Association of tones to prosodic trees was introduced in Pierrehumbert & Beckman (1988). This included: (i) tonal association to higher-level prosodic nodes such as intonational phrases, and (ii) multiple association of a tone to a higher-level prosodic node in addition to a tone bearing unit such as a syllable. Since then, these concepts have been broadly assumed in intonational phonology without much comment, even though Pierrehumbert & Beckman (1988)’s stipulation that tones associated to higher-level prosodic nodes are peripherally realized does not fit all the empirical data. We show that peripherally-realized tones associated to prosodic nodes can be naturally represented with bottom-up tree transducers. Additionally, multi bottom-up tree transducers provide a way to represent non-peripheral boundary tones and multiple tonal association, as well as multiple dependencies in prosodic structures in general, including prosodically-conditioned segmental allophony.