This paper argues that when movement maps onto a λ-bound variable (a ‘trace’), that variable must be of an individual semantic type, e.g. type e and type d. Thus, even though natural language has expressions of higher types, these expressions cannot be represented as traces. When an individual-type trace would not be able to semantically compose in the launching site of movement, the moved element is forced to syntactically reconstruct. The motivation for this constraint on traces comes from a detailed investigation of how DPs in their different semantic guises—entities, properties, and generalized quantifiers—are interpreted when they move. I then argue that strong definite descriptions exhibit the same type-based restriction, namely they cannot occur in higher-type positions, which I take as evidence for the theory that traces are definite descriptions.