I saw this cute online sleep calculater. They claim (put in any time, and you'll see it):
Sleep cycles typically last 90 minutes.
Waking up in the middle of a sleep cycle leaves you feeling tired and groggy, but waking up in between cycles lets you wake up feeling refreshed and alert!
They appear to claim that if, for example, you need to choose between sleeping 7 and a half hours (which is a multiple of 90 minutes), or sleeping 8 hours, then 7 and a half would be better for feeling awake in the morning. Is this correct? In particular, a doctor I spoke to said that more sleep is more important than not interrupting sleep cycles.