Abstract: The cover piece for a suction box of a dewatering unit for a fleece made of a pulp material conveyed over the suction box on an endless conveyor belt is provided with at least one zigzag or wavelike passage extending substantially transversely to the conveyor belt travel direction composed of a plurality of passage portions inclined to the travel direction of the conveyor belt and distributed on both sides of the medium plane of the cover piece. Advantageously the distance across the passage in the travel direction of the conveyor belt is maintained constant so that the open surface area per unit length across the passage is substantially constant, although the width across the passage may differ for portions of the passage which widen in the conveyor belt travel direction and portions which constrict in the conveyor belt travel direction.