The imaging effectiveness of an x-ray telescope consisting of a simple conical primary reflector and an aspheric secondary reflector is compared with a paraboloidal primary, hyperboloidal secondary of the same dimensions (Wolter type II). The rms spot size for the Wolter type II is considerably smaller being 1/28 as large as that of the cone-asphere for incident collimated light 1 min off the optical axis and 1/6 as large for incident light 12 min off the optical axis for a typical configuration. The cone-asphere spot size, on the other hand, is one half as large as that for a hyperboloidal primary, asphere secondary telescope of the same dimensions. © 1982, Optical Society of America.