Organic waste is polished to remove floatable contaminants prior to being biologically treated. In one application, pressed organic waste is polished before being sent to a wet anaerobic digester, optionally to be co-digested with wastewater treatment plant sludge. The organic waste is polished by flinging globs of the organic waste against a screen (3,4) while flowing air across the flinging globs. The polishing can be performed in a device having a rotor (6) with discrete paddles (9,10) inside of a cylindrical screen (2,3,4).