Comparison of powers is essential to determine the best test that can be used for data under certain specific conditions. Likewise, several nonparametric methods have been developed for testing the ordered alternatives. The Jonckheere-Terpstra (JT) test and the Modified Jonckheere-Terpstra (MJT) test are for testing nondecreasing ordered alternatives for univariate data. The Dietz test is for testing nondecreasing alternatives based on bivariate data. This paper compares various tests when testing for nondecreasing alternatives specifically when the underlying distributions are bivariate exponential. The JT test and the MJT test are applied to univariate data which is derived by reducing bivariate data to univariate data using various transformations. A Monte Carlo simulation study is conducted comparing the estimated powers of JT tests and MJT tests (based on a variety of transformed univariate data) with the estimated powers of Dietz test (based on bivariate data) under a variety of location shifts and sample sizes. The results are compared with Zhao' s (2011) results for bivariate normal data. The overall best test statistic for bivariate data ordered alternatives is discussed in this paper.