The mixed H-2/H-infinity, control problem can be motivated as a nominal LQG optimal control problem, subject to robust stability constraints, expressed in the form of an H-infinity, norm bound. A related modified problem consisting on minimizing an upper bound of the H-2 cost subject to H-infinity, constraints was introduced in [1]. Although there presently exist efficient methods to solve this modified problem, the original problem remains, to a large extent, still open. In this paper we propose a method for solving general discrete-time SISO H-2/H-infinity problems. This method involves solving a sequence of problems, each one consisting of a finite-dimensional convex optimization and an unconstrained Nehari approximation problem.