Motivation Finding genes that are preferentially expressed in a particular tissue or condition is a problem that cannot be solved by standard statistical testing procedures. A relatively unknown procedure that can be used is the intersection union test (IUT). However, two disadvantages of the IUT are that it is conservative and that it conveys only the information of the least differing target tissue - other tissue pair. Results We propose a Bayesian procedure that quantifies how much evidence there is in the overall expression profile for selective overexpression. In a small simulation study, it is shown that the proposed method outperforms the IUT when it comes to finding selectively expressed genes. An application to publicly available data consisting of 22 tissues shows that the Bayesian method indeed selects genes with functions that reflect the specific tissue functions. The proposed method can also be used to find genes that are under-expressed in a particular tissue. Availability Both MATLAB and R code that implement the IUT and the Bayesian procedure in an efficient way, can be downloaded at http://ppw.kuleuven.be/okp/software/BayesianIUT/. Contact email@example.com.