A controllable packaging device (5) and a method relate to packaging compressed bales (6) on a baling press (2) with a bale-fixing element (11) and a multi-component bale envelope (7) including an upper part (8), a lower part (9) and optionally a sheath-type side part (10). The packaging device includes a fixing device (23) applying the bale-fixing element (11), a supply device (25) supplying the upper part and the lower part and optionally an envelope device (24) applying the side part to the compressed bales. The fixing device and optionally the envelope device are arranged on a transport apparatus (19) that travels along the compressed bale in an advancing direction (22). The supply device is arranged on the transport apparatus and supplies the upper part and the lower part with a supply movement oriented transversely to the advancing direction, from the outside into the baling press.