I did some google-ing, and found one interesting thing about sleep: REM sleep periods increase in duration the longer you sleep.
Every ninety minutes of night-time sleep, your body goes through a series of different stages of sleep from Stage 1 (light sleep) to Stage 4 (very deep sleep). Stage 5 sleep is REM sleep, and that’s when you experience dreams. During the first hour of sleep, you spend more time in the lighter stages of Non-REM sleep, and only about ten minutes in REM sleep. As the night wears on, your REM periods get longer and longer so that during each of the last two hours you may spend thirty or more minutes dreaming.
The main biological purpose of REM sleep appears to be related to memory. While you are dreaming, your brain is busily organizing your “memory files” for long term storage. Perhaps muscle regeneration is also mostly accomplished during REM sleep?
EDIT: Bit of an update - it turns out that Growth Hormone levels are highest during Stage III and Stage IV NREM sleep - the deep sleep that precedes REM sleep. Stage IV sleep periods are actually longer earlier in the night, a couple of hours after you fall asleep.
Not sure what that means, if anything.