Asymptotically optimal experimental designs for animal bio-assays conducted in order to estimate virtually safe levels of exposure to chemical carcinogens are derived under the one-hit model and the probit model with known slope parameter. For these two models, the optimal designs involve assigning all available animals to the dose levels corresponding to the 80% and 50% response rates respectively. In both cases, the optimal designs are highly robust in the sense that the loss in efficiency is minimal if the dose actually employed is at all close to the optimal dose. In addition, the bias, variance and mean square error of the maximum likelihood estimator of the safe level of exposure under these two models are computed and compared with those of the jackknife estimator as well as an alternative estimator with reduced bias proposed by Salama, Koch & Tolley 1978. Twelve different procedures for obtaining approximate lower confidence limits on the safe dose are also compared in terms of their actual coverage probabilities and their precision.