Four experiments investigated 4-year-olds' understanding of adjective-noun compositionality and their sensitivity to statistics when interpreting scalar adjectives. In Experiments 1 and 2, children selected "tall" and "short" items from 9 novel objects called "pimwits" (1-9 in. in height) or from this array plus 4 taller or shorter distractor objects of the same kind. Changing the height distributions of the sets shifted children's "tall" and "short" judgments. However, when distractors differed in name and surface features from targets, in Experiment 3, judgments did not shift. In Experiment 4, dissimilar distractors did affect judgments when they received the same name as targets. It is concluded that 4-year-olds deploy a compositional semantics that is sensitive to statistics and mediated by linguistic labels.