I'm an Ed's Red fan for about the past decade. I run a wet patch down, put the rifle aside for at least 24 hours, and then wipe out the crud with a couple more patches. I usually put a little Ed's Red Oil mixed with Eezox on a bore snake and run it through when I'm done.
Most of my rifles have been DBC'd. If it's really bad, I may use PB Blaster or Brake Cleaner, but an overnight soak in Ed's Red does the bulk of my cleaning.
