Try melatonin.

Melatonin for Sleep: Hormone and Supplement Effects on Sleep

From what I understand, the less you take, the better the effect. I currently take about 2.5mg. I'm still on the fence as to whether or not it works, but perhaps I haven't found the right dose.

I will say that after I take some, about 30 minutes later, I do feel a little sedated / sleepy. However, I will still wake up, from time-to-time, at 3am. Doc said to take another 2.5mg then.

YMMV.