In the context of solving large distributed constraint optimization problems (DCOP), belief-propagation and incomplete inference algorithms are candidates of choice. However, in general, when the factor graph is very cyclic, these solution methods suffer from bad performance, due to non-convergence and many exchanged messages. As to improve performances of the Max-Sum inference algorithm when solving cyclic constraint optimization problems, we propose here to take inspiration from the belief-propagation-guided decimation used to solve sparse random graphs (k-satisfiability). We propose the novel DeciMax-Sum method, which is parameterized in terms of policies to decide when to trigger decimation, which variables to decimate, and which values to assign to decimated variables. Based on an empirical evaluation on a classical BP benchmark (the Ising model), some of these combinations of policies outperform state-of-the-art competitors.