Critical masses have been measured for enriched-uranium-metal cylinders reflected on both ends and on one end only by multiple layers of two and three of the metals Cu, Fe, Zn, Ni, and stainless steel. For other measurements the core was partially moderated with graphite and with polyethylene so as to give the influence of decreased neutron energy upon reflector savings of the multiple reflectors. Critical mass values with composite reflectors are less than the simple averages of values for the elements alone. This reduction of critical mass, most pronounced for the Ni-Fe reflectors, is primarily due to the fact that the self-shielding of the scattering resonances in medium-Z elements is appreciable when one-element reflectors are used, and is reduced when two or more of these elements are mixed in the reflectors.