We present PESMO, a Bayesian method for identifying the Pareto set of multi-objective optimization problems, when the functions are expensive to evaluate. PESMO chooses the evaluation points to maximally reduce the entropy of the posterior distribution over the Pareto set. The PESMO acquisition function is decomposed as a sum of objective-specific acquisition functions, which makes it possible to use the algorithm in decoupled scenarios in which the objectives can be evaluated separately and perhaps with different costs. This decoupling capability is useful to identify difficult objectives that require more evaluations. PESMO also offers gains in efficiency, as its cost scales linearly with the number of objectives, in comparison to the exponential cost of other methods. We compare PESMO with other methods on synthetic and real-world problems. The results show that PESMO produces better recommendations with a smaller number of evaluations, and that a decoupled evaluation can lead to improvements in performance, particularly when the number of objectives is large.