Jon,
It could be one of two-either dawn phenomenon or rebound hyperglycemia due to hypo's in your sleep, if it is DP then you'll need to increase your night-time levemir to overcome this till waking levels are normal, if its RH then you may need to reduce your evening basal insulin or reduce your meal bolus dose depending on what time you eat, sometimes a small 10g snack can be helpful before bed to stop hypo's. Try setting your alarm 2-3am for a few nights and test your bg to see what's going, if your bg is rising it's DP or if it is falling then its definitely nighttime hypo's to blame.
Nigel