One of comedian Lenny Bruce's most hilarious routines involves the resulting culture clash when a hip bebopper saxophonist tries to join Lawrence Welk's band. This legendary Texas reed player, however, is an example of the fine jazz talent that actually has been part of the Welk outfit, all kidding aside. Not that jazz listeners will be forced to watch the Welk show in order to isolate Cuesta from the bubbles and Myron Floren accordion solos. Cuesta also recorded with the great trombonist Jack Teagarden and the brilliant pianist, composer, and bandleader Jelly Roll Morton. But perhaps one of the best documentations of Cuesta's playing is indeed linked to Welk, the 1976 album entitled Lawrence Welk Presents the Clarinet of Henry Cuesta.
Cuesta came from a large musical family, one aspect of which was the Caceres clan: clarinetist Ernie Caceres, violinist Emilio Caceres, and pianist Pinero Caceres are his cousins; saxophonist David Caceres is his nephew. Violin was Cuesta's first instrument, which he was taught by his father and began playing in chamber groups as a teenager. After switching to reeds he at first continued in the classical direction, playing in the Corpus Christi Symphony Orchestra between 1950 and 1953 before being inducted to follow Uncle Sam's baton. He came out of the Army obviously more interested in jazz, perhaps the result of concerts he had been involved with on European bases, such as a tribute to George Gershwin.
Residency in Toronto put him in contact and often on-stage with a series of solidly swinging visiting performers, including Benny Goodman and Bobby Hackett. Solid career connections ensued, including work with both Teagarden and Welk. He also performed with singers Bob Crosby, Mel Tormé, and Bobby Vinton. In 1993 he and David Caceres took part in a tribute to Emilio and Ernie Caceres presented at the Riverwalk venue in San Antonio.