We used conventional and finite mixture removal models with and without time-varying covariates to evaluate availability given presence for 152 bird species using data from point counts in boreal North America. We found that the choice of model had an impact on the estimability of unknown model parameters and affected the bias and variance of corrected counts. Finite mixture models provided better fit than conventional removal models and better adjusted for count duration. However, reliably estimating parameters and minimizing variance using mixture models required at least 200–1,000 detections. Mixture models with time-varying proportions of infrequent singers were best supported across species, indicating that accounting for date- and time-related heterogeneity is important when combining data across studies over large spatial scales, multiple sampling time frames, or variable survey protocols. Our flexible and continuous time-removal modeling framework can be used to account for such heterogeneity through the incorporation of easily obtainable covariates, such as methods, date, time, and location. Accounting for availability bias in bird surveys allows for better integration of disparate studies at large spatial scales and better adjustment of local, regional, and continental population size estimates.