Many wind-power facilities in the United States have established effective monitoring programs to determine turbine-caused fatality rates of birds and bats, but estimating the number of fatalities of rare species poses special difficulties. The loss of even small numbers of individuals may adversely affect fragile populations, but typically, few (if any) carcasses are observed during monitoring. If monitoring design results in only a small proportion of carcasses detected, then finding zero carcasses may give little assurance that the number of actual fatalities is small. Fatality monitoring at wind-power facilities commonly involves conducting experiments to estimate the probability (g) an individual will be observed, accounting for the possibilities that it falls in an unsearched area, is scavenged prior to detection, or remains undetected even when present. When g < 1, the total carcass count (X) underestimates the total number of fatalities (M). Total counts can be 0 when M is small or when M is large and g<<1. Distinguishing these two cases is critical when estimating fatality of a rare species. Observing no individuals during searches may erroneously be interpreted as evidence of absence. We present an approach that uses Bayes' theorem to construct a posterior distribution for M, i.e., P(M | X, ˆg), reflecting the observed carcass count and previously estimated g. From this distribution, we calculate two values important to conservation: the probability that M is below a predetermined limit and the upper bound (M*) of the (1-a)% credible interval for M. We investigate the dependence of M* on a, g, and the prior distribution of M, asking what value of g is required to attain a desired M* for a given a. We found that when g < -0.15, M* was clearly influenced by the mean and variance of ˆg and the choice of prior distribution for M, but the influence of these factors is minimal when g > -0.45. Further, we develop extensions for temporal replication that can inform prior distributions of M and methods for combining information across several areas or time periods. We apply the method to data collected at a wind-power facility where scheduled searches yielded X = 0 raptor carcasses.