Multilayer coatings with a small number of layers were designed and prepared to provide an increase in normal-incidence reflectance in the extreme ultraviolet compared with the reflectance of available single-layer coatings, namely, SiC, B4C, and Ir. Multilayers were designed to produce coatings with the highest possible reflectance at 91.2 and at 58.4 nm. At these wavelengths all the materials absorb radiation strongly, but still a reflectance enhancement can be obtained by means of sub-quarter-wave multilayer coatings with two or more different materials. Sub-quarter-wave multilayer coatings based on Al, MgF2, diamondlike carbon, B4C, SiC, and Ir showed higher reflectance than single-layer coatings of SiC and B4C not only at the target wavelength but in a wide band ranging from 50 nm to the 121.6-nm H Lyman-alpha line. Multilayer coatings suffered some reflectance degradation over time. However, after approximately 80-100 days of aging in a desiccator, the reflectance for the multilayer coatings was greater than for the single-layer coatings.