In this paper, a multiobjective H-2 optimal control problem is considered in which the controllers are constrained to satisfy prescribed upper bounds on the H-2 or H-infinity norms of several closed-loop transfer functions. A sequence of H-2-cost/H-2-constraint problems (i.e. H-2 problems with a single H-2 constraint) is presented which aims at generating approximate solutions to the original problem-this may be viewed as a generalization of the so-called Lawson algorithm for Tchebycheff approximation. Each such H-2/H-2 problem has a unique rational solution which can be computed through line search and spectral factorization. Under appropriate assumptions, it is shown that the sequence of optimal cost values for the H-2/H-2 problems is increasing and bounded from above (hence, it is convergent) and that, whenever the corresponding sequence of solutions converges, it does so to the solution of the original problem. In the special case in which there are only H-2 constraints. convergence is established for the sequence of solutions of the auxiliary H-2-cost/H-2-constraint problems.