Efficiently transmitting data in wireless networks requires an integrated routing, scheduling, and power control strategy. As opposed to the universal dual decomposition we present a method that solve this optimization problem by fully exploiting its combinatorial structure. The method still maintains main requirements such as optimality, distributed implementation, multiple path routing, and per-hop error performance. The method represents a cross-layer approach where we include scheduling in the constraint set of a joint routing and power control optimization problem. Apart from the mathematical framework, the main contribution is a routing and power control decomposition (RPCD) algorithm. For verification, we compare the RPCD algorithm with state-of-art dual decomposition for wireless mesh backhaul networks. Impressive convergence results indicate that the RPCD algorithm calculates the optimum solution in one decomposition step only.