Taking their motivation from the perceived failure of the reductive physicalist project concerning consciousness, panpsychists ascribe subjectivity to fundamental material entities in order to account for macro-consciousness. But there exists an unresolved tension within the mainstream panpsychist position, the seriousness of which has yet to be appreciated. I capture this tension as a dilemma, and offer advice to panpsychists on how to resolve it. The dilemma is as follows: Panpsychists take the micro-material realm to feature phenomenal properties, plus micro-subjects to whom these properties belong. However, it is impossible to explain the generation of a macro-subject (like one of us) in terms of the assembly of micro-subjects, for, as I show, subjects cannot combine. Therefore the panpsychist explanatory project is derailed by the insistence that the world’s ultimate material constituents are subjects of experience. The panpsychist faces a choice of giving up her explanatory ambitions, or of giving up the claim that the ultimates are subjects. I argue that the latter option is preferable, leading to neutral monism, on which phenomenal qualities are irreducible but subjects are reducible. So panpsychists should be neutral monists.