Studies of taxonomic diversity over time commonly count and compare first- and last-appearance data (FADs and LADs) over a succession of temporal intervals, and interpret them with respect to taxon origination and extinction. Singleton taxa, which first appear and last appear in the same temporal interval, are often removed from analyses because they might result from preservational biases rather than evolutionary processes, or they might represent non-independent FADs and LADs. Should singleton taxa always be excluded? We argue that in the case of Paleozoic terebratulide brachiopods, although they may be sensitive to biases in sampling intensity, singleton genera should be included in diversity studies because they do not appear to result from more typical biases, such as Lagerstätten and temporal interval length, that arguably can result in artificially high numbers of singleton genera.Singleton genera can be critical and effective when used to test hypotheses regarding the existence and generation of latitudinal diversity gradients. Contrary to the anti-tropical diversity pattern of modern articulated brachiopods, Paleozoic terebratulides show a latitudinal diversity gradient that peaks in the Tropics. The hypothesis that the Tropics are either a diversity source or sink can be tested by comparing FAD and LAD latitudes. For singleton genera, FAD and LAD latitudes are taken from the same data points and must be removed for statistical comparisons to be valid. We suggest that taxon age distributions can accommodate singleton data, as the taxon age metric considers origination and extinction simultaneously. We generated taxon age distributions to test the hypothesis that the observed Paleozoic diversity gradient results from a latitudinal bias in generic turnover rate. We discovered that singletons are not randomly distributed over latitude, with proportionally more singleton genera occurring in the Tropics. In this case, singleton genera may reflect rapid evolutionary turnover of taxa, rather than simply preservational bias. Methods that can accommodate singleton taxa should be used to study the diversity of Paleozoic terebratulides and possibly other well-skeletonized marine metazoans.