The random nature of cell killing by ionizing radiations sets an upper limit on the steepness of the dose-response (D-R) curve for tumor cure. This theoretical limit was approached but not reached in a carefully controlled experimental system. It would seem unlikely that this result could be achieved in clinical practice because of the potential importance of tumor heterogeneity and treatment error in decreasing the slope of the D-R curve. In attempting to achieve a high degree of precision in treatment administration, the therapist, particularly in a multitreatment course, is aided by certain statistical rules which are applicable to random errors.