An improved procedure is presented for estimating low-dose risks from dichotomous animal data based upon the multistage model of cancer. The procedure embodies both a proper fit to experimental data and an assumption of approximate linearity of the dose-response curve in the low-dose range. Because of this low-dose-linearity the procedure may be also considered to be a generalized method for linear extrapolation which uses all of the data. The extrapolation method is different from an earlier method based upon the multistage model in that an improved procedure is put forward for calculating statistical confidence limits and a recommendation is made for the integration of several data sets in the calculation of risk levels.