Abstract: The aim of the invention is to obtain great final ballistic effectiveness of fragmentation bullets and warheads regardless of the impact speed while using as little explosive material as possible. Said aim is achieved by combining explosive shell (3) with a damming inner member (4) in connection with an accelerated outer jacket (2). This arrangement results in the best possible conversion of the explosive energy while offering great creative flexibility regarding the design. A wide range of additional possible effects is created by blast-compacting the inner damming member (4). Furthermore, the shape of the inner damming member allows the fragments to obtain a directionally controlled effect. Depending on the caliber and technical design, the amount of explosive material used can be reduced by 50 to 80 percent compared to conventional explosive bullets at comparable fragment speeds or sub-bullet speeds. The explosive material economized is available as additional effective mass.