Adding to it. Try using a LEAD AWAY cloth, patches. Works great for removing lead, carbon, burn marks. Hoppes, Klean-bore makes them. The cloth is about 5 dollars. You have to be careful using it on blued firearms(using on the outside...can take the blueing off...if you rub too hard, much). For the inside of the bore you don't have to worry though. Other than that, its safe to use. Hoppes #9 is pretty good for the price. But I find...I have to clean my 500 Magnum twice with it(using the white glove test). Once after shooting and then again the next day. For it to be really clean. The ammo(range use) I use is UltraMax (pretty cheap...but accurate) and its smokey, almost on the line of blackpowder when using lead (not hardcast) bullets. I guessed their not gas checked. Their jacketed H.P. are not as bad.
For really bad bores you can try CLP, or something stronger, Hoppes, Klean-Bore makes their own kind of CLP as well. Some of these faster, all in one (clean/lube/protect) products can get pricey, though. 3,4 times the price of Hoppes #9. Depends on how you feel about cleaning firearms.
My cleaning routine: send a patch down using Hoppes #9, let sit for 5 min. Put a brush (soaked with Hoppes #9) down it. Let sit 5 to 15 min. Dry patch it. Use a lead away patch, or cloth (cut a couple of patches off the cloth). You will be surprised how much lead, carbon comes off on the patch. Send another patch with Hoppes #9 down it. Dry patch it. Do it again, the next day or so..... And yes, you have to be careful pushing the rod down the barrel. Use the muzzel guard.