[Ambidextrous1]

Even at its best, walnut imparts a slight haze finish to the brass; I believe that's caused by very fine surface scratches. It's common practice to add a small amount of Nu Finish automotive polish to the tumbling media, and that helps; but to get a mirror-bright finish, corn cob (with Nu Finish added) is the answer.

I use a vibratory 'tumbler', and run the cases about 2 hours in walnut, followed by a similar time in corn cob.

If you use corn cob, it's available from Grainger's; specify "Grade 2040", which is a particle size small enough that it won't clog primer holes.

Don't load the tumbler too full. If the cases don't tumble, they won't get clean. the tumbler should make quite a bit of noise when the cases are tumbling vigorously.