A comparison, by means of Pitman asymptotic efficiency, is made between the Kolmogorov-Smirnov test and the locally most powerful rank and the locally asymptotically most powerful (Neyman) test for testing two-sided shifts in the two-sample problem under the assumption that the true distribution is different from the one assumed. It is shown that the behavior of the bounds for the Pitman asymptotic efficiencies are the same as those for testing the one-sided shift using the Smirnov test in place of the Kolmogorov-Smirnov test.