You mean does anyone else have Darn Phenomenon? Just about everybody I know. The way I understand it is that everyones liver works overtime in the early hours of the morning clearing the insulin in your blood, so many people find that their basal insulin demands are increased early in the morning. Then when you wake up, you will naturally release blood sugar from your liver to help you wake. All this adds up to give you your highly coveted spikes.
It says in your profile, you are on a pump, but I presume that is outdated. If you were on a pump, the answer is easy, just program an increased basal in the early morning hours. With an injected basal you have fewer options. One thing you might consider is splitting your basal and take like 60% in your nightly dose, tho this works better with Levemir which has less than a 24 hour response. Another thing you could do is instead of spliting your basal, go get some NPH and use that to split/increase your overnight dose. In either case, you need to make sure that any increased overnight basal does not drive you low. You only need a bit of insulin on board to suppress the darn phenomenon. If you do go low at 1-2 am, you may find a late night protein or complex carb snack helps.
In the end, you may just find that you have to inject to suppress the DP. I know it sucks, who wants to take another injection.
Perhaps others have more insight.