<PAGE>   1
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549


                                  Schedule 13G


                    Under the Securities Exchange Act of 1934
                               (Amendment No. 6)

                            Capital Southwest Corp.
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                                (Name of Issuer)


                                     Common
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                         (Title of Class of Securities)

                                  140501 11 0
                  ---------------------------------------------
                                 (CUSIP Number)


Check the following box if a fee is being paid with this statement. [ ] (A fee
is not required only if the filing person: (1) has a previous statement on file
reporting beneficial ownership of more than five percent of the class of
securities described in Item 1; and (2) has filed no amendment subsequent
thereto reporting beneficial ownership of five percent or less of such class.)
(See Rule 13d-7.)

*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 the
disclosures provided in a prior cover page.

The information required in 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 ("Act") 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).

                        (Continued on following pages(s))

                                Page 1 of 5 Pages



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CUSIP No. 140501 11 0                  13G                    Page   2   of   5

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1      NAME OF REPORTING PERSON
       S.S. OR I.R.S. IDENTIFICATION NO. OF ABOVE PERSON

                U.S. Trust Company of New York                     13-5459866

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2      CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*

       N/A                                                         (a) [ ]
                                                                   (b) [ ]

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3      SEC USE ONLY

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4      CITIZENSHIP OR PLACE OF ORGANIZATION

       New York
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                    5   SOLE VOTING POWER

   NUMBER OF                  - 0 -
     SHARES         -----------------------------------------------------------
  BENEFICIALLY      6    SHARED VOTING POWER
    OWNED BY
      EACH                   225,630
   REPORTING        -----------------------------------------------------------
    PERSON          7     SOLE DISPOSITIVE POWER
     WITH
                               - 0 -
                    -----------------------------------------------------------
                    8    SHARED DISPOSITIVE POWER

                               See 6
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9      AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

            See 6
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10     CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES*

            N/A

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11     PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW 9

            5.20
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12     TYPE OF REPORTING PERSON

       HC/BK         
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                        Issuer
                        Capital Southwest Corp.

Item 1 (b)              Address of Issuer's Principal Executive Office

                        12900 Preston Rd.
                        Dallas, TX 75230

Item 2 (a)              Name of Person Filing:

                        U.S. Trust Company of New York

Item 2 (b)              Address or Principal Place of Business:

                        114 West 47th Street
                        New York, NY  10036

Item 2 (c)              Citizenship:

                        NY
Item 2 (d)              Title of Class of Securities:

                        Common

Item 2 (e)              CUSIP Number:

                        140501 11 0                  

Item 3                  If this statement is filed pursuant to Rules
                        13d-1(b), or 13d-2(b), check whether the person
                        filing is a:

                        (a)      Not applicable

                        (b)(X)   United States Trust Company of New York, a
                                 bank as defined in Section 3(a)(6) of Act.

                        (c)      Not applicable

                        (d)      Not applicable

                        (e)      Not applicable

                        (f)      Not applicable

                        (g)(X)   U.S. Trust Corporation is a parent holding
                                 company, in accordance with section 240.13d-1
                                 (b)(1)(ii)(G).

                        (h)      Not applicable

<PAGE>   4
Item 4                  (a)   Amount Beneficially Owned:

                              225,630           

                        (b)   Percent of Class:

                              5.20

                        (c)   Number of shares as to which such person has:

                              (i)   sole power to vote or to direct the vote

                                    -0-

                              (ii)  shared power to vote or to direct the vote
                                    See 4(a)

                              (iii) sole power to dispose or to direct the
                                    disposition of

                                    -0-

                              (iv)  shared power to dispose or to direct the
                                    disposition of

                                    See 4(a)

Item 5                  Ownership of Five Percent or Less of a Class

                        N/A

Item 6                  Ownership of More than Five Percent on Behalf of
                        Another Person.

                        The Reporting Person acquired their Beneficial
                        Ownership, in behalf of others, via either a
                        trust/fiduciary capacity and/or a portfolio
                        management/agency relationship.

Item 7                  Identification and Classification of the Subsidiary
                        which Acquired the Security Being Reported on by the
                        Parent Holding Company.

                        See Items 1 and 12 of  Page 2 and Item 3 herein.

Item 8                  Identification and Classification of the Members of
                        the Group.

                        Not applicable

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Item 9                  Notice of Dissolution of Group.

                        Not applicable

Item 10                 Certification.  By signing below we certify that, to
                        the best of our knowledge and belief, the securities
                        referred to above were acquired in the ordinary
                        course of business and were not acquired for the
                        purpose of and do not have the effect of changing or
                        influencing the control of the issuer of such
                        securities and were not acquired in connection with
                        or as a participant in any transaction having such
                        purpose or effect.

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



Date:   February 4, 2000
        -----------------




                                          UNITED STATES TRUST COMPANY OF
                                          NEW YORK



                                          By: /s/ Joseph A. Tricarico
                                             ----------------------------------
                                             Name:  Joseph A. Tricarico
                                             Title: Vice President and
                                             Trust Counsel