The aim of the invention is to gas-tightly join a jacket to a core of a hard core jacketed bullet comprising an illuminant composition in the area of the hole of the bore in the core to accommodate the illuminant composition. Said aim is achieved by pressing the material (15) of the bottom (11) of the jacket (4), which is displaced when the hole (10) is formed, against the wall of the hole by means of a reshaping process in the area of the hole (10).