In Silozi, High tones are subject to a number of different processes including shift, doubling and deletion. After establishing these on the basis of isolation forms and two-word phrases, this paper examines a range of complex phrases which reveals a very productive process of phrasal High insertion, whereby a High tone is inserted and linked to the final tone bearing unit of any phonological phrase which is not pre-pausal. Tonal processes are sensitive to lexical categories. It is shown, using Match Theory, that phonological phrase boundaries are established on the basis of syntactic phrases. While these prosodic phrase edges are targets for Phrasal High Insertion, the surface realization of the inserted High in these locations can in fact be blocked by the Obligatory Contour Principle. The blocking must consider whether the existing High precedes or follows the target of High Tone Insertion as well as the part of speech of the words on either side of the phonological phrase boundary. The phonological phrasing of a number of different types of pre- and post-verbal constituents is analysed. Finally, adverbs are examined in some detail. Some are shown to straightforwardly phrase with a preceding verb, some apart from a preceding verb, and a final set exhibiting mixed properties.