Max-sum is a version of Belief Propagation, used for solving DCOPs. On tree-structured problems, Max-sum converges to the optimal solution in linear time. Unfortunately, on cyclic problems, Max-sum does not converge and explores low quality solutions. Damping is a method, often used for increasing the chances that Belief Propagation will converge. That been said, it was not mentioned in the studies that proposed Max-sum for solving DCOPs. In this paper wc advance the research on incomplete inference DCOP algorithms by investigating the effect of damping on Max-sum. We prove that Max-sum with damping is guaranteed to converge to the optimal solution in weakly polynomial lime. Our empirical results demonstrate a drastic improvement in the performance of Max-sum, when using damping. However, in contrast to the common assumption, that it performs best when converging, we demonstrate that non converging versions perform efficient exploration, and produce high quality results, when implemented within an anytime framework.