Wilcoxon's signed rank test and a test based on the uniform minimum variance unbiased estimator ofP(X1+X2<Y1+Y2) are considered as competitors of the Mann-Whitney-Wilcoxon (U) test. The criteria used to compare the tests are Bahadur and Pitman efficiency. For pure translation alternativesUis superior, but both tests compare favorably with respect toUfor certain contamination alternatives.