A study is performed to find the minimum-order model that can achieve an accuracy of 1 km in the dynamic propagation of the Saturnian satellites over a period of four years. The need for such an investigation has risen out of recent advances in the accuracy of orbit determination techniques that are to be used in the Cassini mission. Effects such as Saturn’s rings, tides on Saturn and the satellites, gravity harmonics on Saturn and the satellites, other solar system bodies, small Saturnian satellites, coupling of the satellite attitudes with translational dynamics, and general relativity are considered. A conservative assessment of the effects that must be modeled is obtained with numerical simulation using a fixed set of initial conditions for the satellites. This simple method is shown to exaggerate the impact of new modeling effects, so a second method is employed where the initial conditions are adjusted in order to minimize the perturbations of new effects. The second method suggests that, in addition to the point mass interactions of the eight major Saturnian satellites, the minimum order model includes zonal harmonics of Saturn up through eighth order, Saturn’s rings, Janus, the asphericities of Mimas and Enceladus, and the point mass effects of the Sun and Jupiter.