The European Commission's Target Electricity Model (TEM) aims to integrate EU electricity markets. This paper estimates the potential benefit of coupling interconnectors to increase the efficiency of trading day-ahead, intra-day and balancing services across borders. Further gains are possible by eliminating unscheduled flows and avoiding the curtailment of renewables with better market design. In the short run the gains could be as high as €3.9 billion/yr, more than 100% of the current gains from trade. About one-quarter of this total comes from day-ahead coupling and another third from shared balancing. If shared balancing is so valuable, completing the TEM becomes more urgent, and regulators should ensure these gains are paid to interconnectors to make the needed investment in the cross-border links more commercially profitable.