After detecting an approaching predator, animals make a decision when to flee. Prey will initiate flight soon after detecting a predator so as to minimize attentional costs related to on-going monitoring of the whereabouts of the predator. Such costs may compete with foraging and other maintenance activities and hence be larger than the costs of immediate flight. The drivers of interspecific variation in escape strategy are poorly known. Here we investigated the morphological, life history and natural history traits that correlate with variation in avian escape strategy across a sample of 96 species of birds. Brain mass, body size, habitat structure and group size were the main predictors of escape strategy. The direction of the effect of these traits was consistent with selection for a reduction of monitoring costs. Therefore, attentional costs depend on relative brain size, which determines the ability to monitor the whereabouts of potential predators and the difficulty of this task as reflected by habitat and social complexity. Thus brain size, and the cognitive functions associated with it, constitute a general framework for explaining the effects of body size, habitat structure and sociality identified as determinants of avian escape strategy.