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For grizzly bears (Ursus arctos horribilis) in the Greater Yellowstone Ecosystem (GYE), minimum population size and allowable numbers of human-caused mortalities have been calculated as a function of the number of unique females with cubs-of-the-year (F_CUB) seen during a 3-year period. This approach underestimates the total number of F_CUB, thereby biasing estimates of population size and sustainable mortality. Also, it does not permit calculation of valid confidence bounds. Many statistical methods can resolve or mitigate these problems, but there is no universal best method. Instead, relative performances of different methods can vary with population size, sample size, and degree of heterogeneity among sighting probabilities for individual animals. We compared 7 nonparametric estimators, using Monte Carlo techniques to assess performances over the range of sampling conditions deemed plausible for the Yellowstone population. Our goal was to estimate the number of F_CUB present in the population each year. Our evaluation differed from previous comparisons of such estimators by including sample coverage methods and by treating individual sightings, rather than sample periods, as the sample unit. Consequently, our conclusions also differ from earlier studies. Recommendations regarding estimators and necessary sample sizes are presented, together with estimates of annual numbers of F_CUB in the Yellowstone population with bootstrap confidence bounds.