This article presents an argument from ellipsis parallelism that traces of all types of movement receive a bound variable interpretation at LF. MaxElide, a constraint on ellipsis, is used to probe the size of parallelism domains and detect the semantic contribution of a variety of traces. The data examined reveal a detailed interaction between wh -movement from various positions, T-to-C movement, and movement of subjects. I offer an analysis based on the overlapping variable-binder relationships created by these movements. The theoretical conclusion is that Ā-, A-, and head movement all produce traces that feed interpretation. This conclusion argues directly against several proposals that deprive non-Ā movements of (certain) semantic effects—for example, proposals that head movement occurs at PF, or that A-movement does not leave traces.