This paper addresses the problem of relying on H-2-optimization to select a controller that ensures satisfactory closed-loop responses to certain classes of persistent exogenous signals. Quadratic cost functionals are set up for each of the signal classes, corresponding to references, plant and measurement disturbances, which take into account the transient parts of the associated error and control signals. Each of the corresponding separate problems is shown to have unique solutions; this also holds for the problems obtained by combining these functionals in order to seek compromises between the objectives involved. The solutions of these problems are then quite explicitly described.