For birds and many other animal taxa, surveys that collect count data form a primary source of information on population change. Because counts are only indices to population size, care must be taken in using them in analyses of population change. Temporal or geographic differences in the proportion of animals counted can be misinterpreted as differences in population size. Therefore, temporally or geographically varying factors that influence the proportion of animals counted must be incorporated as covariables in the analysis of population parameters from count data. We describe the North American Breeding Bird Survey (BBS) for illustration. The BBS is a major, landscape-level survey of birds in North America; it is typical of many count surveys, in that the same sample units (survey routes) are sampled each year, and change is modeled on these routes over time. We identify covariables related to observer ability, the omission of which can bias estimation of population change from BBS data. Controlling for observer effects or other potential sources of confounding requires the specification of models relating counts to population size. We begin with a partial model specification relating expected counts to population sizes; we describe estimators currently in use in relation to this partial specification. Additional assumptions lead to a class of overdispersed multinomial models, for which we describe estimators of population change and procedures for parsimonious model selection. We illustrate the use of overdispersed multinomial models by an application to data for Carolina Wren (Thryothorus ludovicianus).