I have relatively poor attention span, and have trouble maintaining good sleep patterns. What I've found is that there is a sort of "Ballmer Peak" ( http://xkcd.com/323/ ) when I'm slightly under-slept where I can focus far better than when I'm fully rested. Of course it is a narrow zone and not really sustainable.

I wonder if that is the general experience in our attention deficient generation, and if that might be a contributing factor in people preferring to cut their sleep.