A person's body is extended in space, and parts of their body occupy spatial regions. In that way, the body has a dimension of breadth in space. Yet, there is another, less appreciated dimension of the body: its depth. Roughly speaking, the depth of the body is the level of abstraction of its parts. Characteristically, and in particular for moral purposes, the depth of the body is rather high-level. Low-level objects and properties, such as individual molecules, do not really fall within the purview of the moral body--the body as it figures in various morally significant rights and interests. As I will argue, the depth of the body becomes more salient and relevant when people come to have partly digital embodiments, such as when brain-computer interfaces are integrated into their bodily processes. The dimension of depth, it turns out, is crucial for properly understanding the moral significance of brain-computer interfaces. Here, I develop a theory of depth to complement existing theories of the body and use it to improve our understanding of the purview of bodily rights and interests.