The present Concertino in E-flat major, Op. 5, was composed especially for the Leipzig trombone virtuoso Carl Traugott Queisser (1800–1846), to whom the work is also dedicated. The Concertino was first reviewed by the critic Gottfried Wilhelm Fink (1783–1846) in the Leipzig Allgemeine Musikalische Zeitung (AMZ), issue no. 38, September 1832. The critic discussed the work in detail, calling it a milestone of the trombone literature, “... its public performance should thus be determined by only true masters. The rest, however, may wish to utilize it, in silence, that is not overheard by expectant listeners, to strive with it to strengthen their powers....”

The Concertino’s premiere can be dated to 1828, with Queisser himself as soloist, and the composer conducting. Queisser repeatedly performed the Concertino up to 1843. The work was published under catalogue number 5227 in 1832 by Breitkopf & Härtel. Sometime in the 1940s the work was lost to sight and no performances known to come from then. Together with the Concertino, Op. 4, later composed by Ferdinand David, Müller’s contribution to this genre is among the most often played and most demanding of the trombone literature. The score includes, besides a preface detailing the work’s genesis and reception history, also facsimile pages to round out the edition.