In the literature, English rise-fall-rise (RFR) intonation is known both as a marker of secondary information and as a marker of topics. This paper aims to make plausible that these two uses can be derived from a common core, which in turn can be derived from a recent theory of intonational meaning more generally, according to which rises and falls indicate (non-)compliance with the maxims (Westera 2013, 2014, 2017). The core meaning of RFR, I propose, is that the main question under discussion (Qud) is not compliantly addressed, while some secondary Qud is. Several more concrete predictions are derived from this core meaning, pertaining to secondary information, topic marking, exhaustivity, and discourse strategies. The resulting account is shown to generate certain ingredients of existing accounts, while also doing some things differently in ways that may be empirically accurate. If the proposed account is on the right track, it provides an important new intonational window on Quds.