We present an incremental subgradient algorithm for approximate computation of maximum-a-posteriori (MAP) states in cyclic graphical models. Its most striking property is its immense simplicity: each iteration requires only the solution of a sequence of trivial optimization problems. The algorithm can be equally understood as a degenerated dual decomposition scheme or as minimization of a degenerated tree-reweighted upper bound and assumes a form that is reminiscent of message-passing. Despite (or due to) its conceptual simplicity, it is equipped with important theoretical guarantees and exposes strong empirical performance.