Zooplankton feed on microscopic prey that they either entrain in a feeding current or encounter as they cruise through the water. They generate fluid disturbances as they feed and move, thus elevating their risk of being detected and encountered by predators. Different feeding modes generate different hydrodynamic signals to predators and different predator encounter speeds but may also differ in their efficiency; the optimal behaviour is that which maximizes the net energy gain over the predation risk. Here, we show by means of flow visualization and simple hydrodynamic and optimization models that copepods with a diversity of feeding behaviours converge on optimal, size-independent specific clearance rates that are consistent with observed clearance rates of zooplankton, irrespective of feeding mode, species and size. We also predict magnitudes and size-scaling of swimming speeds that are consistent with observations. The rationalization of the magnitude and scaling of the clearance rates of zooplankton makes it more suitable for development of models of marine ecosystems, and is particularly relevant in predicting the size structure and biomass of pelagic communities.