I'm careful of the cylinder and assembly as they seem to me to be easily knocked out of whack by vigorous movement / cleaning.

I take a bronze pistol bore brush and attach it to a segment from a M16 cleaning rod, few drops of Hoppe's no. 9, push through all chambers and put aside to let the solvent work. After a bit I run a small piece of patch using the rod bore brush to work out the dirty grit and solvent, repeating maybe once. M16 brush / toothbrush the both faces of the cylinder, not worrying that it's going to retain some black. One of my J-frames has a titanium cylinder and I don't worry at all if some black remains. Last patch has a drop of clp.