While there exist numerous nineteenth- and early twentieth-century annotated editions of repertoire such as the violin sonatas of Beethoven, the repertoire for the cello was in general edited significantly less frequently. The cello concertos by or attributed to Haydn constitute an exception, both in the number of versions and the degree of editorial intervention. Three cello concertos were associated with Haydn's name: the well-known concerto in D Hob.VIIb:2, another concerto in D Hob.VIIb:4, and a concerto in C Hob.VIIb:5. The first is now known to be a genuine work of Haydn's although this attribution was not universally accepted in the nineteenth century. The second is an unattributable eighteenth-century concerto claimed to be by Haydn and accepted as such at its publication in 1895. The third was compiled by the cellist David Popper who claimed to have based it on Haydn's sketches, providing orchestration and linking material. This article discusses aspects of the five performing editions of Hob.VIIb:2 by Bockmühl, Servais, Becker, Klengel and Whitehouse, the two editions of Hob.VIIb:4 by Grützmacher and Trowell, and Popper's concerto, considering these texts, the reception of the concertos as compositions, and the reception of individual performances. This article surveys the period of the greatest diversity of editions, a period whose later limit is determined by the eventual entry of this work into the cello canon. It will be suggested that this diversity is a consequence of non-canonicity.