In hypothetical beyond design accidents where all engineered safety systems are assumed to fail, fusion undoubtedly is less hazardous then fission. But for more frequent — though still very unlikely — events the sophisticated safety culture of fission is a challenge which must be taken seriously. For future fission reactors, the admissible accidential radiological doses to members of the public must not exceed a fraction of the natural radiation with a prospective frequency higher than 10−4 to 10−5/a. If this level of safety is transferred to fusion, it requires a degree of retention of mobile radioactive inventory inside the fusion reactor containment which cannot be taken for granted without appropriate analysis. A containment concept with three barriers is proposed. A scoping study of conceivable event progressions shows that several physical phenomena charging the containment come into play in various order for different event progressions. The development of adequate tools for containment safety analysis is encouraged.