Once you are sure what is causing the rise in blood sugar levels, you need to take measures to control them accordingly. You can discuss your condition with your doctor and depending on your condition, he may prescribe you one of the following options.
For the dawn event:
changing the timing or type of your diabetes medicines
increasing your morning dose of medicine
For the Somogi effect:
reducing the dose of diabetes medicines at night
Adding a Carb-Loaded Snack at Bedtime
changing your exercise program