The method involves a waste bin (1) with cover (2) or bridge piece being mounted over the opening of the bin and being secured to the bin with a quick-release bayonet-type coupling. The cover or bridge piece incorporates a nut in which a screw spindle (6) is mounted which can be screwed up or down by means of a crank (7). The spherical end of the spindle engages with a cup on a press plate (5). The volume of waste is reduced by forcing the press plate down, or the waste will be screw spindle.