The Phenomenal Concept Strategy (PCS) offers the physicalist perhaps the most promising means of explaining why the connection between mental facts and physical facts appears to be contingent even though it is not. In this article, we show that the large body of evidence suggesting that our concepts are often embodied and grounded in sensorimotor systems speaks against standard forms of the PCS. We argue, nevertheless, that it is possible to formulate a novel version of the PCS that is thoroughly in keeping with embodied cognition, focuses on features of physical concepts, and succeeds in explaining the appearance of contingency.