In surveys, Europeans routinely express high levels of support for a common security and defence policy of the European Union. Do these responses reflect real demands or superficial support that would crumble if the issue was politicised? This article provides new answers to this question. We conducted pre-registered survey experiments with more than 40,000 respondents from 25 European countries in which we randomly varied whether respondents received information about potential costs of two hypothetical cooperative activities: military operations and defence procurement. Support for these activities was systematically lower when costs were mentioned. We conclude that, in the event of politicisation, there is considerable potential for shifts in opinion and that caution is required in deriving a mandate for specific activities from high approval rates for cooperation in general.