This paper investigates the well-known separation properties that hold in the design of unconstrained output feedback controllers and tries to generalize them to cope with the design of structurally constrained decentralized controls. This problem, which until now has been open, presents additional constraints which destroy the useful properties that lead to separation. Necessary and sufficient conditions for decentralized stability and H-2 norm minimization are given, providing a framework in which a suitable an hoc separation procedure is developed. A numerical algorithm based on cross-decomposition is presented and applied in two situations: first, when separation Fails to provide a feasible solution; and then, to improve the obtained controller. An example and a comprehensive benchmark illustrate and validate the method.