To what extent is the public backlash against European courts driven by substantive concerns over the outcomes of cases and/or procedural concerns over sovereignty? We conducted pre-registered survey experiments in Denmark, France, Poland, Spain, and the United Kingdom using three vignettes: a foreigner who faces extradition, a person fighting a fine for burning Qurans, and a home-owner contesting eviction. Each vignette varies whether a European court disagrees with a national court (deference treatment) and whether an applicant wins a case (outcome treatment). We find little evidence that interventionism influences support for compliance or court authority but ample evidence that case outcomes matter. This is even more so for respondents with nationalist and authoritarian leanings. Nationalist opposition to court decisions is not influenced by European court activism or even a mention of European courts, suggesting that backlash to domestic and international courts may be driven by similar forces. These findings have implications for our understanding of the authoritarian and nationalist challenges to (international) institutions and the legitimacy of international institutions. Moreover, they imply that international courts cannot resurrect their popularity through deference alone.