In the coevolution of predator and prey, different and less well understood rules for threat-assessment apply to freely suspended organisms than to substrate-dwelling ones. Particularly vulnerable are small prey carried with the bulk movement of a surrounding fluid and thus deprived of sensory information within the bow waves of approaching predators. Some planktonic prey have solved this apparent problem, however. We quantified cues generated by the slow approach of larval clownfish (Amphiprion ocellaris) that triggered a calanoid copepod (Bestiolina similis) to escape before the fish could strike. To estimate water deformation around the copepod immediately preceding its jump, we represented the fish’s body as a rigid sphere in a hydrodynamic model that we parameterized with measurements of fish size, approach speed, and distance to the copepod. Copepods of various developmental stages (CII–CVI) were sensitive to water flow caused by the live predator, at deformation rates as low as 0.04 s-1. This rate is far lower than predicted from experiments that used artificial predator-mimics. Additionally, copepods localized the source, with 87% of escapes directed away (greater than or equal to 90 degrees) from the predator. Thus, copepods’ survival in life-threatening situations relied on their detection of small nonlinear signals within an environment of locally linear deformation.