Yes, the tumblers work very well.  However, I use a vibrating polisher
meant for gun shells which cost $50-100.  See  www.berrysmfg.com  or
here's the one I use:

http://www.midwayusa.com/eproductpage.exe/showproduct?saleitemid=910617

Here's my technique:

Step 1: Wash in degreaser such as Mean Green (not Simple Green).
I made a simple metal holder that fastens to the top of my vibration
polisher.  I place the screws and degreasing mixture in sealed plastic
container in holder.  15-60 minutes will clean about anything including
40-year-old bike grime.  Caution: Degreasers may remove or soften
paint.

Step 2: Rinse and dry on terry cloth.  I haven't tried blow drying with
hair dryer or compressed air.

Step 3: If very rusty, I repeat step 1 & 2 using suitable rust remover
such as Lightning Rust Remover.  Caution: Rust removers may remove or
soften paint.

Step 4: Drop into the polisher for 1-48 hours using walnut shells, not
corn cobs.  Walnut shells are available where you purchased your
polisher, and at gun shops or pet stores.  You may wish to add Novus 3
to speed the process.  Caution: This step will remove paint.

Step 5: Remove from polisher.  Compressed air and a kitchen sieve may
be used to remove dust or shell fragments lodged in threads or slots.

Works great for me on bicycle, pinball game, bowler, penny scale and
even player piano parts.

Jim Divoky, Dandridge, Tennessee