The fossil record is incomplete in the sense that taxa for which there are no preserved finds are unrepresented. Because the probability that there is at least one preserved find is greater for long-lived taxa, failure to account for this effect will bias estimation of mean taxonomic duration. This paper describes maximum likelihood estimation of mean taxonomic duration, fossil preservation rate, and completeness of the local fossil record under a model in which duration has an exponential distribution and the locations of preserved finds follow a Poisson process. The estimates under this model have simple closed forms. It is also straightforward to construct confidence regions for the model parameters. The method is applied to data on 110 trilobite species from the Upper Cambrian-Lower Ordovician in Oklahoma.