Two two-parameter models are developed for testing the hypothesis of no treatment effect against the alternative that a subset of the treated patients will show an improvement. To keep the range of measurements the same for treated and control patients, Lehmann alternatives are used in both models. Locally most powerful rank tests are developed for each model and each parameter. The asymptotic relative efficiency leads to a test that uses the scores s(i) = [i/(N + 1)]4. Two examples that support the usefulness of this nonparametric test are presented.