Cjd, Cuba actually had 3 launches. The one you described was the first. The second went about 500 meters and the third crashed off course un the ocean.
A few other rocket mail eaxperiments

Cover from the "First American Rocket Airplane" flown on Feb. 23, 1936. It was also the first rocket mail to fly across a state line. It flew from New York to New Jersey. This cover is signed by Willy Ley (the originator of the flight and a well know science author in later years) and Fred Kessler (the promoter).

This cover from Holland was launched on March 6, 1935 by Gerhard Zucker, who also signed the cover.
Gerhard Zucker began experimenting with Rocket Mail in 1933 in Germany. He launched early Rocket Mail flights in Germany, Great Britain, Italy, Switzerland, Andorra, Belgium and Holland. His launches continued until 1964.

The USPS and Defense Department ran just one test of their missile mail system; on June 8, 1959, the USS Barbaro Navy submarine, stationed near Norfolk, Va., fired an unarmed Regulus I missile holding two containers with 3,000 letters inside them. Twenty-two minutes later, the missile and its postal payload arrived safely at a U.S. Naval Station in Mayport, Fla.
Postmaster General Arthur E. Summerfield, who witnessed the event, considered missile mail the future. He remarked, "Before man reaches the moon, mail will be delivered within hours from New York to California, to Britain, to India or Australia by guided missiles."


1100 letters sent by rockets from McAllen, Texas to Reynosa, Mexico on July 2, 1936. First rocket exploded. 900 sent back from Reynosa by rockets on July 3.
Edit: Cjd and Rod, great stuff very interesting topic.