The way in which language changes diffuse over space—geolinguistic diffusion—is a central problem of both historical linguistics and dialectology. Trudgill (1974) proposed that distance, population, and linguistic similarity are crucial factors in determining diffusion patterns. His hierarchical gravity model has made correct predictions about diffusion from London to East Anglia, but has never been tested across a national boundary. The aim of this article is to do so using data from both sides of the U.S.–Canada border. Two cases are examined: the non-diffusion of phonetic features from Detroit to Windsor and the gradual infiltration into Canadian English of American foreign (a) pronunciations. In both cases, the model makes incorrect predictions. In the first case, it is suggested that the model needs a term representing a border effect, and that the diffusion of phonetic features is constrained by structural, phonological factors; in the second, a traditional wave theory of diffusion appears to fit the data more closely than a hierarchical model.