In this paper we are concerned with the fixed, finite-order H-2-optimal control of linear, infinite-dimensional discrete-time systems. The set of necessary conditions for the existence of the H-2-optimal controller is expressed in terms of four operator equations (two modified Riccati equations and two modified Lyapunov equations) coupled by a projector having the rank given by the dimension of the compensator state. It is shown that, when the order of the compensator is equal to the order of the plant, the four operator equations are decoupled and we obtain the infinite-dimensional generalization of the finite-dimensional state-space solution to the H-2-optimal control problem for time-varying systems, as given by Ionescu and Weiss (1992).