Fasting BG in the morning can be high because your liver kicked in to give you energy. This is a normal liver function, lnown as the Dawn Phenomenon, but not terribly helpful for people with diabetes ! Some drugs are supposed to lessen the effect but personally I haven't seen this. The fasting BG aka FBG is often the last number to improve, for many. I've also seen posts from people in the Paleo and Primal communities, without diabetes, who get a higher than normal FBG.
Some people tame the liver dump beast within, by eating breakfast really early or having a few spoonfuls of yogurt. Some, by having a late night snack of protein or carbs or a glass or two of wine. The basic idea, is to fool the liver, giving the body something to occupy itself with, so that it doesn't dump, because it feels that there's enough energy to get you to breakfast.
The other reason for high FBG is called The Somogyi Effect. A person who experiences this goes low overnight, and the high FBG is a rebound. A simple but sleep-disturbing way to discover this, is to stay up late a few times and monitor BG and get up very early a few times (not simultaneously) and monitor again.
That way, you find out whether you're going too low and rebounding or your liver likes to be helpful and wake you early. If you test a few times and think you're going too low, I suggest discussing this with GP.