Motivated by the testing of genetic pleiotropy, we discuss a general class of hypothesis testing, the exclusive hypothesis test (EHT). A hypothesis test is an EHT if the null hypothesis can be divided into a set of exclusive sub-hypotheses, and a main difficulty for testing an EHT is the calculation of the p-value. To address this problem, we propose a weighted procedure and develop two methods, one likelihood-based and the other Bayesian information criterion (BIC)-based, for determining the corresponding weights. Furthermore, we show that the BIC-based method can control the asymptotic type I error. We conduct an extensive simulation study of these two proposed methods, which suggests that they work well in practice. In particular, the new procedure is shown both theoretically and numerically to exhibit better performance than the existing two-stage decision rule for testing genetic pleiotropy. Our proposed methodology is then applied to a set of data concerning tropical storms.