This Concertino was one of seven compositions Prokofiev was working on simultaneously when he died on March 5, 1953. (Putting so much musical food on his plate at one time was a lifelong trait, enabling him to produce many works, large and small, in a variety of genres.) None of the seven was completed, but this Concertino had a nearly complete first movement—lacking only some of the recapitulation and a coda—and a finished second movement, both in piano score. There were only sketches for the finale, but Prokofiev had discussed the structure and nature of its music with cellist Mstislav Rostropovich, who, with Dmitri Kabalevsky serving as orchestrator, completed the work. A further edition of the Concertino was made by cellist Steven Isserlis and pianist/composer Olli Mustonen, the latter providing a cadenza for the first movement. Both editions last about 20 minutes in performance.

The first movement, marked Andante mosso, features a noble, somewhat melancholy main theme. The intense development section sounds more militaristic in the Kabalevsky scoring, more subtle in the Isserlis version. The second movement (Andante) features a sentimental and quite memorable melody that has an almost Brahmsian quality about it. The finale (Allegretto) uses the third (rather drunken-sounding) theme from the finale of Prokofiev's Symphony-Concerto for Cello and Orchestra, Op. 125 (1950 - 1952) and is generally high-spirited and playful.

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