We investigated the pattern of first sighting of individual seals over the course of a field season, or the “discovery curve,” as a means for estimating abundance of the endangered Hawaiian monk seal, Monachus schauinslandi. We empirically derived a criterion to determine whether or not total enumeration had been accomplished at a given site and year. When greater than 100-h field effort was expended without a new individual being identified, we concluded that total enumeration was likely achieved. To evaluate the potential for estimating abundance through extrapolation of nonlinear asymptotic functions fitted to discovery curves, we conducted simulations under a range of capture probability scenarios, including some based on observed individual variability in monk seal sighting frequencies. We demonstrated that if capture heterogeneity existed among individuals, the fitted asymptotes tended to yield biased estimates of abundance. Moreover, the levels of bias and uncertainty tended to increase inversely with the proportion of the population identified. While extrapolation shows little promise for generating unbiased abundance estimates, discovery curves have practical appeal for determining whether total enumeration has been achieved, and for optimizing field effort allocation. This is especially true for relatively small, closed populations of marked individuals.