Embodiment is typically given insufficient weight in debates concerning the moral status of Novel Synthetic Beings (NSBs) such as sentient or sapient Artificial Intelligences (AIs). Discussion usually turns on whether AIs are conscious or self-aware, but this does not exhaust what is morally relevant. Since moral agency encompasses what a being wants to do, the means by which it enacts choices in the world is a feature of such agency. In determining the moral status of NSBs and our obligations to them, therefore, we must consider how their corporeality shapes their options, preferences, values, and is constitutive of their moral universe. Analysing AI embodiment and the coupling between cognition and world, the paper shows why determination of moral status is only sensible in terms of the whole being, rather than mental sophistication alone, and why failure to do this leads to an impoverished account of our obligations to such NSBs.