The rim of the bowl I usually just try to use spit,a rag and a lot of rubbing.
I'll have the rag over my thumb and just concentrate on one little spot for awhile then move on.
For this one though I followed the same procedure but had to use water and a tiny, tiny, tiny, amount of dish detergent on a very well rung out rag. (didn't want anything getting into the bowl)
It takes some time but as long as the bowl hasn't been burnt all the carbon build up will come off.
Well I fired it up last night with some McClelland Virginia Woods. That is one big deep bowl. Deep. Very deep. Did I mention it was deep?
Didn't seem that way until most of my finger disappeared shoving tobacco in it.
Smoked ok but what this pipe really needs is flake tobacco folded and stuffed into just the upper half of the bowl. I think then it will be a winner.