The presence of random errors in the individual radiation dose estimates for the A-bomb survivors causes underestimation of radiation effects in dose-response analyses, and also distorts the shape of dose-response curves. Statistical methods are presented which will adjust for these biases, provided that a valid statistical model for the dose estimation errors is used. Emphasis is on clarifying some rather subtle statistical issues. For most of this development the distinction between radiation dose and exposure is not critical. The proposed methods involve downward adjustment of dose estimates, but this does not imply that the dosimetry system is faulty. Rather, this is a part of the dose-response analysis required to remove biases in the risk estimates. The primary focus of this report is on linear dose-response models, but methods for linear-quadratic models are also considered briefly. Some plausible models for the dose estimation errors are considered, which have typical errors in a range of 30-40% of the true values, and sensitivity analysis of the resulting bias corrections is provided. It is found that for these error models the resulting estimates of excess cancer risk based on linear models are about 6-17% greater than estimates that make no allowance for dose estimation errors. This increase in risk estimates is reduced to about 4-11% if, as has often been done recently, survivors with dose estimates above 4 Gy are eliminated from the analysis.