His fame increased dramatically in the early 1970s as he began to play with the band Jazz Q, which was led by Martin Kratochvíl. In 1973, he recorded two albums with Jazz Q - "Pozorovatelna" (Watchtower) and "Symbiosis". The band planned to tour overseas, but due to his father's previous involvement in the political upheaval of 1968, Padrůněk was forbidden to travel to non-communist countries. He had to be replaced on tour each time the band played in the West.