We examine the major changes in the solar wind before, during, and after the Pioneer 10 and 11 encounters with the Jovian magnetosphere during 1973 and 1974, respectively. In an earlier study, Smith et al. (1978) concluded that the Jovian magnetosphere was subjected to large-scale compression during at least three or four intervals during which it appeared that the spacecraft had reentered the solar wind or magnetosheath near 50 RJ after having first entered the magnetosphere near 100 RJ. They based this suggestion on the observations of the sister spacecraft, which indicated--on the basis of a kinematic translation of corotating interaction regions (CIR's)--that these structures would be expected to arrive at Jupiter at the appropriate beginning of these three intervals. Our reexamination of this suggestion involved the numerical simulation of the multiple CIR evolutions from one spacecraft to the sister spacecraft. This approach, considered to be a major improvement, confirms the suggestion by Smith et al. (1978) that Jupiter's magnetosphere was compressed by interplanetary CIR's during three or four of these events. Our MHD simulation also suggests that Jupiter's magnetosphere reacts to solar wind rarefactions in the opposite way--by expanding. A previously unexplained pair of magnetopause crossings on the Pioneer 11 outbound pass may simply be due to a delayed reexpansion of Jupiter's magnetosphere from a compression that occurred during the inbound pass.