Detecting positive Darwinian selection at the DNA sequence level has been a subject of considerable interest. However, positive selection is difficult to detect because it often operates episodically on a few amino acid sites, and the signal may be masked by negative selection. Several methods have been developed to test positive selection that acts on given branches (branch methods) or on a subset of sites (site methods). Recently, Yang, Z., and R. Nielsen (2002. Codon-substitution models for detecting molecular adaptation at individual sites along specific lineages. Mol. Biol. Evol. 19:908-917) developed likelihood ratio tests (LRTs) based on branch-site models to detect positive selection that affects a small number of sites along prespecified lineages. However, computer simulations suggested that the tests were sensitive to the model assumptions and were unable to distinguish between relaxation of selective constraint and positive selection (Zhang, J. 2004. Frequent false detection of positive selection by the likelihood method with branch-site models. Mol. Biol. Evol. 21:1332-1339). Here, we describe a modified branch-site model and use it to construct two LRTs, called branch-site tests 1 and 2. We applied the new tests to reanalyze several real data sets and used computer simulation to examine the performance of the two tests by examining their false-positive rate, power, and robustness. We found that test 1 was unable to distinguish relaxed constraint from positive selection affecting the lineages of interest, while test 2 had acceptable false-positive rates and appeared robust against violations of model assumptions. As test 2 is a direct test of positive selection on the lineages of interest, it is referred to as the branch-site test of positive selection and is recommended for use in real data analysis. The test appeared conservative overall, but exhibited better power in detecting positive selection than the branch-based test. Bayes empirical Bayes identification of amino acid sites under positive selection along the foreground branches was found to be reliable, but lacked power.