In the early days of the modern US commemorative coin series, it was not necessarily the rule that a new commemorative coin had to have a private sponsor behind it to get it approved. The 1982 George Washington half dollar, for example, did not have any private sponsor and the surcharges collected from its sale were deposited in the General Fund of the Treasury for the purpose of reducing the national debt.
The same was true for the 1987 US Constitution Bicentennial silver dollar and gold half eagle ($5.00 coin). The surcharges collected via sales of the two coins were earmarked for the General Fund and national debt reduction.
In 1983, the 98th Congress established the Commission on the Bicentennial of the US Constitution. In 1986, Public Law 99-549 authorized the Commission to retain and spend the proceeds it collected from the licensing of its bicentennial logo in order to fulfill its legislated purpose "to promote and coordinate activities to commemorate the bicentennial of the Constitution." The Act authorizing the 1987 commemorative coin program for the Constitution's bicentennial references the Commission as one of the two groups to be consulted regarding the coin designs - the other was the Commission of Fine Arts. Though involved with the coin, the Commission did not receive surcharge funds from coin sales (as noted above). It did, however, raise revenue via its logo licensing and royalty contracts.
One group that the Commission sold a license to was Fleetwood of Cheyenne, Wyoming. Collectors with an interest in stamps and first day covers (FDCs) are likely aware of Fleetwood as a major producer of FDCs and other related philatelic products - these 'other' products included philatelic-numismatic covers/combinations (PNCs).
Fleetwood created a range of FDCs that used the Commission's licensed logo and each included the text "An official First Day Cover of the Commission on the Bicentennial of the US Constitution." One FDC product they created in 1987 included the 1987 Constitution silver dollar; images of the one in my collection are presented below.
In addition to an uncirculated version of the silver dollar, the cover includes the new-at-the-time 22-cent US Constitution stamp (seen in the upper right corner), along with three other historic stamps that related to the theme: the 1937 3-cent stamp marking the Constitution's sesquicentennial, a 10-cent stamp from 1956 depicting Independence Hall (site of the Constitutional Convention of 1787) and a 13-cent stamp from 1975-81 that presents Independence Hall and the 13-star flag most often attributed to Betsy Ross.
The Commission's logo can be seen on the back of the PNC along with a statement from the Deputy Staff Director of the Commission attesting to the cover's official status.
The current market price of the PNC reflects the low price of the Constitution silver dollar which is generally tied to its intrinsic/bullion value vs. being a coin that carries a strong numismatic premium. Finding one of the covers for a price in the range of $25 to $35 should not be too much of a problem.

