It depends I suppose how stable your figures are. If you 'always' have the same pattern of 0.5 mmol rise from bedtime till morning, I wouldn't worry.
I am on Levemir and NovoRapid myself. I tend to want to go to bed at around 5. I would get a little uneasy if my number was lower than that, but that is more like a built-in buffer.
I am slightly uncertain about how good low-carb livers are at doing liver-dumps. We tend to suggest lower carb will get rid of some of the excessive dawn phenomena, so if that is true, it's likely the opposite is true too...
I think unless I'd just done something crazy exercise wise or had just taken rapid acting, I would measure 4.4, grab a handful of almonds or a sausage and go to land of nod thinking that the body will convert/use stuff if needed.
I tend to trust in protein more than carbohydrate for slow drops in glucose and overnight. For rapid drops, it's a different case.
Bit of a ramble, I guess - but just my own personal experience and preference.
Low-moderate carber myself - 50-75g area most days, slightly more when I'm super-active.
-M