My most recent experience in this area was a 74 hour straight stretch of work, where I was totally exhausted past sleep... I hurt physically and my mental performance was non existant, I literally told the staff that I had to sleep. After a few hours I was 300% better but still not up to my normal capacity, another 8-9 hours of work and I was lucky to go home.

In the college years, I used to run on 3-4 hours of sleep period. Two hours helped more than staying up, as my focus started to drive after about 30 hours straight awake...

So i am a proponent of whatever you can get, even if you feel like shit when you wake up.