Homogeneity effects with definite plurals have been argued to constitute a phenomena that is distinct from other types of truth-value gaps (Kriz, 2015; Kriz and Spector, 2021). This paper makes the case for a return to early accounts of homogeneity that treat it as a presupposition. I provide empirical support for this view by showing that homogeneity is sensitive to constraints on presupposition accommodation. I argue that connectedness (Enguehard and Chemla, 2021) mediates the distribution of local accommodation and that the differences between standard presuppositions and homogeneity are due to the fact that only the latter is non-connected (c.f. Fox (2018), which argues for an alternative based on plausibility considerations).