Some relatively new issues that augment the usual practice of ignoring model uncertainty, when making inference about parameters of a specific model, are brought to the attention of the radiation protection community here. Nine recently published leukaemia risk models, developed with the Japanese A-bomb epidemiological mortality data, have been included in a model-averaging procedure so that the main conclusions do not depend on just one type of model or statistical test. The models have been centred here at various adult and young ages at exposure, for some short times since exposure, in order to obtain specially computed childhood Excess Relative Risks (ERR) with uncertainties that account for correlations in the fitted parameters associated with the ERR dose-response. The model-averaged ERR at 1 Sv was not found to be statistically significant for attained ages of 7 and 12 years but was statistically significant for attained ages of 17, 22 and 55 years. Consequently, such risks when applied to other situations, such as children in the vicinity of nuclear installations or in estimates of the proportion of childhood leukaemia incidence attributable to background radiation (i.e. low doses for young ages and short times since exposure), are only of very limited value, with uncertainty ranges that include zero risk. For example, assuming a total radiation dose to a 5-year-old child of 10 mSv and applying the model-averaged risk at 10 mSv for a 7-year-old exposed at 2 years of age would result in an ERR=0.33, 95% CI: -0.51 to 1.22. One model (United Nations scientific committee on the effects of atomic radiation report. Volume 1. Annex A: epidemiological studies of radiation and cancer, United Nations, New York, 2006) weighted model-averaged risks of leukaemia most strongly by half of the total unity weighting and is recommended for application in future leukaemia risk assessments that continue to ignore model uncertainty. However, on the basis of the analysis presented here, it is generally recommended to take model uncertainty into account in future risk analyses.