The key results of an extensive series of numerical simulations of the evolution of comet orbits due to the gravitational perturbations of the giant planets are presented. The results show that the inclination distribution of comets with large perihelion that evolve to observable comets is approximately preserved. Thus, the short-period (SP) comets, which are mostly in prograde, low-inclination orbits, cannot arise from gravitational scattering of any spherical population of comets. However, the distribution of orbital elements of SP comets arising from a population of low-inclination Neptune-crossing comets is in excellent agreement with observations. It is concluded that the SP comets arise from a cometary belt in the outer solar system. 25 references.