Numerous methods exist for estimating the true stratigraphic range of a fossil taxon based on the stratigraphic positions of its fossil occurrences. Many of these methods require the assumption of uniform fossil recovery potential—that fossils are equally likely to be found at any point within the taxon's true range. This assumption is unrealistic, because factors such as stratigraphic architecture, sampling effort, and the taxon's abundance and geographic range affect recovery potential. Other methods do not make this assumption, but they instead require a priori quantitative knowledge of recovery potential that may be difficult to obtain. We present a new Bayesian method, the Adaptive Beta method, for estimating the true stratigraphic range of a taxon that works for both uniform and non-uniform recovery potential. In contrast to existing methods, we explicitly estimate recovery potential from the positions of the occurrences themselves, so that a priori knowledge of recovery potential is not required. Using simulated datasets, we compare the performance of our method with existing methods. We show that the Adaptive Beta method performs well in that it achieves or nearly achieves nominal coverage probabilities and provides reasonable point estimates of the true extinction in a variety of situations. We demonstrate the method using a dataset of the Cambrian mollusc Anabarella.