Auto-suggestion seems to work. Several people I know seem to be able to tell themselves I'll wake up after 'N' hours/minutes, and do so within a minute or two of that duration. I thought for a moment that it might be that the duration defined is typical to the person, but even defining a weird figure (e.g., 23 minutes), it appears to work just as well as that person's regular duration of 15 minutes. Personally it works for me sometimes (usually when I'm under pressure), other times it does not.How does the brain/body know to power-up after N minutes? 
How are people able to wake themselves up after a pre-specified amount of time?
sleep;physiology