Linear regression models with random effects are applied to estimating the population means of indirectly measured variables in small areas. The proposed method, a hybrid with design- and model-based elements, takes account of the area-level variation and of the uncertainty about the fitted regression model and the area-level population means of the covariates. The method is illustrated on data from the U.S. Department of Labor Literacy Surveys and is informally validated on two states, Mississippi and Oregon, for which statewide surveys have been conducted.