The (dis)continuism debate in the philosophy and cognitive science of memory concerns whether remembering is continuous with episodic future thought and episodic counterfactual thought in being a form of constructive imagining. I argue that settling that dispute will hinge on whether the memory traces (or “engrams”) that support remembering impose arational, perception-like constraints that are too strong for remembering to constitute a kind of constructive imagining. In exploring that question, I articulate two conceptions of memory traces—the replay theory and the prop theory—that return conflicting answers to whether remembering is constructive imagining. The prop theory’s vision of traces is suggestive of continuism, while the replay theory’s is a natural fit for discontinuism. Which view of traces is in fact correct remains undetermined by current empirical work. Nevertheless, it may already be possible to reach a compromise in the (dis)continuism debate, through the development of a conciliatory continuist causal theory. This view—only outlined here—accepts the continuism-friendly prop theory of traces, while still requiring that genuine remembering fulfills an appropriate causation condition, as required by the kinds of causal theories of remembering typically favored by discontinuists.