We present a study of the response of the geosynchronous magnetic field to abrupt enhancements of the solar wind dynamic pressure. Results are obtained separately for cases of northward and southward interplanetary magnetic field (IMF) prior to and after the solar wind pressure jump. For pressure enhancements with southward IMF we find that the response of the geosynchronous magnetic field on the dayside is mostly compression. However, on the nightside it can be a dipolarization-like change that is similar to that which occurs during substorms. We report four events showing the dipolarization-like response on the nightside. Analysis using low-latitude geomagnetic data as well as the geosynchronous energetic particle flux data leads us to argue that this dipolarization is part of the global disturbance directly driven by the solar wind pressure enhancement. We also find that the nightside magnetosphere is remarkably sensitive to small solar wind dynamic pressure enhancements when the IMF is strongly southward (i.e., Bz is below ~-10 nT). For northward IMF, solar wind pressure enhancements generally lead to magnetic compression, with a few cases of depression on the nightside, neither of which is a dipolarization-like response. The compression is strongest near noon, decreases toward dawn and dusk, and increases with the amount of increase in dynamic pressure.