Many species show behavioural responses to predators that reduce predation mortality but are assumed to be costly. We tested whether an induced behavioural response is predator-specific and whether the strength is related to the risk of being killed by a predator. We used tadpoles of the neotropical frog Phyllomedusa tarsius as prey, and larvae of an aeshnid dragonfly and belostomatid bugs as predators. Belostomatids killed twice as many tadpoles within 24 hours as aeshnids did. Tadpoles reduced activity in the presence of aeshnids by 30% but did not respond at all to the more dangerous belostomatids. Tadpoles did not show spatial avoidance of predators. We favour the explanation that tadpoles of P. tarsius did not respond to belostomatids because belostomatids are encountered too rarely for evolution to favour an induced response to belostomatids.