Pereboom on the Frankfurt cases

According to the principle of alternative possibilities (PAP), a person is morally responsible for what he has done only if he could have done otherwise. In what follows, I want to defend this principle against an apparent counterexample offered recently by Derk Pereboom (Living without free will, 2001; Midwest Studies in Philosophy, 29:228-247, 2005). Pereboom's case, a variant of what are known as 'Frankfurt cases,' is important for it attempts to overcome a dilemma posed for earlier alleged counterexamples to PAP. However, I will argue that by paying closer attention to the details of Pereboom's example, we see that his example fails to show a way between the horns of the dilemma posed for the earlier Frankfurt examples.