I've been using something recommended to me a while back, and it seems to work great.
It's Nu Finish auto polish/wax with a small addition of a small amount of mineral spirits. The measurements are critical - basically a couple good glops of the new finish in new tumbling media, and a capfull of mineral spirits; tumble a while to evenly distribute and then add the brass.
On average tarnish/grimy cases, it can get them looking like new in 2-3 hours.
When the mix gets 'dry' - add a little more spirits and polish and tumble to distribute.
After the media starts getting old, I add cut up t-shirt material, couple patches or so, to help gather up the grime and dust. Discard the patches when they get filthy.
What's your recipes?