Stravinsky's reduction of his Concertino for piano duet followed the composition of the work's original version for string quartet. Composed in the summer of 1920 at Carantec and Garches, the work was suggested by Alfred Pochon, the leader of the Flonzaley String Quartet. According to Stravinsky's Chronicles:

"M. Pochon wished to introduce a contemporary work into their almost exclusively classical repertoire, and asked me to write them an ensemble piece, in form and length of my own choosing, to appear in the programs of their numerous tours. So it was for them that I composed my Concertino, a piece in one single movement, treated in the form of a free sonata allegro with a definitely concertante part for the first violin."

Stravinsky's assertion that the Concertino is in "free sonata" form is accurate as far as it goes: the work does open with thematic material which does return more or less intact later in the work. However, the central section of the score is in a wholly different tempo, Andante, and is of an entirely different character than the outer sections, thus making the work seem more an ABA form than a sonata allegro form. Yet his claim that the work has "a definitely concertante part for the first violin" is thoroughly accurate. The central Andante section comes complete with a cadenza and the Andante's return at the end of the work features an even more extended cadenza. Indeed, throughout the work, the first violin is treated as a solo instrument for which the other three instruments essentially provide an accompaniment.

The reduction for piano duet follows the string quartet closely with a florid part for the treble and an accompanimental role for the bass. Stravinsky's composition is rarely heard in this form.

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