Stravinsky's Concertino for string quartet was the first of three versions of the piece. Composed in the summer of 1920 at Carantec and Garches, the work was suggested by Alfred Pochon, the leader of the Flonzaley 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. But the central section of the score is in a wholly different tempo, Andante, and is of a wholly different character than the outer sections, making the work seem to be cast more in an ABA form than in a sonata-allegro form. However, 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.
Thirty-two years later, Stravinsky himself seems to have realized the extent to which the concertante principal determined the form of the composition. In 1952, he rearranged the work for solo violin, joined occasionally by a solo cello as part of a concertante group, plus a ripieno of flute, oboe, English horn, clarinet in A, two bassoons, two trumpets in B, tenor trombone, and bass trombone. In its new form, the Concertino was premiered in Los Angeles on November 11, 1952. In the program notes for that concert, Stravinsky wrote, "My present intentions towards my earlier work have led me to re-bar it rather extensively, to clarify some of the harmony, and to punctuate and phrase it more clearly. Although the violin part remains untouched, the three other string parts are re-distributed among the ten wind and brass instruments." This form of the Concertino has proven much more popular than original string quartet version, and it is in this form that it is most often heard.