In this note, the structured H-2 optimization problem is defined and two methods are outlined for its solution. The first method involves a vectorization/Kronecker product technique and reduces the optimization problem to two nested projections. To circumvent the dimension inflation implicit in this method, an iterative algorithm is proposed as an alternative. This is an application of von-Neumann’s alternating projection algorithm in Hilbert space and can be shown to be applicable to the present problem under two standard rank assumptions. A short version of this paper has appeared in Halikias (1993).