While predicates in taxonomies (e.g. colour terms) are interpreted as mutually incompatible, this paper shows that their incompatibility is in many cases not lexical. Rather, it is the result of a previously undescribed exhaustivity effect. What is more, this class of exhaustivity effects displays novel behaviour. Exhaustivity is both obligatory and tightly constrained: at first approximation, any taxonomic predicate must be in the immediate scope of the exhaustivity operator it requires. Taxonomic predicates, in this sense, are argued to "control" exhaustivity.