Long ago I heard this story about the original Pete the Chop, but I can't remember whether it came from a band member, Bono, or an even less reliable source.
The original version of Pete the Chop (created during the bands formative years in the late 1970s and played live thru 1980) was unquestionably a very catchy tune. Realizing the potential radio-worthiness of that piece of music if properly developed, the band intended to keep in in their treasure chest (hence, "Treasure") and use it only if/when they were desperately in need of a hit.
As things turned out, they never needed it. The band was barely able to finish the War album and only completed mixing the minimum 10 songs in their last minutes in the studio (or, as Bono says they were being thrown out of the studio). Having no B-sides to use for the New Years Day single, someone asked "Whatever happened to Pete the Chop" - the old recording was found, revised, and molded into the musically strong, lyrically-absent Treasure. I think the song is as compelling in capturing Bono's passion and the band's early strengths as other, better work, and I would much enjoy hearing it live - but of course that's a pipe dream of the highest order.