The work was completed on March 15, 1784, a period when Mozart's popularity in Vienna was on the rise. The premiere took place on March 24 at a subscription concert, the second of the “Trattner Casino Concerts” hosted by Mozart, held at the casino located in Trattnerhof (a building erected by the publisher Trattner), where the Mozarts resided at the time.

As noted in a letter to his father, both No. 15 and No. 16 are “concertos that make one sweat,” but “in terms of difficulty, the B-flat major [No. 15] is superior.” This work prominently features technical brilliance, evoking scenes where the immensely popular Mozart, then a star performer, would have received thunderous applause from the audience. Another characteristic feature of this work is the effective use of wind instruments.

Cadenzas by Mozart himself are preserved for both outer movements.

I. Allegro, B-flat major, 4/4 time. Concerto-Sonata Form.

The solo piano, as anticipated by its entrance with an improvisatory introduction rather than the main theme, is dedicated to unfolding brilliant passages throughout the entire movement.

II. [Andante], E-flat major, 3/8 time. Variation Form.

It consists of a melodic theme, two variations, and a coda. While the piano sometimes takes on the theme, it often adorns the background with arpeggiated figures. This movement unfolds more through such brilliant piano ornamentation than through variations of the theme melody itself.

III. Allegro, B-flat major, 6/8 time. Rondo-Sonata Form.

This rondo finale is characterized by prominent virtuosic piano passages that proceed with a sense of urgency. It is also noteworthy for the appearance of fugal sections.