Besides cleaning the bore, I'll occasionally clean the lug recesses with the Dewey tool and cotton swab for that purpose. Fouling tends to collect down in there. And clean/re-grease the bearing surfaces of the lugs.
No one mentioned a bore guide to fit in the action and keep solvent out and keep the cleaning rod centered, I always use one. Or a vise to keep the rifle from moving--if you run a tight-fitting jag and patch down the bore the rifle will move unless you have a way to hold it in place. And a good quality one-piece rod. I use Hoppe's on a plastic brush followed by a couple patches to get out the bulk of carbon, and then let the bore soak overnight with Wipeout sitting horizontally with the muzzle slightly down and the chamber plugged with a big patch. I built a simple wood rack that holds 4 rifles for that.
If there's a lot of copper in the bore, after cleaning I'll run a patch soaked with Hoppe's through and let it sit for 2-3 hours. Then run a clean patch through. If there's any copper left the clean patch will come out blue, and I'll soak it with Wipeout again. That rarely happens though.
