A switchable bucket tappet for a valve drive of an internal combustion engine, which has a bucket basic body with a ring-like base. A hollow-cylindrical projection protrudes from an inner edge of the base, and in the bore of the projection an inner body extends. Two coupler pistons lie opposite one another and, to achieve a full valve stroke, engage in sections with a driver surface of the bucket basic body which run in a radial hole of the inner body. A zero valve stroke is achieved when the coupler piston is displaced completely into the radial hole of the inner body, which is baseless and free of contact with a cam. The projection has a window-like aperture, with the underside acting as the driver surface for an upper side of the coupler piston during coupling. The region of the base is an approximately symmetrical and continuously thin-walled formation.