The Annual Survey of Local Government Finances is a multipurpose survey selected every five years that publishes annual estimated totals of local government expenditures, revenues, debts, and assets for individual states and at the national level. As in many repeated, multipurpose economic surveys the design weights of this survey will not necessarily be strongly predictive of all variables of interest in all survey years. It is therefore possible for small units with large survey weights to report unusual values for key variables making classical design-based estimators highly unstable. In this study we investigate several methods for treating such influential units, including Winsorized, model-assisted, and model-based approaches. We also investigate the question of preserving consistency across domains in production.