OT, we cut the spikes of everything back once the flowers have dropped (and sometimes a little before). Occasionally, the spikes of some intergenerics will put out a little side branch or two if we didn't get to cut in time, but these have maybe four or five flowers on them, and that's it. Not a show worth saving an old spike for, and keeping that spike going reduces the plant's energy and makes it take longer for the plant to bloom next time.
Cut 'em all the way down. The plant will go dormant for a couple months where it won't do anything but shed old leaves and scare people. Then, new growth will start sprouting and the spikes and blooms from those will be really strong.