Tom makes a great bore cleaner, sold under his TM label.
It's great on carbon build up as well as copper fouling. There are a lotta products that will remove copper, not as many effective against carbon.
My guns are Dyna Bore Coated and don't do much copper fouling. I do see carbon and powder residue thru the Hawkeye. TM takes is out with a couple of applications and occasionally soaking. I don't use brushes, haven't since I discovered DBC.
DF
