I have a two bore scopes.
I have noticed that the soaking solutions seem to be very lacking in their ability to remove carbon deposit when 40 or more shots have been fired through the barrel...soaking.
Now use those same soaking solutions with good bronze bristle brushes, you will get the carbon out. Copper is easy to get out with the soaking solutions.
Typically when I examine a barrel when a guy has been soaking only, the barrel is usually black with carbon from one end to another...patches were coming out with only a slight trace of grey and the barrel was loaded with carbon to where accuracy was effected.
