The Oxford Handbook of Compounding surveys a variety of theoretical and descriptive issues, presenting overviews of compounding in a number of frameworks and sketches of compounding in a number of languages. Much of the book deals with Germanic noun–noun compounding. I take up some of the theoretical questions raised surrounding such constructions, in particular, the notion of attributive modification in noun-headed compounds. I focus on two issues. The first is the semantic relation between the head noun and its nominal modifier. Several authors repeat the argument that there is a small(-ish) fixed number of general semantic relations in noun–noun compounds (‘Lees's solution’), but I argue that the correct way to look at such compounds is what I call ‘Downing's solution’, in which we assume that the relation is specified pragmatically, and hence could be any relation at all. The second issue is the way that adjectives modify nouns inside compounds. Although there are languages in which compounded adjectives modify just as they do in phrases (Chukchee, Arleplog Swedish), in general the adjective has a classifier role and not that of a compositional attributive modifier. Thus, even if an English (or German) adjective–noun compound looks compositional, it isn't.