Metal multilayer mirrors have been designed for the ALEXIS satellite, which is to carry six wide field telescopes to perform an all-sky survey in three or four narrow wavelength bands in the EUV. Comprised of alternating layers of molybdenum and silicon, the mirrors are optimized to provide maximum reflectivity at angles from 11.5 to 17° off normal incidence and at wavelengths of 133, 171, or 186Å. Simultaneously, the mirrors use a "wavetrap" described below to suppress reflectivity at 304Å, where the extremely strong geocoronal line of He II causes severe background problems. Low reflectivity at 304Å is achieved by superposing two layer pairs that provide destructive interference with an effective 2d spacing of 152Å. The Mo layers in this wavetrap must be very thin, about 10Å each, in order to allow the shorter wavelengths desired for peak reflectivity to penetrate without significant attenuation. Because refraction changes the effective angle of passage through the wavetrap, a joint optimization between layer thicknesses in the deep layers and the wavetrap layers must be performed for each target peak wavelength. For the 186Å mirror, the optimum design from substrate upward is 40 layer pairs, each 74Å Si and 31Å Mo, followed by 2 layer pairs, each 55Å Si and 10Å Mo. Calculations predict this design will have a peak reflectivity at 186Å of 35 percent and a 304Å reflectivity less than le, if available optical constants are correct and the multilayer can be fabricated without difficulty. We will present details of the calculations and laboratory measurements of the reflectivity performance attained with prototype mirrors.