Policymakers communicate complex messages to multiple audiences; we investigate how complexity impacts messages `getting through' effectively. We distinguish `semantic' complexity - the focus of existing empirical studies - from `conceptual' complexity, which better reflects information-processing costs identified by theory. We conduct an information-provision experiment using central bank communications; conceptual complexity - captured by a novel measure we construct - matters more for getting through, even for economics-trained individuals. Yet, recent Bank of England efforts to simplify language reduced traditional semantic measures, but conceptual complexity has actually increased. Our findings can direct efforts for effective policy communication design. (with Matthew Naylor)