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An increasingly popular view is that abstracta are thin—their existence alone makes little or no demand on the world. The most sophisticated defence of this view to date is the version of abstractionism found in Linnebo’s recent book Thin Objects (2018). On this view, good abstraction principles should be understood as involving claims about asymmetric metaphysical dependencies between abstracta (e.g., directions, letter types, sets) and more familiar objects (e.g., lines, letter tokens, pluralities). In many ways, such a view is a highly promising development of more traditional versions of abstractionism. However, in this paper, I argue that it, and any view sufficiently like it, should ultimately be rejected, since it cannot adequately respond to a neglected explanatory challenge—what I call the characterisation challenge. This is the demand that any theory of abstracta should accommodate explanations for why abstracta are the way they are. In short, I argue that the nature of abstracta problematically outstrips the explanatory resources available to this kind of ‘metaphysically serious’ abstractionism.