A compression punch for a rotary press, with a punch shaft that has a punch head at its one end and means for accommodating a separate punch insert at the other end, and with fastening means for detachably fastening the punch insert on the punch shaft, wherein the punch head and the punch shaft have an axial through bore, the axial through bore accommodates a drawbar that has a tensioning head at the end turned away from the punch head, said tensioning head having at least one connection portion, the punch insert has a recess at the end facing the punch shaft which is realized to be detachably connectable with the connection portion, and that tensioning means are arranged in the axial through bore, by which the drawbar can be tensioned in the direction of the punch head.