Fat, in the context of dissection, is a nuisance, an obstruction to anatomical order and orientation. Yet it makes up a large part of the human body, and in the practice of dissection becomes one of the most prominent materials in the room, as it sticks to gloves and spreads through the dissection hall, making chairs greasy and instruments slippery. In this article I explore the role and significance of fat tissue in anatomical dissection for medical students. In anatomy, fat remains largely an excess material; something superfluous, insignificant, left-over when the body is turned into an anatomical body consisting of muscles, nerves, blood vessels, and bones, cleaned and displayable. But fat is also something which appears in experience as excessive, omnipresent, proliferating, and resistant to attempts to keep it in order. Much anthropological work within dissection practices has described the process of ‘cleaning’ the bodies, but often—mirroring medicine—these accounts follow the becoming of the anatomical body and leave the fat behind. In this article, I try to ‘stick with’ the fat and suggest that fat tissue, as an embodiment or material manifestation of the more-than-anatomical-body, may tell us something about bodies, subjectivity, scientific order, and dissection.