Big brains are hypothesized to enhance survival of animals by facilitating flexible cognitive responses that buffer individuals against environmental stresses. Although this theory receives partial support from the finding that brain size limits the capacity of animals to behaviourally respond to environmental challenges, the hypothesis that large brains are associated with reduced mortality has never been empirically tested. Using extensive information on avian adult mortality from natural populations, we show here that species with larger brains, relative to their body size, experience lower mortality than species with smaller brains, supporting the general importance of the cognitive buffer hypothesis in the evolution of large brains.