Sleep has been assumed to be necessary for development and to be a vital function in mammals and other animals. However, Lyamin et al. claim that in bottlenose dolphins (Tursiops truncatus) and killer whales (Orcinus orca), neonates and their mothers show almost no sleep behaviour for the first month after birth; this conclusion is based on their observation that the cetaceans keep swimming, avoid obstacles and rarely close their eyes for 24 hours a day throughout that period. Here we analyse the behaviour and eye closure of three neonate-mother pairs of bottlenose dolphins and find that, although the animals tend to open both eyes when surfacing to breathe, one or both eyes are closed during 'swim rest', an underwater sleeping behaviour that is associated with continuous activity. This observation calls into question the conclusions of Lyamin et al., who overlooked this type of sleep by analysing the animals' eye state only when they surfaced to breathe.