The time it takes copepods to handle prey can vary depending on the properties of the prey, but it is still largely unknown how handling times may affect copepod feeding efficiency. We compiled data on prey-handling times derived from video observations in 10 species of calanoid and cyclopoid copepods consuming a large variety of prey. Prey-handling times vary by five orders of magnitude, and the largest fraction of this variation is explained by relative prey size: larger prey takes longer to handle. When normalized by prey volume (volume of prey handled per unit time), however, larger prey are handled more efficiently than smaller prey. Within this overarching pattern there are distinct differences among species. Thus, large species handle a certain prey size much faster than small species. However, when further normalizing by predator size, the data for all species (except Mesocyclops spp.) collapse on a common relationship. Handling times are generally not limiting maximum consumption rates, and less so for large prey. This allows room for prey selectivity, and indeed copepods are known to be highly selective feeders. Our data predict that copepods can afford to be more selective when feeding on larger than on smaller prey and when consumption is not limited by prey encounter rate, and this is consistent with observations of copepod feeding behavior. We argue that the fast handling times allow copepods to optimize their diet through prey selectivity, and that this is one key to the evolutionary success of pelagic copepods.