The dispersion diagrams of surface plasmon polaritons have been calculated for rectangular gratings, with very narrow wires, of varying depths. For gratings with a moderate height a family of vertical-standing-wave resonances may be excited, which consist of surface plasmons, oscillating on either vertical surface, coupling together through the metal wires. These modes evolve similarly to the manner in which shallow-grating surface-plasmon dispersion curves evolve into cavity modes in the grooves of the structure. However, on further increase in grating height these vertical standing waves evolve into a second resonant feature, which is independent of yet further increases in height. This new mode is shown to be equivalent to the resonances found on infinite multilayer metal/dielectric structures illuminated at normal incidence.