A generalized method for calculating confidence intervals on the position of the true end point of a stratigraphic range when the distributions of fossil horizons is nonrandom is presented. The method requires a quantitative measure of collecting and/or preservation biases with stratigraphic position. This fossil recovery potential function may be based on (among other variables) bedding-plane surface areas, or, given a water depth curve, an a priori estimate of the preservation potential with water depth. The approach assumes that the observed distribution of fossil horizons is consistent with the distribution predicted by the fossil recovery potential function, an assumption that must be tested before the method is applied. Unlike previous methods for calculating confidence intervals on the end points of stratigraphic ranges, this method may be applied when the number of fossil horizons is correlated with stratigraphic ranges, this method may be applied when the number of fossil horizons is correlated with stratigraphic position. The approach should only be applied to sections that have been sampled continuously, or approximately continuously. Its efficacy will depend on how accurately fossil recovery potentials can be determined. A method is also presented for estimating the probability that a species became extinct during a major hiatus in the rock record.