I posted a msg on these forums years ago (under an old name too) regarding nighttime hypos. I too get a little worried, especially as my nighttime/morning hypos end up with me sleepwalking and being completely unaware of anything that's happening.
As I inject levemir pretty much an hour before I go to bed, I've recently reduced my dose by around 4 units and I'm ok, only slightly higher than usual in the morning (around 7-8 mmol/l) but this has worked so well! It's strange though because as soon as I stop doing weights at the gym and exercising my levemir requirements shoot up over the course of around a week!