1 Mammalian sleep is composed of two distinct states – rapid-eye-movement (REM) and non-REM (NREM) sleep – that alternate in cycles over a sleep bout. The duration of these cycles varies extensively across mammalian species. Because the end of a sleep cycle is often followed by brief arousals to waking, a shorter sleep cycle has been proposed to function as an anti-predator strategy. Similarly, higher predation risk could explain why many species exhibit a polyphasic sleep pattern (division of sleep into several bouts per day), as having multiple sleep bouts avoids long periods of unconsciousness, potentially reducing vulnerability. 2 Using phylogenetic comparative methods, we tested these predictions in mammals, and also investigated the relationships among sleep phasing, sleep-cycle length, sleep durations and body mass. 3 Neither sleep-cycle length nor phasing of sleep was significantly associated with three different measures of predation risk, undermining the idea that they represent anti-predator adaptations. 4 Polyphasic sleep was associated with small body size, shorter sleep cycles and longer sleep durations. The correlation with size may reflect energetic constraints: small animals need to feed more frequently, preventing them from consolidating sleep into a single bout. The reduced daily sleep quotas in monophasic species suggests that the consolidation of sleep into one bout per day may deliver the benefits of sleep more efficiently and, since early mammals were small-bodied and polyphasic, a more efficient monophasic sleep pattern could be a hitherto unrecognized advantage of larger size.