Unusually, each movement received a distinct number in the first edition of the Köchel catalogue: The concerto is scored for solo horn in D, two oboes, two bassoons, and strings.

Compared to the other three horn concertos, it is shorter in duration (two movements rather than three) and is much simpler in regard to both range and technique, perhaps in a nod to the horn player (Mozart's great friend) Joseph Leutgeb's advanced age and (presumably) reduced capabilities at the time of composition.

Mozart's autograph score contains, arranged in strategic places throughout the sketch of the Rondo, a bizarre written narrative in Italian almost certainly directed at Leutgeb:[3] For you, Mr. Donkey—Come on—quick—get on with it—like a good fellow—be brave—Are you finished yet?—for you—beast—oh what a dissonance—Oh!—Woe is me!

!—Well done, poor chap—oh, pain in the balls!—Oh God, how fast!—you make me laugh—help—take a breather—go on, go on—that's a little better—still not finished?—you awful swine!—how charming you are!—dear one!—little donkey!—ha, ha, ha—take a breath!—But do play at least one note, you prick!—Aha!

Mozart and Süssmayr would then have been working from and correcting the same Leutgeb draft, which contained the passages that their versions have in common.