I didn't and haven't read all the replies to the original question, and maybe someone has already brought up this solution. If not, one of the best cleaning systems I have really ever seen is Stainless Steel Media. I started using this system about a year ago, utilizing Thumler's Tumbler, a teaspoon of dawn, and a 1/2 teaspoon of Lemi Shine. It cleans everything, outside, inside, primer pockets, all looking better than new factory brass.
This past spring I found a bunch of PPU 5.56 brass that had been under the ice, snow, dirt, and mud for who knows how long, and looking at it I knew that it would be the true test for the SSM to be able to clean it up. I brought it home threw it into the tumbler for about 4 hours, and here's a couple of pics to show before and after results .
I did take a couple of minutes to finally look thru some of the replies, and see now that the SSM was covered pretty thoroughly. Anyway, hope the pics might have given a better idea of the effectiveness of the system...