During prolonged temporal isolation in caves or windowless rooms, human subjects often develop complicated sleep-wake patterns. Seeking lawful structure in these patterns, we have reanalyzed the spontaneous timing of 359 sleep-wake cycles recorded from 15 internally desynchronized human subjects. The observed sleep-wake patterns obey a simple rule: The phase of the circadian temperature rhythm at bedtime determines the lengths of both prior wake (alpha) and subsequent sleep (rho). From this rule we derive an average alpha:rho relationship that depends on circadian phase. The relationship reconciles the established negative alpha:rho correlation observed in synchronized subjects with the positive alpha:rho correlation found in desynchronized subjects. Our most surprising result concerns the residual deviations of alpha and rho from their circadian phase-adjusted mean values. We report that there is no significant positive correlation between the residuals of alpha and rho, contrary to the prediction of restorative models of sleep duration. Our findings illuminate the mechanisms underlying sleep regulation and provide much-needed tests of mathematical models of the sleep-wake cycle.