Four groups off& subjects have been studied in an isolation unit on an irregular schedule of sleep and waking. Sleep periods of 6 h duration were taken at irregular times during the 9-day protocol; they were arranged such that the waking periods lasted 6, 12 or 18 h and were also in an irregular sequence. One-hour naps were taken after 6 and 12 h ofwaking if the next sleep was not due then. Just before either a nap or a full sleep, subjects assessed their sleepiness and, on rising, they assessed how well sleep had been initiated and maintained. A mathematical model was developed which enabled theeffects upon sleepiness of circadian rhythmicity, of the length of the waking period since the last full sleep (time-since-sleep), and of the subjective value of the previous full sleep or nap to be independently quantified. Results showed that there was a tendency for sleepiness to increase, in some cases quite markedly, as the irregular schedule proceeded. There were also effects upon sleepiness due to circadian changes an! the amount of time since the last full sleep. These two effects were similar in size and larger than the bene-iits to be derived from a previous nap or full sleep that had been assessed at the tide as having been a good one. We conclude that one-hour naps can play a small role in decreasing an individual's sleepiness and suggest possible means by which their subjective value might be increased.