For most organisms, the number of described species considerably underestimates how many exist. This is itself a problem and causes secondary complications given present high rates of species extinction. Known numbers of flowering plants form the basis of biodiversity "hotspots"--places where high levels of endemism and habitat loss coincide to produce high extinction rates. How different would conservation priorities be if the catalog were complete? Approximately 15% more species of flowering plant are likely still undiscovered. They are almost certainly rare, and depending on where they live, suffer high risks of extinction from habitat loss and global climate disruption. By using a model that incorporates taxonomic effort over time, regions predicted to contain large numbers of undiscovered species are already conservation priorities. Our results leave global conservation priorities more or less intact, but suggest considerably higher levels of species imperilment than previously acknowledged.