Quantitative comparative studies of sleep have focused exclusively on mammals. Such studies have repeatedly found strong relationships between the time spent in various sleep states and constitutive variables related to morphology, physiology, and life history. These studies influenced the development of several prominent hypotheses for the functions of sleep, but the applicability of these patterns and hypotheses to non-mammalian taxa is unclear. Here, we present the first quantitative analysis of sleep in a non-mammalian taxon (birds), focusing on the daily amount of time spent in slow-wave sleep (SWS) and rapid-eye movement (REM) sleep as determined by electrophysiological methods. We examined the relationships between constitutive and sleep variables in 23 avian species following earlier studies in mammals, but also considered an index of exposure to predators while asleep and controlled for shared evolutionary history among taxa. Overall, our results were very different from those obtained for mammals. Most remarkably, the relationships between both SWS time and REM sleep time and all constitutive variables were very weak and markedly non-significant, even though we had adequate power to detect correlations typical of the mammalian data. Only an index of exposure to predation during sleep was significantly related to sleep time, which is the only result common to both birds and mammals. Our results suggest that further insight into the function(s) of sleep across the animal kingdom may require an expansion of sleep research beyond the current mammalian paradigm.