By comparing results of Monte Carlo simulations of the crater population on Callisto with the observed surface, we demonstrate that the relative dearth of large craters on Ganymede and Callisto, compared with the terrestrial planets, can not be totally ascribed either to craters relaxing or to craters piercing a thin icy crust. consequently, the population of objects responsible for the heavy bombardment of the jovian system differed markedly from that responsible for the late heavy bombarment of the terrestrial planets.