The invention relates to a crimping sleeve comprising a base part and at least two deformable crimping blades for producing a crimped connection to a cable, wherein the crimping blades each comprise a first region connected to the base part, a second region, and a middle region disposed between the first and the second regions, and wherein the base part comprises a greater thickness than the middle region of the crimping blades, the first region tapers down from the base part toward the middle region at least on a first side and the second region further tapers down from the middle region, starting at least on a second side opposite the first side, said sleeve thereby being equally suitable for cables having different cross sections for producing a reliable connection between the cables and crimping sleeve. The invention further relates to a connecting element having such a crimping sleeve.