The chemical instability of DNA under physiological conditions requires that cells have highly developed processes for repairing stochastic single-strand damage. It is proposed here that provided ionizing-radiation-induced single-strand damage does not occur at a rate sufficient to perturb the dynamic steady state between degradation and repair, it can be regarded as "irrelevant' to biological effect, leaving double-strand damage and DNA-protein crosslinks as "relevant' damage to biological effect. At dose rates of approximately 0.05 Gy/min low-LET radiation the rate of induced single-strand damage equals that of the spontaneous damage, and in this region a transition, with increasing dose-rate, from constant effect to increasing effect, will be expected. This is observed in studies of specific locus mutation by radiation in the male mouse. The application of this biophysical principle governing the influence of radiation dose-rate, to the association observed between paternal preconceptional dose to Sellafield workers and childhood leukaemia in their offspring, shows that the likelihood of a causal relationship is extremely remote.