We find by the (polygraphic) multiple sleep latency test (MSLT) of daytime sleepiness that some normal, healthy subjects seem to be pathologically sleepy, but by equally discerning psychological tests of vigilance and sleepiness, this is not the case. They show no other symptoms of excessive daytime sleepiness, are good sleepers, and do not complain of daytime sleepiness. When they are given ad libitum sleep at night, the low MSLT scores persist; ie, when there is no underlying sleep debt. Such subjects are not unusual in the scientific literature, but unrecognised as such by many sleep researchers who maintain that they must be sleepy and "chronically sleep deprived'. We find that these "high sleepability no sleepiness' subjects can relax and "switch off' very efficiently, and if they wish, can simply go to sleep in the daytime, seemingly with little real need to sleep then.