The Sobolev approximation for supersonic flows creates an effective opacity distribution that is nonisotropic, because the line-of-sight velocity gradient is different in different directions. To better understand the importance of this phenomenon in a simplified geometry, we consider line-driven flows in the plane-parallel zero-sound-speed limit, and solve for the wind driven by radiation with an arbitrary angular distribution. One conclusion, surprising at first glance, is that the acceleration component normal to the surface is independent of both the strength and angular profile of the driving radiation field. The flow tilt and overall mass-loss rate do depend on the character of the radiation field. Also interesting is that mass loss through a surface may be generated or enhanced by irradiation that originates above the surface.