A problem with recent work about the relationship between metaphysics and science, especially in the theorizing of those who identify as “naturalized metaphysicians”, is the spotty, metaphorical characterization of what it means for science to “constrain” metaphysics. The most robust account of scientific constraint on metaphysical theorizing is advanced by James Ladyman and Don Ross in their 2007 book Every Thing Must Go. Ladyman & Ross claim that the only legitimate metaphysical hypotheses are those that unify two previously disparate scientific explanations. I will critique Ladyman & Ross’ account of naturalized metaphysics (and, by extension, their view of science’s constraint on metaphysics), and offer an alternative view of naturalized metaphysics as a practice of constructing physically possible models of reality. This account yields a different view of science’s constraint on metaphysics, specifically, that models must be physically possible in order to be of methodological and heuristic use to scientists.