We analyzed data for 422 unmarked and 369 radiocollared desert bighorn sheep (Ovis canadensis) translocated into vacant historical habitats in 12 Arizona locations between 1979 and 1995. We evaluated factors potentially influencing predation of radiocollared desert bighorn sheep by mountain lions (Puma concolor) by determining relationships between predation rates, number released, size of releases, escape terrain, available terrain (escape terrain as a percentage of area with slopes ≥40%), habitat quality associated with release locations, and mule deer (Odocoileus hemionus) and predator abundance. We hypothesized that numbers of radiocollared animals released, quality of habitat and available terrain associated with release locations, and relative abundance of mule deer influenced predation of translocated desert bighorn sheep by mountain lions.