It is generally assumed that alarm calls function in intraspecific communication, for example to warn close relatives about the presence of a predator. However, an alternative hypothesis suggests that, in some cases, signallers may also gain fitness benefits in directly communicating to the predator, for example by advertising perception and unprofitability to predators that depend on unprepared prey. In this study, we show that six monkey species in Taï forest, Ivory Coast, produce significantly more alarm calls to leopards than to chimpanzees, although both are notorious monkey predators. The conspicuously high vocalization rates to leopards had adaptive consequences for the monkeys. By following a radio-collared leopard, we found that after detection and high alarm call rates the leopard gave up its hiding location and left the group significantly faster than would be expected by chance. We discuss these data with respect to the various functional hypothesis of alarm call behaviour and conclude that the high alarm call rates to leopards are part of an anti-predator strategy in primates that may have evolved to deter predators that depend on surprise.