Samples designed to provide estimates for large geographic areas are sometimes used to provide estimates for small areas. In such cases the sample in a small area may be "unrepresentative" or of small size. Various estimators, including a composite estimator, which is weighed function of two component estimators, have been suggested for use in these situations. The choice of weights for the composite estimator is considered in this paper. It is shown that with appropriate weights the composite estimator has smaller mean square error than either component estimator and also that this estimator is remarkably robust against poor choices of weights. Data from the National Center for Health Statistics' Health Interview Survey and the Bureau of the Census' Public Use Tapes are used to illustrate results when direct and synthetic estimators are used as components of the composite estimator.