Heim (1979) observed that sentences like "John guessed the price that Mary guessed" are ambiguous between a reading in which John and Mary have guessed the same price (Reading A) and a reading in which John has guessed what price it is that Mary guessed (Reading B). However, in Antecedent Contained Deletion contexts, Reading B disappears—the sentence "John guessed the price that Mary did" can only mean that John and Mary have guessed the same price. To account for this contrast, this paper argues that Reading A and Reading B are derived from different relative clause structures: Reading A from a Matching structure and Reading B from a Raising one. In addition, this paper provides novel evidence corroborating this claim, and shows that numerous, independently developed diagnostics of Matching and Raising structures pattern as expected (Bhatt, 2002; Hulsey & Sauerland, 2006). The paper concludes by sketching how the different relative clause structures might yield different representations for interpretation under a semantics that posits situation variables in the syntax (Percus, 2000).