A growing number of OECD countries are leaning toward adopting quality-selective immigration policies. The underlying assumption behind such policies is that more skill-selection should raise immigrants' average quality (or education level). This view tends to neglect two important dynamic effects: the role of migration networks, which could reduce immigrants' quality, and the responsiveness of education decisions to the prospects of migration. Our model shows that migration networks and immigrants' quality can be positively associated under a set of sufficient conditions regarding the degree of selectivity of immigration policies, the initial pattern of migrants' self-selection on education, and the way time-equivalent migration costs by education level relate to networks. The results imply that the relationship between networks and immigrants' quality should vary with the degree of selectivity of immigration policies at destination. Empirical evidence presented as background motivation for this paper suggests that this is indeed the case.