Could you possibly be experiencing the "Dawn Phenomenon" or "Dawn Effect?"

See this article: http://www.mayoclinic.org/diseases-conditions/diabetes/expert-answers/dawn-effect/faq-20057937

Note that this article talks about the effect as related to those taking insulin or other medications but, if I understand it correctly, it could also happen if you aren't taking those medications. I also have high morning blood sugar. For me it tends to be higher than other times of the day, even though I haven't had anything to eat and my blood sugar was lower before bed. My doctor says that this is not unusual and that my morning blood sugar will likely be the highest reading I get all day.