SEARS MUNICIPAL TRUST INSURED LONG TERM SERIES 31, 497J, 1994-12-29

SEARS MUNICIPAL TRUST INSURED LONG TERM SERIES 31
497J, 1994-12-29

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                                             Rule 497(j)
                                             Reg. No. 33-29834
                                             Reg. No. 33-36864    
                              

Pursuant to Rule 497 (j) promulgated under the Securities Act of
1933, the Registrant, Dean Witter Select Municipal Trust, Insured
California Series 39 and Insured Long Term Series 31, hereby
certifies as follows:

1)   the form of 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.


                    DEAN WITTER SELECT MUNICIPAL TRUST,
                    INSURED CALIFORNIA SERIES 39
                    INSURED LONG TERM SERIES 31
                              
                    By:  Dean Witter Reynolds Inc.
                         (Depositor)


                         Michael D. Browne
                         Michael D. Browne
                         Authorized Signatory