Thanks for the speeding reply. I appreciate the "good" ideas.
I'll start with the vinegar solution. If that doesn't do it, then I'll try to figure out exactly what is an alkaline based detergent. When you say detergent, laundry or dish soap comes to mind.
Unfortunately my chimney sweeper was reluctant to share advice on the exterior elements of the fireplace.
Occasionally the glass door to the insert gets a carbon build-up, depending on the type and condition of the wood I burn. I've used non-fuming oven cleaner on the glass with great success, ignoring recommendations from the Easy Off people. But hey, it's quick, easy and efficient. The dirty brick, which is a flat surface below the door is the only concern and you've been more than helpful.
Again, thanks for the sound advice.
PS. We love Atlanta. Got family down there, too.