In this paper me consider the problem of minimizing the l(1) norm of the transfer function from the exogenous input to the regulated output over all internally stabilizing controllers while keeping its H-2 norm under a specified level. The problem is analyzed for the discrete-time, single-input single-output (SISO), linear-time invariant case. It is shown that an optimal solution always exists. Duality theory is employed to show that any optimal solution is a finite impulse response sequence, and an a priori bound is given on its length. Thus, the problem can be reduced to a finite-dimensional convex optimization problem with an a priori determined dimension. Finally, it is shown that, in the region of interest of the H-2 constraint level, the optimal is unique and continuous with respect to changes in the constraint level.