David Lewis championed a counterfactual account of causation, but counterfactual accounts have a notoriously difficult time handling cases of late preemption. These are cases in which we still count one event as the cause of another although the effect does not depend on the cause in the way taken to be necessary by the account. Lewis recognized these cases, but they have been shown to be problematic even for his final analysis of causation, the Influence Account. In this paper, I (...) show how these cases led to and remain a problem for Lewis’s Influence Account, and I give a new counterfactual account available to a Lewisian that can handle late preemption cases. What is crucial to my account is that a cause not merely has counterfactual influence over its effects, but that the cause has influence of the right kind. I conclude by arguing that even if problems remain with this account, they will not be problems of late preemption, and the problems stemming from other kinds of cases will be no worse for my account than for other counterfactual accounts. (shrink)