MORGAN STANLEY DEAN WITTER SEL EQ TR CO ED BE ID PO JUL 1998, 497J, 1998-07-23

MORGAN STANLEY DEAN WITTER SEL EQ TR CO ED BE ID PO JUL 1998
497J, 1998-07-23

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         (Letterhead of Dean Witter Reynolds, Inc.)










                                        Rule 497(j)
                                        Reg. No. 333-53615


Pursuant to Rule 497 (j) promulgated under the Securities
Act of 1933, the Registrant, Morgan Stanley Dean Witter
Select Equity Trust, The Competitive Edge Best Ideas
Portfolio July 1998 hereby certifies as follows:

1)   the form of the prospectus that would have been filed
under paragraph (b) of Rule 497 does not differ from that
contained in the most recent amendment to the registration
statement, and

2)   the text of the said amendment to the registration
statement has been filed electronically.

                         MORGAN STANLEY DEAN WITTER
                         SELECT EQUITY TRUST,
                         THE COMPETITIVE EDGE BEST IDEAS
                         PORTFOLIO JULY 1998
                         (Registrant)

                         By:  Dean Witter Reynolds Inc.


                              Thomas Hines/s/
                              Thomas Hines
                              Authorized Signatory


Securities and Exchange Commission
450 Fifth Street, N.W.
Washington, D.C. 20549

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