We reexamine cases of coordinated elements that do not match in syntactic category. We show that these fall into two types. The first type includes predicates, modifiers in the clausal domain, and such modifiers apparently coordinated with arguments. We argue that these do not actually involve coordination of unlike categories. The second type involves coordinated arguments of different categories. With this type, unlike the first, noninitial conjuncts may violate selectional restrictions. To account for these violations, researchers have typically posited a special status for the first conjunct in a coordinate structure, such that it alone can determine the category of the coordinate phrase. We show that such accounts are untenable. First, the final conjunct can be what matters for selection, if it is closest to the selecting or selected element. Second, category mismatches are not free, but are extremely limited and exactly match those observed in ellipsis and displacement. This calls for a uniform account of these mismatches, not one specific to coordination. We spell out such an analysis, in which displacement, ellipsis, and coordination permit certain categories to behave as certain other categories through their effects on null syntactic heads.