Avian researchers often uniquely mark birds, and multiple estimators could be used to estimate population size using individually identified birds. However, most estimators of population size require that all sightings of marked birds be uniquely identified, and many assume homogeneous detection probabilities. Bowden's estimator can incorporate sightings of marked birds that are not uniquely identified and relax assumptions required of other estimators. I used computer simulation to evaluate the performance of Bowden's estimator for situations likely to be encountered in bird studies. When the assumptions of the estimator were met, abundance and variance estimates and confidence-interval coverage were accurate. However, precision was poor for small population sizes (N < 50) unless a large percentage of the population was marked (>75%) and multiple (≥8) sighting surveys were conducted. If additional birds are marked after sighting surveys begin, it is important to initially mark a large proportion of the population (p_m ≥ 0.5 if N ≤ 100 or p_m > 0.1 if N ≥ 250) and minimize sightings in which birds are not uniquely identified; otherwise, most population estimates will be overestimated by >10%. Bowden's estimator can be useful for avian studies because birds can be resighted multiple times during a single survey, not all sightings of marked birds have to uniquely identify individuals, detection probabilities among birds can vary, and the complete study area does not have to be surveyed. I provide computer code for use with pilot data to design mark-resight surveys to meet desired precision for abundance estimates.