The article analyses violations of the Obligatory Contour Principle (OCP) above the word level in Tswana, a Southern Bantu language, by investigating the realization of adjacent lexical high tones across word boundaries. The results show that across word boundaries downstep (i.e. a lowering of the second in a series of adjacent high tones) only takes place within a phonological phrase. A phonological phrase break blocks downstep, even when the necessary tonal configuration is met. A phrase-based account is adopted in order to account for the occurrence of downstep. Our study confirms a pattern previously reported for the closely related language Southern Sotho and provides controlled, empirical data from Tswana, based on read speech of twelve speakers which has been analysed auditorily by two annotators as well as acoustically.