You need to watch with dialling up your evening Levemir dose. Although it doesn't claim to have a peak, Levemir definitely does! Usually somewhere between 5-8 hours for me. Initially, I tried increasing my evening Levemir to combat DP and all that happened was I'd hypo in the wee hours and end up with a combination of a rebound high coupled with the already present effects of DP. The end result was worse than DP by itself...
There seems to be no way (personally speaking) for basal insulin to offset the effects of DP. The mechanics behind the way that basal insulin works backs that up too. Some people try to time their evening dose so that the peak occurs around the same time as DP starts to set in and have semi decent results. That may work in very mild forms of DP but isn't an option for me. The only way I can get round it is to either never lie in and bolus on waking - or wake up, bolus and go back to sleep. Both are a total pain but the only real way to work around DP whilst on MDI...
I don't know if you're using or have ever tried the Libre system, but it's really handy for monitoring your overnight BG trends. It helped me set my basal correctly and most importantly, find out that simply dialling up my evening basal dose was causing severe rebound highs. It's not cheap but can really help you work out the best doses and timings for your basal.