According to the Dilemma Defense, it is question-begging against the incompatibilist defender of the principle of alternative possibilities (PAP) to assume that the agent in a deterministic Frankfurt-style case (FSC) cannot do otherwise in light of causal determinism, but is nevertheless morally responsible. As a result, Fischer (Philos Rev 119:315–336, 2010; Analysis 73:489–496, 2013) attempts to undermine PAP in a different manner via a deterministic FSC. More specifically, Fischer attempts to show that if causal determinism rules out an agent’s moral responsibility, it is not in virtue of its eliminating the agent’s alternative possibilities. I contend that, once we focus upon the distinction between entailment and explanation, the incompatibilist defender of PAP can successfully rebut Fischer’s argument. I argue for this claim while granting Fischer a number of assumptions that only render a defense of PAP more difficult. Additionally, I cast doubt upon Palmer’s (Synthese 191:3847–3864, 2014) critique of Fischer’s argument, which in turn renders my defense of PAP all the more critical.