The fouling left by bullets and powder not only degrades accuracy, but if left for extended periods, it can also result in pitting that can destroy the barrel.
Remove powder fouling with a slot tip and patches soaked with a powder solvent. Repeat until the patches come out white. Coat the bore with an ammonia-based copper solvent and let it sit for five minutes. Run a jag tip with a copper-solvent-soaked patch through the bore. Repeat until the bluish-green stains disappear. Follow that with powder solvent to remove all traces of the copper solvent.
Fouling from moly bullets needs to be scrubbed out. To start, coat the bore with a penetrating oil (like Kroil) for five minutes. Shift to a bore brush wrapped with a cleaning patch soaked with J-B Bore Cleaning Compound, and physically scrub the bore. Repeat until the bore is bright.
Like moly, lead fouling needs to be physically removed. After removing the powder fouling with powder solvent, wrap a piece of an all-copper Chore Boy Ultimate Scrubber pad around a slightly undersized bore brush. The soft pad won’t damage the bore, and it whisks away fouling.