A recent algorithm for output-feedback eigenstructure assignment uses a multi-stage design process to assign a combination of left and right eigenvectors. It is possible, depending on the distribution of design freedom between the stages, that not all of the available degrees of freedom will be used by the assignment process. In this paper, an algorithm is presented which exploits unused design freedom to introduce structure to the resulting gain matrix without affecting the assigned eigenstructure. This process will inevitably have an effect on the overall magnitude of the gains, and consideration is given to this.