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For many household and establishment surveys, initial contact and interview attempts by themselves do not produce satisfactory response rates. This often leads data-collection organizations to use various callback procedures to collect data from sample units that initially were nonrespondents. Analyses of the resulting data depend implicitly or explicitly on models for the response mechanism, conditional on the specific callback procedure. These models generally are acknowledged to be, at best, approximations to more complex underlying response processes. Consequently, it is important to explore the extent to which the properties of the callback-adjusted estimators may be sensitive to deviations from the assumed models. This paper develops a framework for exploring the impact of moderate deviations, and presents some related simulation results.