In the late 1980s there were two campaigns to save African elephants. One banned international trade in ivory. The other established common property rights to elephants for local communities. Has either campaign saved the elephants? To answer this question, we constructed and solved two models, a biomass model and an age structured model. We conclude that in countries which successfully establish property rights, local communities will conserve elephants. In countries with poor property rights or open access, poachers will exterminate the elephants. The world cannot save the elephants by banning trade. Instead, African countries must save them by establishing property rights.