That the Lisbon Treaty lays the foundation for a supranational asylum and immigration policyis surprising, even more so for Liberal Intergovernmentalism (LI), whose founder AndrewMoravcsik predicts that no such development will take place. While the article uses LI as its pointof departure, it shows that it runs into problems with regards to the policy area of asylum andimmigration. The article therefore turns to the (neo-)functionalist concept of spillover. Whileworking with the concept, it was deemed necessary to create a more coherent typology ofdifferent spillovers. The article suggests that the concept of spillover may be both descriptiveand explanatory. With regards to descriptive spillover, it seems valuable to differentiate betweenwidening and deepening spillovers, but concerning explanatory spillovers, more options becamevisible: there are unintended or intended functional spillovers, as well as unintended political,cultivated and social spillovers. The argument is illustrated through a detailed study of Sweden – a‘reluctant European’ that within the area of asylum and immigration made a fundamental U-turnwith regards to a supranationalism, a change that can be described as a social spillover.