Not-So-Hypothetical Question

If I go to bed too early ("too early" defined relative to how early I've been getting to sleep on the surrounding days), my body interprets it as a nap instead of actual full-night's sleep. The upshot is that, instead of sleeping for, say, 10 hours (I like to sleep in), I end up sleeping for more like four. And, since I'm already going to bed "early", that means I wake up at around 3:45 in the morning.

Now, I know me, and I know that four hours is sleep is not enough to keep me functional for the entire day. But I also know I'm not going to get back to sleep anytime soon. So most of the time, I just lie there with my eyes closed and hope that it at least counts as a sort of half-sleep. But does it? Is there any somnolent value to lying in bed while conscious with one's eyes closed? Or might I just as well get up, write a blog post (again, oh-so-hypothetically), and just suffer through the day (or take a nap when I'm tired again, probably around noon)?

UPDATE: For those of you who care, the eventual resolution was falling back asleep from 9 AM until 1 PM. Efficient!