Questor--If you want your brass clean and shiny both on the outside and the inside try using an ultrasonic cleaner. Here's a link to a very informative article about using an ultrasonic cleaner to clean your brass.
http://www.6mmbr.com/ultrasonic.htmlI use the "Clean and Shiny" method to clean my brass. I am very pleased with the results. Here are a couple photos of my setup and some of the brass I cleaned two winters ago. I FL resized 635 once-fired .17 Remington casings, cleaned them, and then used my K&M neck turner to turn the necks on them for my .1945" necked super match grade stainless steel Pac-Nor barreled .17 Remington. It was a labor of love
Some of the finished brass. I used a hair dryer (don't tell my wife) to do the final drying after shaking most of the water out of them and rolling them around on the towels. The hair dryer was used to blow warm air into the casings from both ends.