In this paper it is argued that sensitivity theory suffers from a fatal defect. Sensitivity theory is often glossed as: (1) S knows that p only if S would not believe that p if p were false. As Nozick showed in his pioneering work on sensitivity theory, this formulation needs to be supplemented by a further counterfactual condition: (2) S knows that p only if S would believe p if p were true. Nozick further showed that the theory needs a qualification on the method used to form the belief. However, when these complications are spelled out in detail, it becomes clear that the two counterfactuals are in irresolvable tension. To jibe with the externalist intuitions that motivate sensitivity theory in the first place, (1) needs a fine-grained grouping of belief-formation methods, but (2) needs coarse-grained grouping. It is therefore suggested that sensitivity theory is in dire straits: either its proponents need to provide a workable principle of method individuation or they must retrench and give up their claims to providing sufficient conditions for knowledge.