I'm pretty used to not sleeping much.

The body has a way of adjusting maybe. I used to have a difficult time getting through the day because of my lack of sleep. Then my doctor prescribed sleeping pills. They don't really work most of the time so I stopped using them. They also had me drink chamomille or some kind of relaxing tea (I don't like tea but I did it anyway for a few days). Right now what works for me is to write, read, talk to people, watch DVD until the point of exhaustion and sleepiness.
I have a hard time getting sleep even when I'm in bed. Sometimes I force myself and even count sheeps out of desperation, lol. I'm also the type of person who don't want to waste time and it's exactly how I feel when I'm in bed and trying to find sleep when it doesn't come. So I usually end getting up and do other productive things.
Once I get my sleep, I also wake up easily. Little noise would wake me up and then there's the problem of going back to sleep. The advantage of this is that I find it easier to handle "night shifts" for my baby. I'm more alert than some people who are probably used to sleeping 6-8 hours a day.
During the day, I used to nap to make up for my weird night hours. In a way I just take naps daily (2x or 3x/day) spread for the 24 hours. But I have removed my napping time during the day to accommodate some family schedule going on. Even during the summer break, when I could get back to day naps, it was difficult for me to do it. So I'm stuck with night naps.