Summary: When comparing two treatments on the basis of ordinal data, a natural alternative is stochastic order, as it implies that more favorable outcomes receive greater probability. Results of M. L. Eaton [Ann. Math. Stat. 41, 1884-1888 (1970; Zbl 0221.62006)] can be used to provide a complete class of tests. We find that many tests in current use are not in this class and hence are inadmissible. More important, we present methods of improving such tests. Often, the increase in power is substantial although the size remains the same.