In this study, we review various methods of estimating detection probabilities for avian point counts: distance sampling, multiple observer methods, and recently proposed time-of-detection methods. Both distance and multiple observer methods require the sometimes unrealistic assumption that all birds in the population sing during the count interval. We provide a general model of detection where the total probability of detection is made up of the probability of a bird singing, i.e., availability, and the probability of detecting a bird, conditional on its having sung. We show that the time-of-detection method provides an estimate of the total probability, whereas combining the time-of-detection method with a multiple observer method enables estimation of the two components of the detection process separately. Our approach is shown to be a special case of Pollock's robust capture-recapture design where the probability that a bird does not sing is equivalent to the probability that an animal is a temporary emigrant. We estimate Hooded Warbler and Ovenbird population size, through maximum likelihood estimation, using experimentally simulated field data for which the true population sizes were known. The method performs well when singing rates and detection probabilities are high, and when observers are able to accurately localize individual birds. Population sizes are underestimated when there is heterogeneity of singing rates among individual birds, especially when singing rates are close to zero. Despite the additional expense and the potential for counting and matching errors, we encourage field ornithologists to consider using this combined method in their field studies to better understand the detection process, and to obtain better abundance estimates.