In this paper we consider the problem of minimizing the H-2-norm of the closed-loop map while maintaining its l(1)-norm at a prescribed level, The problem is analyzed in the case of discrete-time, SISO closed-loop maps, Utilizing duality theory, it is shown that the optimal solution is unique, and, in the nontrivial case where the l(1) constraint is active, the optimal solution has a finite impulse response. A finite step procedure is given for the construction of the exact solution, This procedure consists of solving a finite number of quadratic programming problems which can be performed using standard methods, Finally, continuity properties of the optimal solution with respect to changes in the l(1)-constraint are established.