Nondetection of a species at a site does not imply that the species is absent unless the probability of detection is 1. We propose a model and likelihood-based method for estimating site occupancy rates when detection probabilities are < 1. The model provides a flexible framework enabling covariate information to be included and allowing for missing observations. Via computer simulation, we found that the model provides good estimates of the occupancy rates, generally unbiased for moderate detection probabilities (>0.3). We estimated site occupancy rates for two anuran species at 32 wetland sites in Maryland, USA, from data collected during 2000 as part of an amphibian monitoring program, Frogwatch USA. Site occupancy rates were estimated as 0.49 for American toads (Bufo americanus), a 44% increase over the proportion of sites at which they were actually observed, and as 0.85 for spring peepers (Pseudacris crucifer), slightly above the observed proportion of 0.83.