His early concerts and recordings show his stature. His first recording, at age 14, was of the "Rococo Variations". In 1946 he performed in Rumania with George Enescu at the piano. In 1954 he recorded Kabalevsky's First cello Concerto, under the baton of the composer. Kabalevsky was sufficiently impressed that he dedicated his Second Cello Concerto to Shafran, who gave the premiere and made the first recording in 1965. In 1956 he made a "legendary recording" of the Shostakovich Cello Sonata, with the composer at the piano. He observed that "No matter what I asked or suggested ... Shostakovich listened to every word ... and agreed to any new details ... even those that went against his original notation in the score", highlighting not only Shostakovich's character, but Shafran's confidence in his own musical vision. In 1962 he performed the Khachaturian Cello Concerto under the direction of the composer.