AlexK,
I probably should have noted the concept of polyphasic sleep, in case it is not known. Basically you nap 20 minutes every 4 hours, giving you a total of 22 waking hours per day. With the same clear-mindness as if you were sleeping 8+ hours. You "trick" the brain into go straight to REM sleep, which is the way for example Leonardo Da Vinci slept. But in order for this to work, you have to go though a hellish sleep deprivation period, lasting a total of about 10-12 days, where as the first week you basically feel like you haven't slept at all.
To get adjusted to the true polyphasic sleep cycle as soon as possible, the cycle has to be followed strictly. Any more sleep during the adjustment period than originally intended only prolongs the time.
Adjusting to this cycle is pure h*ll, I was finally starting to get somewhat adjusted, where the hardest part seemed to have past. Oversleeping would set me back several days, and in the worst case forcing me to go though the same hell again.
Most people trying this fail, and it is really important not to oversleep - or you will not be successful.