I like to use Hoppe's No. 9 for a good soaking ( don't use Hoppe's Bench Rest as I think it may be too caustic. It is designed to dissolve copper fouling) and then while it is still wet I use a Frontier Pad like a scrubbie. It is not as abrasive as 4-0 steel wool and I can even use it to clean case colored areas with no harm to the colors. Works fine on rust blued barrels as well as it does on Damascus.
Click on this
http://www.big45metalcleaner.com/