C. P. E. Bach most likely wrote the Violoncello Concerto in B-flat major Wq. 171 as the last of the little work group in 1753 in Potsdam, at the court of King Frederick the Great. He reworked the composition for flute and harpsichord shortly thereafter.

Various sources prove that copies of the work had made it known quite extensively in the second half of the 18th century. In his new Urtext edition, Ulrich Leisinger bases hid work on two reliable manuscripts.

The concertos in A minor, B flat major and A major were first written as violoncello concertos between 1750 and 1753. They thus rank among the very first concertos for solo cello in Germany. The A minor Concerto, composed in 1750, is performed quite frequently today.