I just bought an ultrasonic cleaner (Lyman) and once I mixed the brass cleaning solution to the recommended heavy duty ratio, I just heat up the solution with the built in heater. While it is warming up, I de-cap my brass with a universal de-capping die, and then place the cases in the ultrasonic cleaner and run it for 480 seconds. The brass comes out looking like it has never been fired. Primer pockets are clean, in side of the case and outside of the case are both clean. Rinse off with warm water (even better use boiling water on a stove so it evaporates more quickly), and shake out any water. Then I allow them to dry, and re-size (Hornady One-Shot case lube since it doesn't seem to require cleaning brass again), and re-prime as normal.
While it may seem slower to have to allow the cases time to dry, I almost never try to sit down and reload cartridges from dirty spent brass back to loaded rounds in the same session. So it works well for me, and the fact it cleans the primer pockets and the rest of the case so much better and so much faster than my old tumbler and primer pocket cleaner is a real bonus. In fact other than processing pistol brass (I don't really care about clean primer pockets in a .45ACP) I may never use my tumbler again.