I also endorse the use Brownell's bronze chamber brushes with superb results, also recommended earlier by dfariswheel. The only difference is that I use it in conjunction with Ballistol CLP. If you're not familiar with Ballistol, it was formulated as a ballistic oil, thus the name, for use as an effective cleaner, to dissolve traces of lead, copper, brass, lead, etc. It's safe to use on any gun finish, including Colt's Royal Blue, CCH, nickel, SS, polished chrome, or whatever the finish. It was formulated to protect against rust, and doesn't gum up and harden. Eliminates the need to aggressively scrape or brush the bore. Spray into the barrel and chamber, rotate the gun around so the liquid reaches all parts and let set for 20-30 minutes, allowing it to break down any build up. Now use the bronze brush to remove the residue, followed by some dry clean patches.
Also, there's no need to remove your grips to clean, because Ballistol lubricates, protects and restores exotic wood, ivory, stag, bone, etc. I don't like removing grips unless being fitted for some customs. Also good to help restore, lubricate and protect your leather goods. Go to ballistol.com for more info and to purchase.
Thoroughly wipe down and remove any access oil on the guns exterior surface with clean micro fibre cloths, preparing the gun for a few final application of Renaissance Wax. This wax was formulated by the British Museum over 50 years ago to restore and protect priceless antiques, firearms, paintings and other rare collectibles. It is acid neutral, water and alcohol resistant. Used to revitalize and guard against humidity, heat, dust, aging and normal wear. I prefer using my fingers to apply the Ren Wax on the metal and any grip materials, and again recommend using a clean micro fibre rag as a buffing cloth. It's available for purchase on line from Restorer Supplies at restorersupplies.com.
I'd imagine this will give you a little something more to think about.
The Shadow