Copperbelt Bemba exhibits several rightward spreading tonal processes which are sensitive to prosodic phrase structure. The rightmost H tone in a word will undergo unbounded spreading if the word is final in a phonological phrase (φ). In an intonational phrase consisting of several single-word φ's, the rightmost H in the first word will spread through all following toneless φ's. From a rule-based perspective, this can only be accounted for by positing mutually feeding iterative rules, as a single H-tone spreading rule cannot account for the long-distance spreading. Rather, a second rule that spreads a H from the final mora of one word onto the initial mora of the following word is required, as a bridge to further unbounded spreading. Three phrase-sensitive OT constraints are proposed to account for H-tone spreading between words. One is of the domain-juncture variety, requiring the specification of two separate prosodic domains.