could i ask if you are using pens ( MDI ) or a pump ? i used to have dawn phenomenon when i was on MDI ( multiple daily injections) but after switching to a pump i was able to tailor my basal rates and avoid this.
If you are doing MDI some things you can try ( with help from your care team ) would be to ask about splitting your basal insulin dose....levemir is the most suited to this due to its profile. This could help to smooth out the dawn phenomenon some.
also one of the things i used to do was to take a fast acting correction dose the moment i woke up and tested / scanned. this does not eliminate the DP but does help to bring you back to range quicker