One of the key issues facing the UK in the wake of the advisory referendum result to leave the European Union is the precise nature of its relationship with the European Union. At one extreme would be continued membership in the European Economic Area, including membership in the single market. Other options would be either no free trade agreement (FTA) with the EU at all or a less comprehensive FTA which stops short of single market membership. This paper compares the ability of EEA membership and less comprehensive FTAs to generate trade in goods and services. We investigate this question using empirical gravity model methodology and the most recent available data from 42 countries. We use recently developed econometric methods to deal with observations of zero trade flows and issues connected with endogeneity. The main finding is that while EEA membership is associated with substantial and statistically significant increases in bilateral services trade flows, membership in less comprehensive FTAs is not associated with any significant increase in bilateral services trade. For goods, EEA membership is associated with larger bilateral trade flows than are less comprehensive FTAs. These results suggest that it might be difficult to replace, on an exit from a European Union, lost trade flows with the EU by means of shallower FTAs with the EU or with third countries.