I use Eliminator, it's one of the best kept secrets kinda. It doesn't use ammonia so you can use it in doors. It will attack carbon but it's better suited to attack copper. Once you apply it in your barrel, let it sit for a few minutes and then scrub it will a brush. Run a jag through your barrel from the breach end or at least a tight fitting patch to remove all the crud, repeat as needed.
If you read the article you'll notice that copper and carbon can build up in layers. Using a copper solvent and a carbon cleaner together will be the best way to insure that you remove everything.