Methods are presented for developing design toolsfor plane symmetric systems composed of spherical mirrors. Thesetools consist of constraints on individual system parameters thatensure a given set of low-order imaging properties. Theseconstraints remove available degrees of freedom to the opticaldesigner, thus reducing the dimensionality of the configurationspace. This simplifies the process of identifying viableconfigurations, and in some cases allows definitive studies to bemade. Example design studies are performed forone, two, three, and four-mirror systems both at finite conjugates,and with the object at infinity. In each study, several resultingsystems are illustrated. A systematic search over all availabledegrees of freedom is performed for systems with one and twomirrors, and three- mirrors with the object at infinity. Theconfiguration space is plotted, and definitive statements are madeabout these classes of systems. For systems with three and four-mirrors, there are too many degrees of freedom for such asystematic search to be effective. Therefore, the search over theindependent degrees of freedom is directed by a global optimizer.This provides an effective means to search for viable systems overa larger number of degrees of freedom.