Summary. The selection of a single method of analysis is problematic when the data could have been generated by one of several possible models. We examine the properties of two tests designed to have high power over a range of models. The first one, the maximum efficiency robust test (MERT), uses the linear combination of the optimal statistics for each model that maximizes the minimum efficiency. The second procedure, called the MX, uses the maximum of the optimal statistics. Both approaches yield efficiency robust procedures for survival analysis and ordinal categorical data. Guidelines for choosing between them are provided.