We describe a new algorithm, Relaxed Survey Propagation (RSP), for finding MAP configurations in Markov random fields. We compare its performance with state-of-the-art algorithms including the max-product belief propagation, its sequential tree-reweighted variant, residual (sum-product) belief propagation, and tree-structured expectation propagation. We show that it outperforms all approaches for Ising models with mixed couplings, as well as on a web person disambiguation task formulated as a supervised clustering problem.