Apparent variation in rates of origination and extinction reflects the true temporal pattern of taxonomic rates as well as the distorting effects of incomplete and variable preservation, effects that are themselves exacerbated by true variation in taxonomic rates. Here I present an approach that can undo these distortions and thus permit estimates of true taxonomic rates, while providing estimates of preservation in the process. Standard survivorship probabilities are modified to incorporate variable taxonomic rates and rates of fossil recovery. Time series of these rates are explored by numerical optimization until the set of rates that best explains the observed data is found. If internal occurrences within stratigraphic ranges are available, or if temporal patterns of fossil recovery can otherwise be assumed, these constraints can be exploited, but they are by no means necessary. In its most general form, the approach requires no data other than first and last appearances. When tested against simulated data, the method is able to recover temporal patterns in rates of origination, extinction, and preservation. With empirical data, it yields estimates of preservation rate that agree with those obtained independently by tabulating internal occurrences within stratigraphic ranges. Moreover, when empirical occurrence data are artificially degraded, the method detects the resulting gaps in sampling and corrects taxonomic rates. Preliminary application to data on Paleozoic marine animals suggests that some features of the apparent record, such as the forward smearing of true origination events and the backward smearing of true extinction events, can be detected and corrected. Other features, such as the end-Ordovician extinction, may be fairly accurate at face value.