The etiology of childhood leukemia remains generally unknown, although risk models based on the Japanese A-bomb survivors imply that the dose accumulated from protracted exposure to low-level natural background ionizing radiation materially raises the risk of leukemia in children. In this paper a novel Monte Carlo score-test methodology is used to assess the statistical power of cohort, ecological and case-control study designs, using the linear low-dose part of the BEIR V model derived from the Japanese data. With 10 (or 20) years of follow-up of childhood leukemias in Great Britain, giving about 4600 (or 9200) cases, under an individual-based cohort design there is 67.9% (or 90.9%) chance of detecting an excess (at 5% significance level, one-sided test); little difference is made by extreme heterogeneity in risk. For an ecological design these figures reduce to 57.9% (or 83.2%). Case-control studies with five controls per case achieve much of the power of a cohort design, 61.1% (or 86.0%). However, participation bias may seriously affect studies that require individual consent, and area-based studies are subject to severe interpretational problems. For this reason register-based studies, in particular those that make use of predicted doses that avoid the need for interviews, have considerable advantages. We argue that previous studies have been underpowered (all have power <80%), and some are also subject to unquantifiable biases and confounding. Sufficiently large studies should be capable of detecting the predicted risk attributable to natural background radiation.