This paper discusses several Slavic and Baltic dialects which have undergone stress shifts as a result of language contact. Two types of change are discussed: (1) stress retractions from the final syllable onto the initial syllable of a prosodic word, and (2) the rise of fixed stress replacing earlier free stress. It is argued that in all cases discussed in the paper, contact with a language with fixed initial stress caused a stress shift. Examples from Croatian and Lithuanian demonstrate that pitch contours played an important role in these shifts. The results of the shifts are not always identical, but the underlying mechanism is the same in each of these cases: the lexical pitch contour of the donor language was imposed on the target language, thereby introducing constraints on the position of stress in the target language. It is argued that a similar mechanism operated in West Slavic, where languages with free stress introduced fixed stress on the initial or penultimate syllable due to contact with German and possibly Hungarian.