A tractable mixed numerical-analytic method is given for the approximate design of reflected reactors with cores having simultaneously flat power density, fuel loading, absorber distribution, and moderator distribution. The method as applied to finite cylinders yields a fast digital routine (about 1 sec/calculation on the IBM 704) which gives trustworthy criticality values in systems with important neutron capture at energies above thermal. Corroborative experiments on critical assemblies containing molybdenum and tungsten show power distributions flat to within ±5%.