Background: Analyses of Japanese A-bomb survivors' cancer mortality risks are used to establish recommended annual dose limits, currently set at 1 mSv (public) and 20 mSv (occupational). Do radiation doses below 20 mSv have significant impact on cancer mortality in Japanese A-bomb survivors, and is the dose-response linear? Methods: I analyse stomach, liver, lung, colon, uterus, and all-solid cancer mortality in the 0-20 mSv colon dose subcohort of the 1950-90 (grouped) mortality cohort, by Poisson regression using a time-lagged colon dose to detect latency, while controlling for gender, attained age, and age-at-exposure. I compare linear and non-linear models, including one adapted from the cellular bystander effect for a particles. Results: With a lagged linear model, Excess Relative Risk (ERR) for the liver and all-solid cancers is significantly positive and several orders of magnitude above extrapolations from the Life Span Study Report 12 analysis of the full cohort. Non-linear models are strongly superior to the linear model for the stomach (latency 11.89 years), liver (36.90), lung (13.60) and all-solid (43.86) in fitting the 0-20 mSv data and show significant positive ERR at 0.25 mSv and 10 mSv lagged dose. The slope of the dose-response near zero is several orders of magnitude above the slope at high doses. Conclusion: The standard linear model applied to the full 1950-90 cohort greatly underestimates the risks at low doses, which are significant when the 0-20 mSv subcohort is modelled with latency. Non-linear models give a much better fit and are compatible with a bystander effect.