Sleep in birds involves a period of eye closure interrupted by short ‘peeks’ of eye-opening. These peeks allow a bird to scan the sleeping site for predators. Peeking and eye closure were recorded for eight focal birds in flocks of 1, 2, 3 and 6 doves. Half these doves were high risk (predator presented before the sleeping bout) and half low risk (no predator). Individual vigilance fell with increasing flock size, and was higher in high-risk birds. However, corporate vigilance increased with flock size. High-risk flocks were more vigilant than low-risk flocks. These results are discussed with reference to the costs and benefits of eye closure and peeking.