Multilayer coatings vastly improve the performance of most x-ray optical elements and allow operation at angles and wavelengths otherwise inaccessible. They have been used successfully in analytical instruments, astronomical telescopes on satellites, and in plasma diagnostic instruments, and will likely be an important component of x-ray microlithography exposure systems in the semiconductor industry. Multilayers made by conventional techniques are not as reflective as theory predicts. They do not reflect the short wavelength x-rays of interest in medicine and nondestructive testing. To solve these problems, we propose the fabrication of multilayers by using atomic layer epitaxy to produce thinner layers with smoother, more abrupt interfaces than can be made by traditional methods.