I'd heard the same about the 15 minute limit. I've experimented with more and less and have settled on 13 minutes, which works well for me, and I'm sure it varies among everyone. If I'm really sleepy (usually from lack of sleep), even a 5 minute nap clears almost everything out the mind.

I think that the key to going right into the nap, nearly as soon as your head hits the pillow, is to have a routine of using a timer, and get up quickly as soon as the time is up. Then, you won't lie there worrying that you'll oversleep or thinking you should be doing something else more important. Your mind is given permission to fall off, knowing it will come right back with the timer beeping.

I've found it helps to cover my head with another pillow, blocking out some light and noise. The head sandwich feeling is also relaxing and may contribute to my falling right out of consciousness in 10 seconds or less.

I have not tried this, but have read about this technique: When you start your nap, hold something in your hand that will make a noise if you drop it. As your body relaxes and you start to sleep, you will eventually relax your grip enough that the object will fall to the floor and wake you up. This happens at just about the ideal wake time for a short power nap.

That's a nice trick.

During meditation retreats, I often fell asleep during the first morning sessions. My teacher said that this was ok, but gave me comparable tip if I wanted to stay awake: meditate standing, when falling asleep, your body will always wake up in moments to stay balanced.

Dali did this, but to put himself into the creative delirious state you're in right when you wake up in a daze.