Double elimination tournament
Single kill, double elimination is the title given (in Lochac at least) to a style of tournament that is commonly used if large numbers of fighters are involved. "Single kill" refers to each round being the best of one, meaning that double kills normally have to be resolved. "Double-elimination" refers to the fact that a fighter is removed from the tournament once they have been defeated a second time.
This shortens tourneys but also puts pressure on those left 'in' because bouts come faster and faster, as the number of fighters falls. But the idea is also that every fighter gets to fight at least twice. In order to enhance the enjoyment of the fighters, a lists officer should where possible try and make sure that at least one of these fights will be against someone who is roughly their equal in fighting, or someone who they rarely fight against.