Recent theoretical and experimental work has established minimum critical masses for uranium and plutonium reactor fuels. Studies at Los Alamos show a minimum of 300 to 600 g in the critical mass of 235U for H2O or D2O moderator and D2O or Be reflectors. An H2O-moderated, Be-reflected core containing 0.070 g 235U/mliter has a very low critical mass, which is of interest in the design of small power reactors and has attractive features for a new high neutron flux reactor concept. This report relates nuclear parameter studies to specific design objectives and shows how special effects of geometry and materials are important to such studies.