The electromagnetic energy transmitted over a path in which a thin, dispersive, dielectric medium is introduced is studied from the viewpoint of maximizing the transmitted energy. Two cases are treated in detail: a dispersionless dielectric and a plasma dielectric, including the effects of collisions. It is shown that the form of the solution that maximizes the energy transmitted through a dispersionless dielectric minimizes the energy transmitted through a plasma dielectric. Expressions specifying the energy transferred in each case are presented. The cases treated illustrate the importance of dispersion in choosing a suitable pulse shape for maximum energy transmission.