEMS 1-7
     (INCLUDING EXHIBITS) OF THE SCHEDULE, AND THE SIGNATURE ATTESTATION.

                               Page 2 of 8 Pages

 
                                 SCHEDULE 13D
- -----------------------                                  ---------------------
  CUSIP NO. 760114108                                      PAGE 3 OF 8 PAGES
- -----------------------                                  ---------------------
 
- ------------------------------------------------------------------------------
      NAME OF REPORTING PERSON
 1    S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON
                          
              Apollo Overseas Partners IV, L.P.
- ------------------------------------------------------------------------------
      CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*
 2                                                              (a) [_]
                                                                (b) [x]
- ------------------------------------------------------------------------------
      SEC USE ONLY
 3
 
- ------------------------------------------------------------------------------
      SOURCE OF FUNDS*
 4    
              OO
- ------------------------------------------------------------------------------
      CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED PURSUANT 
      TO ITEMS 2(d) or 2(e) [_]
 5    
- ------------------------------------------------------------------------------
      CITIZENSHIP OR PLACE OF ORGANIZATION
 6    
              Delaware
- ------------------------------------------------------------------------------
                          SOLE VOTING POWER
                     7     
     NUMBER OF            
                                455,736 shares of Common Stock
      SHARES       -----------------------------------------------------------
                          SHARED VOTING POWER
   BENEFICIALLY      8    
                          
     OWNED BY                   357,974 shares of Common Stock
                   -----------------------------------------------------------
       EACH               SOLE DISPOSITIVE POWER
                     9     
    REPORTING             
                                455,736 shares of Common Stock
      PERSON       -----------------------------------------------------------
                          SHARED DISPOSITIVE POWER
       WITH          10   
                                357,974 shares of Common Stock
- ------------------------------------------------------------------------------
      AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON
11    
      
              813,710 shares of Common Stock
- ------------------------------------------------------------------------------
      CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES CERTAIN SHARES*
12                  
      [x]
- ------------------------------------------------------------------------------
      PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)
13    
              3.3%
- ------------------------------------------------------------------------------
      TYPE OF REPORTING PERSON*
14
              PN
- ------------------------------------------------------------------------------
                     *SEE INSTRUCTIONS BEFORE FILLING OUT!
         INCLUDE BOTH SIDES OF THE COVER PAGE, RESPONSES TO ITEMS 1-7
     (INCLUDING EXHIBITS) OF THE SCHEDULE, AND THE SIGNATURE ATTESTATION.

                              Page 3 of 8 Pages

 
                                 SCHEDULE 13D
- -----------------------                                  ---------------------
  CUSIP NO. 760114108                                      PAGE 4 OF 8 PAGES
- -----------------------                                  ---------------------
 
- ------------------------------------------------------------------------------
      NAME OF REPORTING PERSON
 1    S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON
                          
              Apollo Advisors IV, L.P.
- ------------------------------------------------------------------------------
      CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*
 2                                                              (a) [_]
                                                                (b) [x]
- ------------------------------------------------------------------------------
      SEC USE ONLY
 3
 
- ------------------------------------------------------------------------------
      SOURCE OF FUNDS*
 4    
              OO
- ------------------------------------------------------------------------------
      CHECK BOX IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED PURSUANT 
      TO ITEMS 2(d) or 2(e) [_]
 5    
- ------------------------------------------------------------------------------
      CITIZENSHIP OR PLACE OF ORGANIZATION
 6    
              Delaware
- ------------------------------------------------------------------------------
                          SOLE VOTING POWER
                     7     
     NUMBER OF            
                                8,949,346 shares of Common Stock
      SHARES       -----------------------------------------------------------
                          SHARED VOTING POWER
   BENEFICIALLY      8    
                          
     OWNED BY                   357,974 shares of Common Stock
                   -----------------------------------------------------------
       EACH               SOLE DISPOSITIVE POWER
                     9     
    REPORTING             
                                8,949,346 shares of Common Stock
      PERSON       -----------------------------------------------------------
                          SHARED DISPOSITIVE POWER
       WITH          10   
                                357,974 shares of Common Stock
- ------------------------------------------------------------------------------
      AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON
11    
      
              9,307,320 shares of Common Stock
- ------------------------------------------------------------------------------
      CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES CERTAIN SHARES*
12                  
      [x]
- ------------------------------------------------------------------------------
      PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)
13    
              27.9%
- ------------------------------------------------------------------------------
      TYPE OF REPORTING PERSON*
14
              PN
- ------------------------------------------------------------------------------
                     *SEE INSTRUCTIONS BEFORE FILLING OUT!
         INCLUDE BOTH SIDES OF THE COVER PAGE, RESPONSES TO ITEMS 1-7
     (INCLUDING EXHIBITS) OF THE SCHEDULE, AND THE SIGNATURE ATTESTATION.

                               Page 4 of 8 Pages

 
                       STATEMENT PURSUANT TO RULE 13d-1

                                    OF THE

                         GENERAL RULES AND REGULATIONS

                                   UNDER THE

                  SECURITIES EXCHANGE ACT OR 1934, AS AMENDED

================================================================================


     This Amendment No. 1 amends and supplements the following Items of the
Schedule 13D (the "Schedule 13D") of Apollo Investment Fund IV, L.P., Apollo
Overseas Partners IV, L.P. and Apollo Advisors IV, L.P. (the "Reporting
Persons") originally filed on August 17, 1998 with the Securities and Exchange
Commission with respect to the shares of Common Stock, par value $.01 per share,
of Renters Choice, Inc. ("Renters Choice" or the "Issuer"). Unless otherwise
indicated, all capitalized terms used but not defined herein have the meanings
set forth in the Schedule 13D.

     Responses to each item below are incorporated by reference into each other
item, as applicable.

Item 5.  Interest in Securities of the Issuer.
- -------  ------------------------------------ 

     Item 5 is hereby amended and restated in its entirety to read as follows:

     (a)  The Reporting Persons beneficially own 134,414 shares of Series A
Preferred Stock and 115,586 shares of Series B Preferred Stock. Each share of
Series A Preferred Stock is convertible into approximately 35.797 shares of
Common Stock as described in Item 4, or an aggregate of 4,811,670 shares of
Common Stock. Assuming approval of the Series A-to-B Conversion on or prior to
December 3, 1998, each share of Series B Preferred Stock would be automatically
converted into approximately 35.797 shares of Common Stock, or an aggregate of
4,137,676 shares of Common Stock. Assuming the conversion of all of the shares
of Preferred Stock as of the date hereof, the Reporting Persons would own in the
aggregate 8,949,346 shares of Common Stock of the Issuer, representing
approximately 26.3% of the outstanding Common Stock of the Issuer. The number of
shares of Common Stock into which shares of Series B Preferred Stock are
convertible may be increased upon the occurrence of certain events as described
in Item 4. Beneficial ownership of such shares of Series A Preferred Stock and
Series B Preferred Stock was acquired as described in Item 3 and Item 4.

     Pursuant to an Agreement entered into among AIFIV, Overseas IV, RC
Acquisition Corp. and the Issuer (described in Item 6 below), the Reporting
Persons may be deemed to have shared voting and/or dispositive power with
respect to an additional 5,377 shares of Series A Preferred Stock, which are
convertible into approximately 192,483 shares of Common Stock, and an additional
4,623 shares of Series B Preferred Stock, which are convertible into
approximately 165,491 shares of Common Stock, or 357,974 shares of Common Stock
in the aggregate.

                              Pages 5 of 8 Pages

 
     See also the information contained on the cover pages to this Amendment to
Schedule 13D which is incorporated herein by reference.

     (b)  See the information contained on the cover pages to this Amendment to
Schedule 13D which is incorporated herein by reference.

     (c)  There have been no reportable transactions with respect to the Common
Stock of the Issuer within the last 60 days by the Reporting Persons, except as
described in the Schedule 13D.

     (d)  Not applicable.

     (e)  Not applicable.

Item 6.  Contracts, Arrangements, Understandings or Relationships With Respect
- -------  ---------------------------------------------------------------------
to the Securities of the Issuer.
- ------------------------------- 

     Item 6 is hereby amended and restated in its entirety to read as follows:

     The response to Item 3 and Item 4 are incorporated herein by reference.

     Pursuant to an Agreement dated as of August 18, 1998 (the "RC Acquisition
Agreement") among AIFIV, Overseas IV, RC Acquisition Corp., a wholly-owned
subsidiary of The Bear Stearns Companies Inc. ("RC Acquisition"), and the
Issuer, RC Acquisition has agreed not to transfer 5,377 shares of Series A
Preferred Stock and 4,623 shares of Series B Preferred Stock (collectively, the
"RC Preferred Stock") owned by it except to certain affiliated entities.
Pursuant to the RC Acquisition Agreement, RC Acquisition has granted to AIFIV
and Overseas the right to vote the RC Preferred Stock and to participate in,
consent to or ratify any corporate or stockholders' action afforded to holders
of the RC Preferred Stock. In addition, pursuant to the RC Acquisition
Agreement, if AIFIV or Overseas shall at any time convert any shares of Series A
Preferred Stock into Common Stock, Series B Preferred Stock into Series A
Preferred Stock, or Series B Preferred Stock into non-voting Common Stock, RC
Acquisition shall be required to convert a pro rata number of shares of its
Series A Preferred Stock into Common Stock, Series B Preferred Stock into Series
A Preferred Stock or Series B Preferred Stock into non-voting Common Stock, as
the case may be. The RC Acquisition Agreement also provides that, in connection
with a sale by AIFIV and Overseas of Preferred Stock to a third party, AIFIV and
Overseas shall be entitled to cause RC Acquisition to sell in such sale to such
third party upon the same terms and conditions as the sale by AIFIV and Overseas
a pro rata amount of the shares of Preferred Stock owned by RC Acquisition. The
RC Acquisition Agreement terminates upon the earliest to occur of the following
events: (i) the mutual agreement of the parties thereto; (ii) with respect to
any party, such party ceasing to own any Preferred Stock; and (iii) the eleventh
anniversary of the date of the RC Acquisition.

     Pursuant to a Letter Agreement dated July 8, 1998 among Apollo Management
IV, J. Ernest Talley and Mark E. Speese, an Amendment to Letter Agreement dated
August 5, 1998 between Apollo Management IV and Mr. Talley, and an Amendment to
Letter Agreement dated August 5, 1998 between Apollo Management IV and Mr.
Speese, Mr. Talley and Mr. Speese have agreed to vote the shares of Common Stock
owned by them in favor of the

                               Page 6 of 8 Pages

 
Series A-to-B Conversion. To the knowledge of the Reporting Persons, Mr. Talley
and Mr. Speese own 4,903,166 and 2,288,432 shares of Common Stock,
respectively.

     The foregoing descriptions do not purport to be complete and are qualified
in their entirety by reference to (i) the RC Acquisition Agreement, the full
text of which has been filed as an Exhibit to this Amendment and is incorporated
herein by reference, and (ii) the Letter Agreement, the full text of which has
been filed as Exhibit 4 to the Schedule 13D and is incorporated herein by
reference.

     The amounts reported on the cover pages and in Item 5 to this Amendment do
not include shares owned by Mr. Talley and Mr. Speese, and the Reporting Persons
disclaim beneficial ownership of all shares owned by each of them. Nothing in
this Schedule 13D shall constitute an admission that any Reporting Person
constitutes a group with RC Acquisition, Mr. Talley and/or Mr. Speese.

Item 7.  Material to be Filed as Exhibits.
- -------  ---------------------------------

     Item 7 is hereby amended by adding the following item as an Exhibit:

     Exhibit 5    Agreement dated as of August 18, 1998 among AIFIV, Overseas IV
                  and RC Acquisition Corp.

                               Page 7 of 8 Pages

 
                                   SIGNATURE

     After reasonable inquiry and to the best of their knowledge and belief, the
undersigned certify that the information set forth in this statement is true,
complete and correct.

Dated:  August __, 1998

                    APOLLO INVESTMENT FUND IV, L.P.

                    By:  Apollo Advisors IV, L.P.,
                             its General Partner
                         By: Apollo Capital Management IV, Inc.,
                                its General Partner


                         By:_________________________________
                            Name:   Michael D. Weiner
                            Title: Vice President, Apollo Capital Management IV,
                                   Inc.

                    APOLLO OVERSEAS PARTNERS IV, L.P.

                    By:  Apollo Advisors IV, L.P.,
                             its Managing General Partner
                         By: Apollo Capital Management IV, Inc.,
                                its General Partner


                         By:_________________________________
                            Name:   Michael D. Weiner
                            Title: Vice President, Apollo Capital Management IV,
                                   Inc.

                    APOLLO ADVISORS IV, L.P.

                    By:  Apollo Capital Management IV, Inc.,
                               its General Partner



                         By:_________________________________
                            Name:   Michael D. Weiner
                            Title: Vice President, Apollo Capital Management IV,
                                   Inc.

                                  Page 8 of 8


                                                                       EXHIBIT 5
 
                                   AGREEMENT

          AGREEMENT (the "Agreement"), dated as of  August 18, 1998, by and
among (i) each of Apollo Investment Fund IV, L.P., a Delaware limited
partnership, and Apollo Overseas Partners IV, L.P., an exempted limited
partnership registered in the Cayman Islands acting through its general partner
(individually and collectively with their Permitted Transferees (defined below),
"Apollo"), (ii) RC Acquisition Corp., a Delaware corporation (individually and
collectively with its Permitted Transferees, "RC Acquisition") and a wholly-
owned subsidiary of The Bear Stearns Companies Inc., (iii)  Renters Choice,
Inc., a Delaware corporation (the "Company") and (iv) each other Person (defined
below) who becomes a party to this Agreement in accordance with the terms
hereof.

                             W I T N E S S E T H:
                             - - - - - - - - - - 

          WHEREAS, this Agreement shall become effective (the "Effective Date")
on the date of, and simultaneously with, the closing under the Stock Purchase
Agreement, dated as of August 18, 1998, between the Company and RC Acquisition
(the "Stock Purchase Agreement") pursuant to which the Company will sell and RC
Acquisition will purchase 10,000 shares of Preferred Stock of the Company; and

          WHEREAS, the parties hereto desire to restrict the sale, assignment,
transfer, encumbrance or other disposition of the Preferred Stock (as defined
herein), and to provide for certain rights and obligations in respect to the
Preferred Stock as hereinafter provided.

          NOW THEREFORE, the parties hereto agree as follows:


                                   ARTICLE I

                                  DEFINITIONS

          Section 1.1   Definitions.  As used in this Agreement, the following
                        -----------                                           
terms have the following meanings:

          "Affiliate" as applied to any specified Person, shall mean any other
           ---------                                                          
Person directly or indirectly controlling or controlled by or under direct or
indirect common control with such specified Person and, in the case of a Person
who is an individual, shall include (i) members of such specified Person's
immediate family (as defined in Instruction 2 of Item 404(a) of Regulation S-K
under the Securities Act) and (ii) trusts, the trustee and all beneficiaries of
which are such specified Person or members of such Person's immediate family as
determined in accordance with the foregoing clause (i).  For the purposes of
this definition, control when used with respect to any Person means the power to
direct the management and policies of such person, directly or indirectly,
whether through the ownership of voting securities, by contract or 

 
otherwise; and the terms "affiliated," "controlling" and "controlled" have
meanings correlative to the foregoing. Notwithstanding the foregoing, Apollo and
its Affiliates shall not be deemed Affiliates of the Company for purposes of
this Agreement.

          "Apollo Included Shares" shall mean those shares of Preferred Stock
           ----------------------                                            
beneficially owned by Apollo.

          "beneficial owner" of a security shall mean any person who, directly
           ----------------                                                   
or indirectly, through any contract, arrangement, understanding, relationship,
or otherwise has (i) the power to vote, or to direct the voting of, such
security or (ii) the power to dispose, or to direct the disposition of, such
security.

          "Business Day" shall mean each day other than Saturdays, Sundays and
           ------------                                                       
days when commercial banks are authorized to be closed for business in New York,
New York.

          "Certificates of Designations" shall mean the Certificates of
           ----------------------------                                 
Designations of the Series A and B Preferred Stock in the forms attached as
exhibits to the Stock Purchase Agreement.

          "Common Stock" shall mean the Common Stock of the Company.
           ------------                                             

          "Company" shall have the meaning set forth in the preamble.
           -------                                                   

          "Effective Date" shall have the meaning set forth in the recitals.
           --------------                                                   

          "Notices" shall have the meaning set forth in Section 5.5.
           -------                                                  

          "Permitted Transferee" shall mean:
           --------------------             

               (a)  in the case of Apollo (i) any officer, director or partner
of, or Person controlling, Apollo, (ii) any other Person that is (x) an
Affiliate of the general partners, investment managers or investment advisors of
Apollo, (y) an Affiliate of Apollo or a Permitted Transferee of an Affiliate or
(z) an investment fund, investment account or investment entity whose investment
manager, investment advisor or general partner thereof is Apollo or a Permitted
Transferee of Apollo or (iii) if a Permitted Transferee of a Person set forth in
the foregoing clauses (i) and (ii) is an individual, (x) any spouse or issue of
such individual, or any trust solely for the benefit of such individual, spouse
or issue, and (y) upon such individual's death, any Person to whom Preferred
Stock is transferred in accordance with the laws of descent and/or testamentary
distribution, in each case in a bona fide distribution or other transaction not
                                ---- ----                                      
intended to avoid the provisions of this Agreement;

               (b)  in the case of RC Acquisition, (i) any Person that is solely
controlled by RC Acquisition, (ii) any partnership in which the general partner
is The Bear Stearns Companies

                                       2

 
Inc. or one of its Affiliates or (iii) any fund in which the manager is The Bear
Stearns Companies Inc. or one of its Affiliates; and

               (c) any Person who is a party to this Agreement.

          "Person" shall mean an individual or a corporation, limited liability
           ------                                                              
Company, partnership, trust, or any other entity or organization, including a
government or political subdivision or an agency or instrumentality thereof.

          "Preferred Stock" shall mean the Series A Preferred Stock and the
           ---------------                                                 
Series B Preferred Stock issued on or prior to the Effective Date, together with
any Preferred Stock issued after the Effective Date by way of a stock dividend,
distribution, exchange or conversion of the Preferred Stock.  "Preferred Stock"
shall not include any shares of Common Stock issued as a result of conversion of
Preferred Stock or otherwise.

          "RC Acquisition Included Shares" shall mean those shares of Preferred
           ------------------------------                                      
Stock beneficially owned by RC Acquisition or any its Transferees.

          "Securities Act" shall mean the Securities Act of 1933, as amended,
           --------------                                                    
and the rules and regulations thereunder.

          "Series A Preferred Stock" shall mean the Series A Preferred Stock of
           ------------------------                                            
the Company.

          "Series B Preferred Stock" shall mean the Series B Preferred Stock of
           ------------------------                                            
the Company.

          "Stock Purchase Agreement" shall have the meaning set forth in the
           ------------------------                                         
recitals.

          "Transfer" shall mean (i) when used as a noun: any direct or indirect
           --------                                                            
transfer, sale, assignment, pledge, hypothecation, encumbrance or other
disposition and (ii) when used as a verb: to directly or indirectly transfer,
sell, assign, pledge, hypothecate, encumber, or otherwise dispose of.

          "Transferee" shall mean any Person to whom Preferred Stock has been
           ----------                                                        
Transferred in compliance with the terms of this Agreement.


                                  ARTICLE II

                           RESTRICTIONS ON TRANSFERS

          Section 2.1    Transfers in Accordance with this Agreement.  Any
                         -------------------------------------------      
attempt to Transfer, or purported Transfer of, the RC Acquisition Included
Shares in violation of the terms of this Agreement shall be null and void.  The
Company will not register upon its books, and 

                                       3

 
shall instruct its transfer agent not to register on its books, any such
Transfer. A copy of this Agreement shall be filed with the Secretary of the
Company and the Company's transfer agent and kept with the records of the
Company.

           Section 2.2   Agreement to be Bound.
                         --------------------- 

     (a)   RC Acquisition shall not Transfer any RC Acquisition Included Shares
except to a Permitted Transferee.

     (b)   No Transfer to a Permitted Transferee of RC Acquisition Included
Shares as provided in the foregoing clause (a) of this Section 2.2 shall be
permitted unless (i) the certificates representing such RC Acquisition Included
Shares issued to the Transferee bear the legend provided in Section 2.3 and (ii)
the Transferee (if not already a party hereto) has executed and delivered to
each other party hereto, as a condition precedent to such Transfer, an
instrument or instruments, reasonably satisfactory to the non-transferring
parties hereto, confirming that the Transferee agrees to be bound by the terms
of this Agreement in the same manner as RC Acquisition.

           Section 2.3    Legend.  Each outstanding certificate representing
                          ------                                            
Apollo Included Shares or RC Acquisition Included Shares shall bear a legend
reading substantially as follows:

           THE SHARES REPRESENTED BY THIS CERTIFICATE ARE SUBJECT TO
RESTRICTIONS ON TRANSFER AND OBLIGATIONS, TO WHICH ANY TRANSFEREE AGREES BY HIS
ACCEPTANCE HEREOF, AS SET FORTH IN THE AGREEMENT, DATED AS OF AUGUST 18, 1998,
COPIES OF WHICH MAY BE OBTAINED FROM THE COMPANY. NO TRANSFER OF SUCH SHARES
WILL BE MADE ON THE BOOKS OF THE COMPANY UNLESS ACCOMPANIED BY EVIDENCE OF
COMPLIANCE WITH THE TERMS OF SUCH AGREEMENTS AND BY AN AGREEMENT OF THE
TRANSFEREE TO BE BOUND BY THE RESTRICTIONS SET FORTH IN SUCH AGREEMENTS.

                                  ARTICLE III

                           VOTING, CONVERSION, SALES

           Section 3.1    Powers and Rights Granted to Apollo.  During the term
                          -----------------------------------                  
of this agreement, Apollo shall be the sole possessor of the following
stockholders' rights in the RC Acquisition Included Shares:

           (a) the right to vote the RC Acquisition Included Shares in person or
               by nominee, agent, attorney-in-fact or proxy at all meetings of
               stockholders;

           (b) the right to participate in, consent to, or ratify any corporate
               or stockholders' action afforded to holders of the RC Acquisition
               Included Shares; and

                                       4

 
          (c)  without limiting the foregoing, the voting rights set forth in
               section 4 of the Certificate f Designations, Preferences and
               Relative Rights and Limitations of Series A Preferred Stock, and
               the consent rights set forth in section 5 of the Certificate of
               Designations, Preferences and Relative Rights and Limitations of
               Series B Preferred Stock.

          Section 3.2    Conversion.  If Apollo shall at any time or from time
                         ----------                                           
to time convert pursuant to the terms of the Certificates of Designations any
shares of (i) Series A Preferred Stock into Common Stock, (ii) Series B
Preferred Stock into Series A Preferred Stock, or (iii) Series B Preferred Stock
into Non-Voting Common Stock, in each such case, RC Acquisition shall also
convert a pro rata number of shares of its Series A Preferred Stock into Common
Stock, Series B Preferred Stock into Series A Preferred Stock or Series B
Preferred Stock into Non-Voting Common Stock, as the case may be.  The parties
understand that such pro rata number shall be equal to the product of (i) the
total number of shares of the series of Preferred Stock being converted by
Apollo times (ii) a fraction, the numerator of which is equal to the aggregate
number of shares of such series of Preferred Stock owned by RC Acquisition and
the denominator of which is equal to the total number of shares of such series
of Preferred Stock owned by Apollo.  Without limiting the foregoing, each party
hereto agrees that if Apollo converts all of its shares of (i) Series A
Preferred Stock into Common Stock, (ii) Series B Preferred Stock into Series A
Preferred Stock or (iii) Series B Preferred Stock into Non-Voting Common Stock,
as the case may be, then all other parties shall also convert all of their
shares of such series of Preferred Stock.  For example, if Apollo elects to
convert all of its shares of Series B Preferred Stock into Series A Preferred
Stock, then RC Acquisition shall convert all of its shares of Series B Preferred
Stock into Series A Preferred Stock. Notwithstanding the foregoing, RC
Acquisition may elect to convert the RC Acquisition Included Shares as provided
in the Certificates of Designations.

          Section 3.3    Non-Revocable; Further Assurance.  The rights granted
                         --------------------------------                     
to Apollo under Sections 3.1, 3.2 and 3.5 shall not be revocable and shall
survive (i) any Transfer by RC Acquisition of its Preferred Stock and (ii) the
conversion of the Series B Preferred Stock into Series A Preferred Stock.
Further, each party agrees to take all further acts necessary, if any, to convey
to Apollo the voting, consent and approval rights intended to be conveyed to it
under Sections 3.1 and 3.2, including, without limitation, executing a proxy or
entering into a voting trust or other agreement.

          Section 3.4    Tag-Along Rights.
                         ---------------- 

          (a)  If Apollo at any time or from time to time, enters into an
agreement to transfer, sell or otherwise dispose of, directly or indirectly (a
"Tag-Along Sale"), any shares of Apollo Included Shares to a Third Party (as
hereinafter defined), then RC Acquisition shall have the right, but not the
obligation, to participate in such Tag-Along Sale by selling up to the number of
shares of such series of Preferred Stock owned by RC Acquisition (the "RC
Acquisition Allotment") equal to the product of (i) the total number of shares
of such series of Preferred Stock proposed to be sold by Apollo in the Tag-Along
Sale times (ii) a fraction, the numerator of which is equal to the 

                                       5

 
aggregate number of shares of such series of Preferred Stock owned by RC
Acquisition immediately prior to the Tag-Along Sale and the denominator of which
is equal to the total number of shares of such series of Preferred Stock owned
by Apollo. RC Acquisition understands and agrees that it has the right to
include in a Tag-Along Sale only the particular series of Preferred Stock that
Apollo is proposing to transfer, and then only to the extent provided above.

               Any such sales by RC Acquisition shall be on the same terms and
conditions as the proposed Tag-Along Sale by Apollo; provided, however, any
indemnification required to be given by RC Acquisition shall not be joint and
several with Apollo and shall be limited to the extent of the proceeds received
by RC Acquisition in such sale.

          (b)  The foregoing notwithstanding, this Section 3.4 shall not apply
to any sale of shares of Preferred Stock distributed to the public pursuant to
an effective registration statement under the Securities Act of 1933, as amended
(the "Act").

          (c)  Apollo shall provide RC Acquisition with written notice (the
"Sale Notice") prior to such Tag-Along Sale. Such notice shall set forth: (i)
the name and address of the proposed transferee or purchaser; (ii) the number of
shares proposed to be sold or transferred; and (iii) the proposed amount and
form of consideration to be received for such shares and the terms and
conditions of payment offered by the proposed transferee or purchaser.

               RC Acquisition shall provide written notice (the "Tag-Along
Notice") to Apollo within 10 days after receiving the Sale Notice. The Tag-Along
Notice shall set forth the number of shares owned by RC Acquisition, if any,
that RC Acquisition elects to include in the Tag-Along Sale, which shall not
exceed the RC Acquisition Allotment calculated pursuant to Section 3.3(a) above.

               The Tag-Along Notice given by RC Acquisition shall constitute its
binding agreement to sell such shares on the terms and conditions applicable to
such sale.

               If the Tag-Along Notice is not received by Apollo within the 10-
day period specified above, Apollo shall have the right to sell or otherwise
transfer the Preferred Stock to the proposed purchaser or transferee without any
participation by RC Acquisition, but only on the terms and conditions stated in
the Sale Notice and only if such sale occurs not later than 90 days after the
Notice Date.

          (d)  "Third Party" means any person or entity other than a Permitted
Transferee of Apollo.

          Section 3.5    Drag-Along Rights.  In connection with a sale by Apollo
                         -----------------                                      
of its Preferred Stock to a Third Party, Apollo shall be entitled to cause RC
Acquisition to sell in such sale to such Third Party upon the same terms and
conditions as the sale by Apollo to such Third Party up to the number of shares
of such series of Preferred Stock owned by RC Acquisition equal to the 

                                       6

 
product of (i) the total number of shares of such series of Preferred Stock
proposed to be sold by Apollo in such sale to such Third Party times (ii) a
fraction, the numerator of which is equal to the aggregate number of shares of
such series of Preferred Stock owned by RC Acquisition immediately prior to such
sale by Apollo to such Third Party and the denominator of which is equal to the
total number of shares of such series of Preferred Stock owned by Apollo.
Provided, however, any indemnification required to be given by RC Acquisition in
connection with a drag-along sale shall not be joint and several with Apollo and
shall be limited to the extent of the proceeds received by RC Acquisition in
such sale. Notwithstanding the foregoing, RC Acquisition may elect to convert
the RC Acquisition Included Shares as provided in the Certificates of
Designations.


                                  ARTICLE IV

                                  TERMINATION

          Section 4.1    Termination.  Except as otherwise provided herein with
                         -----------                                           
respect to certain specific provisions, this Agreement shall terminate upon the
earlier to occur of:

                  (i)    the mutual agreement of the parties hereto,

                  (ii)   with respect to any party hereto, such party ceasing to
     own any Preferred Stock, or

                  (iii)  on the eleventh anniversary of the Effective Date.


                                   ARTICLE V

                                 MISCELLANEOUS

          Section 5.1    No Inconsistent Agreements.   RC Acquisition represents
                         --------------------------                             
and agrees that, as of the Effective Date, there is no (and from and after the
Effective Date it will not, and will cause its respective Subsidiaries and
Affiliates not to, enter into any) agreement with respect to any securities of
the Company or any of its Subsidiaries (and from and after the Effective Date RC
Acquisition shall not take, or permit any of its Subsidiaries or Affiliates to
take, any action) that is inconsistent in any material respect with the rights
granted to Apollo in this Agreement.

          Section 5.2    Successors and Assigns.  This Agreement shall be
                         ----------------------                          
binding upon and shall inure to the benefit of the parties hereto, and their
respective successors and permitted assigns; provided that neither this
                                             --------                  
Agreement nor any rights or obligations hereunder may be transferred or assigned
by Apollo or RC Acquisition except to any Person to whom it has Transferred
Preferred Stock in compliance with this Agreement and who has become bound by
this Agreement pursuant to Section 2.2 hereof.

                                       7

 
          Section 5.3    Amendments.  This Agreement may not be amended or
                         ----------                                       
modified, nor may any provision hereof be waived, other than by a written
instrument signed by the parties hereto.

          Section 5.4    Notices.  All notices, demands, requests, consents or
                         -------                                              
approvals (collectively, "Notices") required or permitted to be given hereunder
or which are given with respect to this Agreement shall be in writing and shall
be personally delivered or mailed, registered or certified, return receipt
requested, postage prepaid (or by a substantially similar method), or delivered
by a reputable overnight courier service with charges prepaid, or transmitted by
hand delivery or facsimile, addressed as set forth below, or such other address
(and with such other copy) as such party shall have specified most recently by
written notice.  Notice shall be deemed given or delivered on the date of
service or transmission if personally served or transmitted by facsimile. Notice
otherwise sent as provided herein shall be deemed given or delivered on the
third business day following the date mailed or on the next business day
following delivery of such notice to a reputable overnight courier service.

          To Apollo:

               Apollo Investment Fund IV, L.P. and/or
               Apollo Overseas Partners IV, L.P.
               c/o Apollo Management IV, L.P.
               1999 Avenue of the Stars, Suite 1900
               Los Angeles, California  90067
               Attn:  Michael D. Weiner
               Facsimile: (310)201-4166

          with a copy (which shall not constitute notice) to:

               Morgan, Lewis & Bockius LLP
               300 South Grand Avenue, Suite 2200
               Los Angeles, California  90071
               Attn:  John F. Hartigan, Esq.
               Fax:   (213)612-2554

          To RC Acquisition:

               The Bear Stearns Companies Inc.
               c/o RC Acquisition Corp.
               245 Park Avenue
               New York, New York
               Attn:  John Howard
               Fax:   (212) 272-7425

          with a copy (which shall not constitute notice) to:

                                       8

 
               Latham & Watkins
               885 3rd Avenue, Suite 1000
               New York, New York  10022
               Attn: Roger H. Kimmel
               Fax:  (212) 751-4864

          Section 5.5    Governing Law.  This Agreement shall be governed by and
                         -------------                                          
construed in accordance with the laws of the State of New York, as applied to
contracts made and performed within the State of New York, without regard to
principles of conflict of laws, except as to matters of corporate governance,
which shall be interpreted in accordance with the General Corporation Law of the
State of Delaware.   Each party hereto consents to the non-exclusive
jurisdiction of the federal and state courts within the State of New York.

          Section 5.6    Section Headings.  The section headings contained in
                         ----------------                                    
this Agreement are for reference purposes only and shall not affect the meaning
or interpretation of this Agreement.

          Section 5.7    Entire Agreement.  This Agreement constitutes the
                         ----------------                                 
entire agreement and understanding among the parties hereto with respect to the
subject matter hereof and thereof and supersedes any and all prior agreements
and understandings, written or oral, relating to the subject matter hereof.

          Section 5.8    Severability.  Any term or provision of this Agreement
                         ------------                                          
which is invalid or unenforceable in any jurisdiction shall, as to such
jurisdiction, be ineffective to the extent of such invalidity or
unenforceability without rendering invalid or unenforceable the remaining terms
and provisions of this Agreement or affecting the validity or enforceability of
any of the terms or provisions of this Agreement in any other jurisdictions, it
being intended that all rights and obligations of the parties hereunder shall be
enforceable to the fullest extent permitted by law.

          Section 5.9    Counterparts.  This Agreement may be signed in
                         ------------                                  
counterparts, each of which shall constitute an original and which together
shall constitute one and the same agreement.

                                    *  *  *

                                       9

 
     IN WITNESS WHEREOF, the parties hereto have executed this Agreement as of
the date first above written.

                              APOLLO INVESTMENT FUND IV., L.P.
                              a Delaware limited partnership

                              By:   Apollo Advisors IV, L.P.
                                    its General Partner

                                    By:  Apollo Capital Management IV, Inc.
                                         its General Partner

                                         By:    ____________________________
                                         Name:  ____________________________
                                         Title: ____________________________

                              APOLLO OVERSEAS PARTNERS IV, L.P.
                              an exempted limited partnership registered
                              in the Cayman Islands

                              By:   Apollo Advisors IV, L.P.
                                    its Managing Partner

                                    By:  Apollo Capital Management IV, Inc.
                                         its General Partner

                                         By:    ____________________________
                                         Name:  ____________________________
                                         Title: ____________________________


                              RC ACQUISITION CORP.
                              a Delaware corporation

                              By:    __________________________
                              Name:  __________________________
                              Title: __________________________


                              RENTERS CHOICE, INC.
                              a Delaware corporation

                              By:    __________________________
                              Name:  __________________________
                              Title: __________________________

                                       10