Stars typically eject a continuous supersonic flow of gas known as a stellar wind. Most stars are in multiple systems with two or more members, and their orbital motions affect the wind morphology. The Wilkin and Hausner (2017) orbiting wind model made the assumption that the wind was initially isotropic at launch. Here, we generalize this wind to a non-isotropic launch that is concentrated to the poles or equator of the star. This paper presents a self-consistent solution to this problem for the wind velocity and density structure.