Rózsa's experience with Jascha Heifetz was considerably less happy when he came to write the Sinfonia Concertante, Op. 29. Rozsa was first approached by his long-time friend, cellist Gregor Piatigorsky, with the notion of writing a double concerto for himself and Heifetz. Rózsa was excited by the prospect, and in the summer of 1958 he went off to his beloved Rapallo and finished the work in just three months. But when he showed the draft to the soloists back in Hollywood, Heifetz was dissatisfied; the violinist complained that the violin and cello parts were unequal, with the cello having the more featured rôle. Rózsa tried to address these concerns, making the work longer as a result and even composing an entirely new second movement. Ultimately, Heifetz did not like the new movement but agreed to perform the original one (a theme and variations) with a reduced chamber orchestra accompaniment which the composer reluctantly supplied. Heifetz and Piatigorsky even recorded this segment of the concerto, but it was the only part of it they ever played. The entire work eventually had its première in Chicago under the baton of Jean Martinon; it was deemed over-long by the critics and the frustrated composer agreed, subjecting it to numerous cuts before it reached its final published form.

The cellist gets things underway immediately in the first movement with a muscular theme that is soon echoed by the violinist. Gently rocking thirds in the clarinets herald the second theme, this time played first by the violinist. The ensuing development section subjects both themes to a thorough working-out, culminating in a double cadenza that builds to a fiery climax before subsiding and yielding to the second theme which begins the recapitulation.

The theme of the second movement is introduced by the cellist (a source of irritation for Heifetz) and then subjected to a series of five variations, some lyrical and some playful. The movement ends with a moment of exquisite calm, the mood of which is immediately dispelled by the long, rhythmically complex orchestral introduction to the last movement. The soloists enter with a vigorous Hungarian folk-dance, against which Rózsa juxtaposes a more lyrical, haunting second subject. The development includes another double cadenza (considerably shortened by Rózsa after the première) before the inexorable drive to the final Vivace, volatile and breathless.