Much of the recent philosophical discussion about free will has been focused on whether compatibilists can adequately defend how a determined agent could exercise the type of free will that would enable the agent to be morally responsible in what has been called the basic desert sense (see, e.g., Pereboom in Living without free will, Cambridge University Press, New York, 2001; Pereboom in Free will, agency, and meaning in life, Oxford University Press, Oxford, 2014; Strawson in Freedom and belief, Oxford University Press, Oxford, 1986; Strawson in Philos Stud 75(1):5–24, 1994; Fischer in Four views on free will, Wiley, Hoboken, 2007; Vargas in Four views on free will, Wiley, Hoboken, 2007; Vargas in Philos Stud, 144(1):45–62, 2009). While we agree with Derk Pereboom and others that the compatibilist’s burden should be properly understood as providing a compelling account of how a determined agent could be morally responsible in the basic desert sense, the exact nature of this burden has been rendered somewhat unclear by the fact that there has been no definitive account given as to what the basic desert sense of moral responsibility amounts to. In Sect. 1 we set out to clarify the compatibilist’s burden by presenting our account of basic desert moral responsibility—which we call retributivist desert moral responsibility for purposes of clarity—and explain why it is of central philosophical and practical importance to the free will debate. In Sect. 2 we employ a thought experiment to illustrate the kind of difficulty that compatibilists of any stripe are likely to encounter in attempting to explain how determined agents can exercise the kind of free will needed for retributivist desert moral responsibility.