Most people believe that it is permissible to kill a nonresponsible threat, or someone who threatens one's life without exercising agency. Defenders of this view must show that there is a morally relevant difference between nonresponsible threats and innocent bystanders. Some philosophers, including Jonathan Quong and Helen Frowe, have attempted to do this by arguing that one who kills a bystander takes advantage of another person, while one who kills a threat does not. In this paper, I show that the proposals offered by Quong and Frowe have unacceptable implications. I then argue that those who claim that nonresponsible threats may be killed face a dilemma generated by the possibility of a stationary threat, or someone who endangers another person's life without moving. Unless we arbitrarily distinguish between stationary and moving nonresponsible threats, it is unclear how the permission to kill nonresponsible threats is to be explicated. I conclude that nonresponsible threats are not legitimate targets of self-defence.