Bodily sensations are mental states typically suitable to be reported in judgments in which a first-person indexical is used to qualify the felt body. In other words, subjects typically have a sense of bodily ownership for the body that they feel in bodily sensations. This paper puts forward, firstly, three desiderata that theories on the sense of bodily ownership should meet. Secondly, it assesses two views that account for the sense of bodily ownership in terms of the spatial content of (...) bodily sensations, appealing to a notion of a sense of boundedness, and argues that they do not meet the goals defined. (shrink)