Abstract: Background-reducing x-ray multilayer mirror. A multiple-layer "wavetrap" deposited over the surface of a layered, synthetic-microstructure soft x-ray mirror optimized for reflectivity at chosen wavelengths is disclosed for reducing the reflectivity of undesired, longer wavelength incident radiation incident thereon. In three separate mirror designs employing an alternating molybdenum and silicon layered, mirrored structure overlaid by two layers of a molybdenum/silicon pair anti-reflection coating, reflectivities of near normal incidence 133, 171, and 186 .ANG. wavelengths have been optimized, while that at 304 .ANG. has been minimized. The optimization process involves the choice of materials, the composition of the layer/pairs as well as the number thereof, and the distance therebetween for the mirror, and the simultaneous choice of materials, the composition of the layer/pairs, and their number and distance for the "wavetrap.