External pressures to comply with EU rules have allegedly eroded the opportunities of national governments to autonomously adopt and implement policies and respond to national constituencies. Conversely, flexible supranational policies enable governments to implement the most appropriate policy options and respond to the demands of citizens. Moreover, the increased competences of the EU are coupled with differentiation, where EU legislation does not equally apply to all countries.Currently, we lack understanding whether flexibility and differentiation at the EU level contribute to autonomous and responsive policies in the EU countries. This study fills this gap by developing and testing a new theoretical framework about the relationship between EU-level differentiation and national policy implementation. In particular, I expect and find that differentiation resulting from capacity limitations constrains national policies more than differentiation driven by sovereignty concerns. This is because low-capacity governments that are excluded from EU policies have reputational incentives to demonstrate full convergence to the EU demands even when these diverge from national preferences. The results are based on a unique data set on the implementation of immigration, asylum and Schengen directives in 27 countries. The findings have important implications for the alleged trade-off between EU integration and national sovereignty.