Getting my Cordyline to thicken?

Hi Mary welcome to goy hope the rain has stopped not called the Emerald Isle for nothing! In answer to your question if you look closely at your cordyline youll see that new shoots grow from outer edge - these can be cut to keep in shape but to trim existing leaf kills it. You end up with a mass of dead central growth surrounded by new leaf on the outside of the plant.There is no way to restrict height only width - would be rather like trying to make a palm tree bush out instead of growing up. Oh you may find that peeling off dead lower leaves[gloves required] encourages bushier growth but wont stop height Im afraid.