This paper provides a semantic analysis of English rise-fall-rise (RFR) intonation as a focus quantifier over assertable alternative propositions. I locate RFR meaning in the conventional implicature dimension, and propose that its effect is calculated late within a dynamic model. With a minimum of machinery, this account captures disambiguation and scalar effects, as well as interactions with other focus operators like ‘only’ and clefts. Double focus data further support the analysis, and lead to a rejection of Ward and Hirschberg’s (Language (...) 61:747–776, 1985) claim that RFR never disambiguates. Finally, I draw out connections between RFR and contrastive topic (CT) intonation (Büring, Linguist Philos 26:511–545, 2003), and show that RFR cannot simply be reduced to a sub-case of CT. (shrink)