He then pursued his graduate studies at Moscow Conservatory under Semen Kozolupov [ru] until 1957, and master classes at Accademia Musicale Chigiana under French cellist André Navarra.

In 1956 he took over from Miloš Sádlo playing cello in the Czech Trio, in which he continued to perform concerts and record until his death 33 years later.

[1] Along with Sádlo, Večtomov was considered one of Czechoslovakia's leading classical artists,[citation needed] drawing comparisons in the international press to Russian cellist Mstislav Rostropovich, who had been his contemporary at the Moscow Conservatory.

It constitutes an experiment rooted in the tradition of the technique of music, an endeavor to discover the sources of musical expression, a renaissance of an approach which, while overtaken by the past development, has lost nothing of its aesthetic validity or of the potential to resurrect it and develop it in the modern spirit.

[citation needed] Večtomov played on two instruments, a 1712 Alessandro Gagliano and a 1754 Giovanni Battista Guadagnini.