The theory of electromagnetic wave propagation in a uniformly accelerated simple medium is generalized to cover the case of arbitrary initial wave direction. The wave splits into two natural modes relative to the plane of acceleration and the wave vector. The case of high frequency and weak acceleration is solved in detail; to observers at rest with respect to the medium, a drag effect due to apparent gravity is demonstrated, and to inertial observers a drag effect due to medium acceleration is demonstrated. A preferred asymptotic cone of propagation determined by (μϵ – 1)½ is found in the accelerated frame. Various drag effects are physically interpreted.