Since the discovery of rapid eye movement (REM) sleep (Aserinsky and Kleitman, 1953), sleep has been described as a succession of cycles of non-REM (NREM) and REM sleep episodes. The hypothesis of short-term REM sleep homeostasis, which is currently the basis of most credible theories on sleep regulation, is built upon a positive correlation between the duration of a REM sleep episode and the duration of the interval until the next REM sleep episode (inter-REM interval): the duration of REM sleep would therefore predict the duration of this interval. However, the high variability of inter-REM intervals, especially in polyphasic sleep, argues against a simple oscillator model. A new "asymmetrical" hypothesis is presented here, where REM sleep episodes only determine the duration of a proportional post-REM refractory period (PRRP), during which REM sleep is forbidden and the only remaining options are isolated NREM episodes or waking. After the PRRP, all three options are available again (NREM, REM, and Wake). I will explain why I think this hypothesis also calls into question the notion of NREM-REM sleep cycles.