Detection of positive Darwinian selection has become ever more important with the rapid growth of genomic data sets. Recent branch-site models of codon substitution account for variation of selective pressure over branches on the tree and across sites in the sequence and provide a means to detect short episodes of molecular adaptation affecting just a few sites. In likelihood ratio tests based on such models, the branches to be tested for positive selection have to be specified a priori. In the absence of a biological hypothesis to designate so-called foreground branches, one may test many branches, but a correction for multiple testing becomes necessary. In this paper, we employ computer simulation to evaluate the performance of 6 multiple test correction procedures when the branch-site models are used to test every branch on the phylogeny for positive selection. Four of the methods control the familywise error rates (FWERs), whereas the other 2 control the false discovery rate (FDR). We found that all correction procedures achieved acceptable FWER except for extremely divergent sequences and serious model violations, when the test may become unreliable. The power of the test to detect positive selection is influenced by the strength of selection and the sequence divergence, with the highest power observed at intermediate divergences. The 4 correction procedures that control the FWER had similar power. We recommend Rom's procedure for its slightly higher power, but the simple Bonferroni correction is useable as well. The 2 correction procedures that control the FDR had slightly more power and also higher FWER. We demonstrate the multiple test procedures by analyzing gene sequences from the extracellular domain of the cluster of differentiation 2 (CD2) gene from 10 mammalian species. Both our simulation and real data analysis suggest that the multiple test procedures are useful when multiple branches have to be tested on the same data set.