Total sleep deprivation (TSD) of rats for 24 hours or less by continually enforced locomotion has consistently produced subsequent rebounds of slow-wave or high-amplitude EEG activity in NREM sleep, which has contributed to the widely held view that this EEG activity reflects particularly "intense" or restorative sleep. These rebounds usually have been accompanied by substantial rebounds of REM sleep. In contrast, chronic TSD (2 weeks or longer) by the disk-over-water (DOW) method has produced only huge, long-lasting rebounds of REM sleep with no rebound of high-amplitude NREM sleep. To evaluate whether the different rebounds result from different methods or from different lengths of deprivation, rats were subjected to 24-hour TSD by the DOW method. Rebounds included increases in high-amplitude and slow-wave activity; i.e., the methods produced similar rebound patterns following short-term TSD. (Chronic TSD by continually enforced locomotion would be strategically difficult and severely confounded with motor fatigue.) Rats subjected to DOW-TSD for 4 days, well before the development of severe TSD symptoms, showed primarily REM sleep rebounds. Rats subjected to 1 day of selective REM sleep deprivation, but not their closely yoked control rats, showed large, significant REM sleep rebounds, which evidently were not induced by the stress of the deprivation method per se. The combined findings prompted reexamination of published evidence relevant to "sleep intensity," including "negative rebounds," rebounds in other species, the effects of stress and fatigue, depth of sleep indicators, and extended sleep. The review points out pitfalls in the designation of any specific pattern as intense sleep.