The nonparametric two-sample test recently proposed by Baumgartner,Wei,and Schindler [1] is not suitable for one-tailed analyses. We propose a modification of the original Baumgartner-Wei-Schmdler statistic which enables one-sided tests. The test based on the new modified statistic has a less conservative size and is, according to simulation results, more powerful than the one-sided Wilcoxon-Mann-Whitney test. With the modified statistic a Jonckheere-type trend test can be constructed. Simulation studies indicate that this new trend test is superior to the often employed Jonckheere-Terpstra test. Furthermore, the new tests based on the modified statistic are also powerful in case of heteroscedasticity. For all tests the exact permutation distribution was used for inference