Risk-based radiation protection policy is influenced by estimated risk and by theuncertainty of that estimate. Thus, if the upper limit, at (say) 95% probability, ofrisk associated with a given radiation dose is at an ‘acceptable’ level, it isunlikely (or not credible) that the true level of risk associated with the doseis at an unacceptable level. Central estimates presented alone, in theabsence of probability limits, lack this safety factor. Estimating cancerrisks from low doses of ionising radiation involves extrapolation of riskestimates based on high-dose data to the much lower dose levels thatcharacterize the vast majority of exposures of regulatory concern. Proof of auniversal low-dose threshold, below which there is no radiation-related risk,would revolutionise radiation protection. Available data fail to providesuch proof and, in fact, leave considerable room for the possibility thatDNA damage from a single photon can contribute to the carcinogenicprocess. Allowing for the possibility of a threshold would, however, removevery little of the regulatory burden associated with the so-called linear,no-threshold hypothesis, unless that possibility were a virtual certainty.