Estimators of the number of additional species expected in the next Δn samples offer a potentially important tool for improving cost-effectiveness of species inventories but are largely untested. We used Monte Carlo methods to compare 11 such estimators, across a range of community structures and sampling regimes, and validated our results, where possible, using empirical data from vascular plant and beetle inventories from Glacier National Park, Montana, USA. We found that B. Efron and R. Thisted’s 1976 negative binomial estimator was most robust to differences in community structure and that it was among the most accurate estimators when sampling was from model communities with structures resembling the large, heterogeneous communities that are the likely targets of major inventory efforts. Other estimators may be preferred under specific conditions, however. For example, when sampling was from model communities with highly even species-abundance distributions, estimates based on the Michaelis-Menten model were most accurate; when sampling was from moderately even model communities with S = 10 species or communities with highly uneven species-abundance distributions, estimates based on Gleason’s (1922) species–area model were most accurate. We suggest that use of such methods in species inventories can help improve cost-effectiveness by providing an objective basis for redirecting sampling to more-productive sites, methods, or time periods as the expectation of detecting additional species becomes unacceptably low.