Count survey data are commonly used for estimating temporal and spatial patterns of population change. Since count surveys are not censuses, counts can be influenced by 'nuisance factors' related to the probability of detecting animals but unrelated to the actual population size. The effects of systematic changes in these factors can be confounded with patterns of population change. Thus, valid analysis of count survey data requires the identification of nuisance factors and flexible models for their effects. We illustrate using data from the Christmas Bird Count (CBC), a midwinter survey of bird populations in North America. CBC survey effort has substantially increased in recent years, suggesting that unadjusted counts may overstate population growth (or understate declines). We describe a flexible family of models for the effect of effort, that includes models in which increasing effort leads to diminishing returns in terms of the number of birds counted.