What semantic and pragmatic constraints are placed on the conjunction of DP quantifiers by the contrastive conjunction but? Based on the results of an experimental investigation, this paper argues that but-conjunction of quantifiers is felicitous only if the quantifiers are semantically disjoint. The paper proposes that this constraint follows from a theory of how contrastive sentences with but engage with and resolve extant Questions Under Discussion. The paper argues against previous analyses of the phenomenon which argue that but-conjunction of quantifiers is constrained by the monotonicity of the two quantifiers.