Many species of typically diurnal songbirds experience sleep loss during the migratory seasons owing to their nocturnal migrations. However, despite substantial loss of sleep, nocturnally migrating songbirds continue to function normally with no observable effect on their behaviour. It is unclear if and how avian migrants compensate for sleep loss. Recent behavioural evidence suggests that some species may compensate for lost night-time sleep with short, uni- and bilateral 'micro-naps' during the day. We provide electrophysiological evidence that short episodes of sleep-like daytime behaviour (approx. 12s) are accompanied by sleep-like changes in brain activity in an avian migrant. Furthermore, we present evidence that part of this physiological brain response manifests itself as unihemispheric sleep, a state during which one brain hemisphere is asleep while the other hemisphere remains essentially awake. Episodes of daytime sleep may represent a potent adaptation to the challenges of avian migration and offer a plausible explanation for the resilience to sleep loss in nocturnal migrants.