Some philosophers dismiss putative cases of causal overdetermination as joint causation underdescribed. In this paper I identify a special kind of causal overdetermination that cannot be reduced to joint causation, and use it to shed light on other kinds of redundant causation. Some effects are insensitive to the additive force of multiple causes. They are to be contrasted with sensitive effects, which physically and counterfactually vary according to the number and sorts of causes they have. I argue that sensitive effects are symptoms of joint causation; insensitive effects are symptoms of overdetermination. Insensitive effects resulting from multiple causes cannot be classified as “joint causation underdescribed,” but only as overdetermination. Finally, I suggest that cases of “trumping preemption” should be understood as cases of overdetermination with insensitive effects, and that Lewis’ “influence” account of causation cannot handle these cases.