Point counts are used widely to index bird populations. Variation in the proportion of birds counted is a known source of error, and for robust inference it has been advocated that counts be converted to estimates of absolute population size. We used simulation to assess nine methods for the conduct and analysis of point counts when the data included distance-related heterogeneity of individual detection probability. Distance from the observer is a ubiquitous source of heterogeneity, because nearby birds are more easily detected than distant ones. Several recent methods (dependent double-observer, time of first detection, time of detection, independent multiple-observer, and repeated counts) do not account for distance-related heterogeneity, at least in their simpler forms. We assessed bias in estimates of population size by simulating counts with fixed radius w over four time intervals (occasions). Detection probability per occasion was modeled as a half-normal function of distance with scale parameter sigma and intercept g(0) = 1.0. Bias varied with sigma/w; values of sigma inferred from published studies were often <25 m, which suggests a bias of >50% for a 100-m fixed-radius count. More critically, the bias of adjusted counts sometimes varied more than that of unadjusted counts, and inference from adjusted counts would be less robust. The problem was not solved by using mixture models or including distance as a covariate. Conventional distance sampling performed well in simulations, but its assumptions are difficult to meet in the field. We conclude that no existing method allows effective estimation of population size from point counts.