Pre-print, Working paper: We propose and construct novel measures of the effectiveness and potential of trade blocs, combining estimation with granular data and simulation with a New Quantitative Trade Model. We deploy our methods and new indexes to quantify the potential benefits from (i) further integration within the largest and most successful trade liberalization effort in the world -the Single European Market -and (ii) a possible enlargement. Three main results and implications stand out from our analysis. First, European integration has been very effective in promoting trade among its members, with heterogeneous effects across industries and member states. Second, and most novel and important, our estimates reveal that only half of the potential benefits from EU membership have been realized to date. Third, EU accession will generate very large gains from trade for the new joiners and moderate gains for existing members, with larger benefits for some small and peripheral EU members. Importantly, our methods enable us to construct confidence bounds for the effects of EU enlargement.