Trailers are described that include a chassis, a set of wheels for rollably supporting the chassis on the ground, and a rigid container carried by the chassis. The rigid container comprises a floor, a sidewall, an access door for loading/unloading materials into the container, and a convertible rigid roof. The convertible roof is movable between a closed position which permits waste or other materials to be compressed into the trailer, and an open position which permits the trailer to be loaded with bulk goods from the top. The convertible roof includes movable rigid panels, and a locking bar for holding the panels closed and connecting the opposite sidewalls of the trailer to each other against the expansion pressure exerted by loosely compressed materials transported in the trailer. The panels may be rotating panels hinged to a wall, or may be provided as sliding panels running in tracks.