Existing research (Muller, Jenny, Ecker 2012) shows that several aspects of strenthening EU integration and fostering its supranational governance are practically uncontroversial and elicit broad support among national political elites and masses. On some other accounts, related to the EU governance and Europeanness, the gap between elites and masses is more pronounced (Matonyte, Morkevicius 2013). Seemingly, these gaps are mostly in the instensity of the support and self-identification with Europe rather than gaps created by the conflicting feelings and views of elites and masses. Yet, the „constraining dissensus“ (Hooghe, Marks 2008) thesis should be better scrutinized. In this paper we examine the scope and explanatory factors of the eventual inconguence between elites‘ and masses attitudes towards supranational governance in six particular public policy areas (fighting unemployment, immigration, environment, fight against crime, health care and agriculture). We use comparative data from a big scale quantitative survey (Intune project) and Eurobarometer.