Layered synthetic microstructure (LSM) X-ray optics is investigated as a system for coupling a conventional glancing incidence X-ray mirror to a high sensitivity X-ray detector. It is shown that, by the use of figured LSM optics, it is possible to magnify the X-ray image produced by the primary mirrors so as to maintain their high inherent spatial resolution. The results of theoretical and design analyses of several spectral slicing X-ray telescope systems that utilize LSM mirrors of hyperboloidal, spherical, ellipsoidal, and constant optical path aspheric configurations are presented. It is shown that the spherical LSM optics are the preferred configuration, yielding subarcsecond performance over the entire field. The Stanford/Marshall Space Flight Center Rocket X-ray Telescope, which will utilize normal incidence LSM optics to couple a Wolter-Schwarzschild primary mirror to high resolution detectors for solar X-ray/EUV studies, is discussed. Design diagrams are included.