According to the principle of alternative possibilities (PAP), people are morally responsible for what they do only if they could have done otherwise. Over the last few decades, this principle has dominated discussions of free will and moral responsibility. One important strand of this discussion concerns the Frankfurt-type cases or Frankfurt cases, originally developed by Frankfurt (J Philos 66:829–839, 1969), which are alleged counterexamples to PAP. One way in which proponents of PAP have responded to these purported counterexamples is by arguing that they fall prey to a dilemma, both horns of which undermine their cogency. Recently, Fischer (Philos Rev 119: 315–336, 2010) has defended the Frankfurt cases against one horn of this dilemma. In this essay, I criticize Fischer’s defense of the Frankfurt cases and argue that he does not successfully show how the cases can avoid this horn of the dilemma. If I am right, then, despite Fischer’s claims to the contrary, the original dilemma plaguing the cases still stands.