Velebný was its leader, composer, arranger, played as a multi-instrumentalist and taught the younger band members.

Jiří Stivín, Luděk Hulan, František Uhlíř, Rudolf Dašek, Josef Vejvoda, and Jan Konopásek were among his regular collaborators.

As a composer, Velebný concentrated solely on jazz, in compositional styles and arrangements reminiscent of Gerry Mulligan, Chick Corea, Gary Burton and Benny Golson.

As a teacher, Velebný emphasised knowledge of techniques which could be broadly applied on jazz standards.

He co-founded the Jára Cimrman Theatre, under the pseudonym dr. Evžen Hedvábný (actually, Karel Velebný has invented Jára Cimrman as a polyhistor and a Greatest Czech of all centuries), and made occasional onstage appearances - as an actor - during its early days.