I never use a tumbler.
I examine and polish every part (even screws and washers) individually, and after that I ziploc bag every part by assembly number.
For small metallic parts like washers, I usually use my dremmel tool with an appropriate shaped cloth or wool wheel and polishing compounds (usually brown and then blue or red).
For small plastic parts I use such polishing micro-wheels (usually foam) with meguiars or novus polishers.
Before I polish I run every part one or two times in the ultrasonic cleaner.