A new tolerance distribution and inference procedure for quantal response assays is presented. This method is capable of fitting a wide variety of shapes of response curves. Specific cases of this new method include quantal response assay analyses based on the double exponential distribution, the logistic distribution (logit analysis), and the uniform distribution (linit analysis) in a limiting case. Computational techniques used to implement the likelihood procedures associated with this method are described. Comparisons are made for 22 sets of published data. These comparisons suggest that interval estimates of extreme dosages (e.g., ED95 and ED99) based on logit and probit analyses are, for the most part, either overly optimistic (too small) or overly pessimistic (too large). This interval estimation problem should be partially overcome by the added flexibility of the method introduced here.