My cleaning looks like this:
1) Solvent sprayed/dipped/soaked nylon brush for 2 or 3 passes to push out loose carbon.
2) Copper Solvent soaked patch, let sit for 20min or more (usually cleaning action parts during this time).
3) Dry patch until it comes out dry or clean.
4) Hornady One Shot patch down the barrel
5) Dry patches until clean
6) Repeat 2-5 or 4-5 as needed.
It's amazing how quickly hand lapped custom barrels come out clean.
I'll also say, when I cleaned my first barrel with Hornady - after using almost everything else under the sun and rarely seeing any significant difference between leading products - I wasn't paying attention to how long it took, but it came clean so quickly, it caught my attention. A barrel has to be VERY nasty for me to need more than 10 passes with a rod and the above process.