The Jovian magnetospheric field measured by Pioneer 10 and 11 can be well modeled by a combination of current systems composing an azimuthally symmetric current disc, a dusk-dawn sheet in both the dayside and the nightside magnetosphere, and an image dipole to represent the effects of currents on the magnetopause. The inclusion of a dusk-dawn current sheet in the dayside magnetosphere allows observations obtained both inbound and outbound to be simultaneously fit by an azimuthally symmetric current disc (i.e., without the need for local time dependent current densities). Similar disc current intensities are found to describe both Pioneer 10 and Pioneer 11 encounters. During the Pioneer 10 inbound passage the magnetopause was rapidly pushed inside the spacecraft position by a solar wind compression event. The changes that occurred in the magnetosphere field at this time can be described by relatively simple changes in our model parameters. When the field lines of our model are extended beyond the region of fitting, both the Pioneer 10 and the Pioneer 11 encounters give similar profiles with magnetopause distances that are consistent with the actual encounters. The most striking feature of the models is that they suggest that the Jovian cusp is at much lower latitudes than is the case with the earth's magnetosphere.