The disabled body has come to occupy more than an ‘absent presence’ in critical disability studies. Disability theory has addressed an original somatophobia through debates between social modellists, realists, phenomenologists, psychoanalysts and postconventionalists. We briefly trace these debates and then the present article considers two readings of non-normative impaired bodies. Through a focus on the embodiment stories of disabled children we consider those times when their bodies demonstrate some forms of ‘leakage, excess, lack or displacement’. Our first reading, ‘disability’, adopts a social psychoanalytic lens to alert us to the cultural constitution of the disabled body as lack. Our second reading, ‘possability’, adopts a postconventionalist stance and considers the disabled body as productively demanding imaginative theoretical and practical responses. We aim to explore the ways in which the impaired body can be embraced as a unique embodied entity through which to revise how bodies should and could be lived in. Our hope is that understanding these dual parallel processes allows us to keep together disability and possability as key elements of the difference of disability.