Can voters be persuaded by referendum campaigns? This article develops a theoretical model that synthesises the existing literature on campaign effects and issue-voting by arguing that the strength of pre-existing attitudes conditions voter receptivity to campaign arguments, thereby also determining their eventual vote choice. Using original panel data for the 2015 Danish opt-out referendum, there is evidence that attitude strength matters for whether voters are responsive to persuasion during campaigns. The article finds that voters with the most strongly-held attitudes felt well informed and certain about the consequences of the vote even before the start of the campaign, whereas voters with moderately-held attitudes are found to be more prone to believe those campaign arguments that are consistent with their EU attitudes, changing their vote intentions accordingly. Finally, voters with weakly-held attitudes were equally persuadable for the No and the Yes side of the campaign, but they are also the least pre-disposed to pay attention to campaign messages. The conclusions discuss the broader implications of the findings for our understanding of EU referendum campaigns.