I have it too, no matter how good my levels are before bed time i very often wake up high (+200 mg/dl). Generally eating low carb does seem to lower it to better or even perfect results. I even checked it a few times around 4-5 am and my BG was still in the green, hour of two later they shot up. When i sleep in during the weekends it seems to be worse though but i really can't bring myself to waking up around 6.30 in the morning during weekends. A lot seems to effect it like illness, stress, sleeping in or general bad sleeping.
As said though avoid carbs, completely, if possible a few hours before you go to bed. What helped me a bit was injecting my lantus at a later time (10 PM) which is also the last time of the day i check my BG. For me it's about half an hour or hour tops before i go to sleep.