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A high-altitude communications reflector can be supported by radiation pressure beamed at it from below. Potential applications of such a communications device are reviewed. The supporting radiation can balance the weight of the mirror as well as inertial effects, including mirror drift toward the equator. Approximately polarized supporting radiation can rotate the mirror. The reflected signal may serve to monitor mirror orientation. Questions of stability are investigated when the mirror is made of fibers that can support only tension (not compression, shear, or bending.) If the supporting radiation beam is appropriately configured, the mirror can be stabilized with respect to vertical and horizontal displacements, libration, and distortion.