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The aim of this paper is to present a version of the principle of alternate possibilities (PAP) which is not susceptible to the Frankfurt-style counter-example. I argue that PAP does not need to be endorsed as a necessary condition for moral responsibility and, in fact, presenting PAP as a sufficient condition maintains its usefulness as a maxim for moral accountability whilst avoiding Frankfurt-style counter-examples. In addition, I provide a further sufficient condition for moral responsibility – the twin world condition – and argue that this provides a means of justifying why the protagonist in Frankfurt-style scenarios (e.g., Jones) is still felt to be morally responsible. I conclude with the claim that neither the amended PAP nor the twin world condition is necessary for the ascription of moral responsibility; rather, what is necessary is simply that one of these conditions is satisfied.