In order to get the best night's sleep, sleep in multiples of your REM cycle. Circadian rhythm is what governs the duration of these cycles and is made up of systems of Nerve Centers, Hormones and Neurotransmitters.

The average person's REM cycle is 90 minutes long. If you control the duration of your sleep so that it is a multiple of this, then when you wake up it is more likely that your body and mind will be ready to wake up. Being "ready" to wake up means that your body has experienced REM sleep, which is said to categorize your thoughts and repair your mind, and also "Deep" sleep which relaxes your muscles and repairs your body.

4.5 hours, 6 hours, or 7.5 hours are all multiples of a REM cycle. Although 7.5 hours may be too much for some. I've managed to get 4.5 hours of sleep over long periods of time without feeling like I'm not getting enough sleep. I find it's generally good to leave about 30 minutes to fall asleep, that is, if you're obeying rules number 1 and 2. And each night before lying down verify that your alarm is set for the correct time -- a multiple of a sleep cycle plus 30 minutes to fall asleep.