Guggenheim Funds Distributors, LLC
                           2455 Corporate West Drive
                             Lisle, Illinois 60532


                                 April 6, 2017


Securities and Exchange Commission
100 F Street, N.E.
Washington, DC 20549


                 Re: Guggenheim Defined Portfolios, Series 1587
                        File Nos. 333-216603 & 811-03763
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Ladies/Gentlemen:

     The undersigned, Guggenheim Defined Portfolios, Series 1587 (the "Trust"),
by Guggenheim Funds Distributors, LLC, as the sponsor and depositor of the Trust
and of the units covered by the subject Registration Statement, pursuant to the
provisions of Rule 461 of the General Rules and Regulations of the Securities
and Exchange Commission (the "Commission") under the Securities Act of 1933,
hereby respectfully requests that the Commission consent to the filing of the
amendment to the Registration Statement and grant acceleration of the
effectiveness of said Registration Statement, as amended, so that the same may
become effective by 1 p.m. Eastern time on April 12, 2017, or as soon thereafter
as possible.

                                                               Very truly yours,

                                      Guggenheim Defined Portfolios, Series 1587

                                          By: Guggenheim Funds Distributors, LLC


                                                                 By: /s/ Amy Lee
                                                                 ---------------
                                                                         Amy Lee
                                                    Vice President and Secretary