In 1969 Harry Frankfurt published his hugely influential paper 'Alternate Possibilities and Moral Responsibility' in which he claimed to present a counterexample to the so-called 'Principle of Alternate Possibilities' ('a person is morally responsible for what he has done only if he could have done otherwise'). The success of Frankfurt-style cases as counterexamples to the Principle has been much debated since. I present an objection to these cases that, in questioning their conceptual cogency, undercuts many of those debates. Such cases all require a counterfactual mechanism that could cause an agent to perform an action that he cannot avoid performing. I argue that, given our concept of what it is for someone to act, this requirement is inconsistent. Frankfurt-style alleged counterexamples are cases where an agent is morally responsible for an action he performs even though, the claim goes, he could not have avoided performing that action. However, it has recently been argued, e.g. by John Fischer, that a counterexample to the Principle could be a 'Fischer-style case', i.e. a case where the agent can either perform the action or do nothing else. I argue that, although Fischer-style cases do not share the conceptual flaw common to all Frankfurt-style cases, they also fail as counterexamples to the Principle. The paper finishes with a brief discussion of the significance of the Principle of Alternate Possibilities.