Alternate configurations for a two-channel three-mirror glancing incidence a:-ray telescope have been designed and evaluated. A Wolter-Schwarzschild type I telescope is used as a base system for one channel of operation. The second channel consists of the secondary mirror of the Wolter-Schwarzschild type I telescope used as a primary mirror and a third aspheric mirror as a secondary for the inner channel. Two alternate aspheric mirror designs for the secondary of the inner channel were produced, one corrected for spherical aberration and the other corrected for coma. A ray-tracing technique was used to calculate the rms blur circle radius on the focal plane for both channels and each configuration. © 1984 Optical Society of America.