A major stumbling block for non-reductive physicalism is Kim’s disjunctive property objection. In this paper I bring certain issues in sparse ontology to bear on the objection, in particular the theses of priority monism and priority pluralism. Priority pluralism (or something close to it, anyway) is a common ontological background assumption, so in the first part of the paper I consider whether the disjunctive property objection applies with equal force to non-reductive physicalism on the assumption that priority monism is instead true. I ultimately conclude that non-reductive physicalism still faces a comparable problem. In the second part, I argue, surprisingly enough, that what I call ‘fine-grained reductionism’, a particular version of which Kim proposes as an alternative to non-reductive physicalism, may work better in the monist framework than the pluralist one. I conclude that issues in sparse ontology, therefore, are more relevant to the debate about physicalism than one may have thought.