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I field strip the pistol, and spray the heck out of everything with brake cleaner, trying to blast dirt out of all the nooks and crannies. (Brake cleaner works as well as Gun Scrubber for less than 1/4 the price.) Scrub with an old toothbrush, maybe use a plastic pick if there's some "grunge" that's a little tougher. Wipe everything off.

I then set the main components aside while I use a bronze brush and use something like Hoppe's to scrub out the bore.

Then several patches with solvent, followed by dry patches, complete the basic cleaning.

At this point, I lube everything with an appropriate amount of Break-Free CLP, and then rub all surfaces with a clean patch treated with CLP, just to get a very thin coating on to prevent rust. (Any excess I wipe off.) Then I reassemble and work the action a few times.

Done.