We apply a wind model, driven by combined cosmic-ray and thermal-gas pressure, to the Milky Way, and show that the observed Galactic diffuse soft X-ray emission can be better explained by a wind than by previous static gas models. We find that cosmic-ray pressure is essential to driving the observed wind. Having thus defined a "best-fit" model for a Galactic wind, we explore variations in the base parameters and show how the wind's properties vary with changes in gas pressure, cosmic-ray pressure, and density. We demonstrate the importance of cosmic rays in launching winds, and the effect cosmic rays have on wind dynamics. In addition, this model adds support to the hypothesis of Breltschwerdt and collaborators that such a wind may help to explain the relatively small gradient observed in y-ray emission as a function of galactocentric radius.