Some of you may know that Mickey Coleman is a highly respected gunsmith and benchrest shooter in South Carolina. Here are some interesting comments he wrote a while back on this subject:
"Copper removal by Mickey Coleman
Seldom will competitors shoot 20 rounds without cleaning. If, however, you're at war then more shots between cleaning is expected but try cleaning more often.
Here is an easy method to get rid of copper but most people get faint when they hear it. Run two wet patches through the bore then take a brush and wrap a few wisps of 0000 steel wool around the brush starting at the handle end of the brush and wrapping toward the tip. Load the brush and steel wool with J-B Bore Paste and make ten complete passes followed by two wet patches then two dry patches.
I promise you that in almost all cases the copper will be gone and it will NOT harm the bore. Lest you think that it will ask yourself how often have you cleaned case necks with steel wool and how many case necks have you ruined by doing it. Is brass harder than barrel steel? "