We present a new discriminative technique for the multiple-source adaptation (MSA) problem. Unlike previous work, which relies on density estimation for each source domain, our solution only requires conditional probabilities that can be straightforwardly accurately estimated from unlabeled data from the source domains. We give a detailed analysis of our new technique, including general guarantees based on R\'enyi divergences, and learning bounds when conditional Maxent is used for estimating conditional probabilities for a point to belong to a source domain. We show that these guarantees compare favorably to those that can be derived for the generative solution, using kernel density estimation. Our experiments with real-world applications further demonstrate that our new discriminative MSA algorithm outperforms the previous generative solution as well as other domain adaptation baselines.