Late-night vs. early-morning writing

I have a night owl writer friend, and I have a 4-early-hours-every-day writer friend. Both claim their time zone as the most creatively stimulating. Ideas, especially poems, come to me at odd, odd times, mostly when I'm nowhere near a keyboard or pen. But 5 a.m. seems to contain a particularly vibrant quiet. Sometimes even 3 a.m. Now, the night owl and the early bird both claim 3 a.m., but if I stay up that late the clearest thought I will have is "Help!" And if I get up that early, I won't have any thoughts at all. Or at least not in words.

Do you have a regular late-night or early-morning time you specially prize for writing?
If a night owl, how late do you actually write?
If a morning writer, how long between getting up and actually beginning to work?

Just curious. And at the moment (8 p.m. my time), I'm just beginning work on a project. Neither late nor early nor really any time at all.