The hope that fusion reactors will have fewer radiological hazards than competing fission technologies is an important rationale for fusion research. Estimates of the radiological hazard due to reactor accidents, occupational exposures, and waste disposal of reference fusion and fission designs; the Mirror Advanced Reactor Study (MARS); and a liquid-metal fast breeder reactor (LMFBR) indicate that fusion may enjoy substantial quantitative advantages over fission but that such advantages are neither sure to be achieved nor necessarily sufficient for fusion to be perceived as qualitatively superior to fission. The possibility of achieving maximum reductions of hazard is explored by analyzing the effects of relatively minor modifications of the MARS design, using completely different structural or breeder/coolant materials, and changing the fusion fuel cycle. Minor modifications, such as elemental tailoring of structural and coolant materials, result in reductions of one to two orders of magnitude in each class of hazard. Using different reactor materials, such as vanadium alloy or high-purity silicon carbide blanket structure, can result in even greater reductions. Other combinations, such as a molybdenum alloy structure cooled by liquid lithium, can be as hazardous as an LMFBR. Using the only other promising fuel cycle, catalyzed deuterium-deuterium, accident hazards can be reduced one to two orders of magnitude and waste disposal hazards by a factor of 4.