I just wet tumble my 357 brass in hot water with Limi Shine and liquid soap for a couple of hours. They come out clean inside and a medium shine outside. Primer pockets come out pretty clean; not perfectly clean but acceptable. They shoot just as good as new brass.

I had some range brass once (about 100 rounds) that was badly tarnished. After tumbling as above I put them on a tight fitting dowel rod and buffed them with my electric drill and 0000 steel wool. Now that got them as shiny as brand new. Haven't needed to do that since.