How do we gure out the fundamental nature of the world from a mathematically formulated physical theory? To gure out the nature of a world’s spacetime, we follow this rule: posit the least spacetime structure to the world that’s required by the fundamental dynamical laws. Applied to special relativity, for example, this rule tells us to not posit an absolute simultaneity structure. I suggest that we use this rule for more than just spacetime structure. We should also posit the least statespace structure required by the fundamental dynamical laws. This rule yields surprising conclusions. Applied to classical mechanics, it suggests that a world governed by the theory has less fundamental structure than we ordinarily think. For the theory’s statespace imparts less structure to a world’s physical space than we ordinarily think. This discussion bears on more general questions: the relation between the mathematical structure of a physical theory and the fundamental nature of a world governed by the theory; the relation between a theory’s statespace structure and its spacetime structure; what possibilities are distinguished by a theory; the difference between a world’s fundamental ontology and structure, and its nonfundamental ontology and structure; when two formulations of a theory are mere notational variants.