The method of Elbers, Lanjouw and Lanjouw (ELL) is the small area estimation method developed by the World Bank for poverty mapping and is widely used in developing countries. However, it has been criticized because of its assumption of negligible between-area variability when used to calculate small area poverty estimates. In particular, the mean-squared errors (MSEs) of these estimates are significantly underestimated when this between-area variability cannot be adequately explained by the model covariates. A method of MSE estimation for ELL-type estimates is proposed which is robust to significant unexplained between-area variability. Simulation results show that the method proposed performs better than standard ELL MSE estimators when the area homogeneity assumption is violated. An application to a Bangladesh poverty mapping study provides some empirical evidence for this robustness.