Species that are frequently introduced to an exotic range have a high potential of becoming invasive. Besides propagule pressure, however, no other generally strong determinant of invasion success is known. Although evidence has accumulated that human affiliates (domesticates, pets, human commensals) also have high invasion success, existing studies do not distinguish whether this success can be completely explained by or is partly independent of propagule pressure. Here, we analyze both factors independently, propagule pressure and human affiliation. We also consider a third factor directly related to humans, hunting, and 17 traits on each species' population size and extent, diet, body size, and life history. Our dataset includes all 2362 freshwater fish, mammals, and birds native to Europe or North America. In contrast to most previous studies, we look at the complete invasion process consisting of (1) introduction, (2) establishment, and (3) spread. In this way, we not only consider which of the introduced species became invasive but also which species were introduced. Of the 20 factors tested, propagule pressure and human affiliation were the two strongest determinants of invasion success across all taxa and steps. This was true for multivariate analyses that account for intercorrelations among variables as well as univariate analyses, suggesting that human affiliation influenced invasion success independently of propagule pressure. Some factors affected the different steps of the invasion process antagonistically. For example, game species were much more likely to be introduced to an exotic continent than nonhunted species but tended to be less likely to establish themselves and spread. Such antagonistic effects show the importance of considering the complete invasion process.