This article explores how different anti-establishment parties (AEPs) can themselves strategically enact an image of both distinctiveness and ‘normality’ behind their political offer. For this purpose, we directly measure and map diverse anti-establishment normalisation strategies by analysing 142 social media campaigns of radical right, left, and ‘centrist’ AEPs and their conventional competitors during 23 elections in Europe during 2010–2019. We find that while AEPs presented themselves as fundamentally distinct from ‘politics as usual’, they simultaneously attempted to normalise their contestation supply across and within two dimensions: mainstreaming and streamlining. Using regression analysis, we further find that the degree to which AEPs rhetorically normalised their supply was positively and significantly associated with their broader electoral appeal ceteris paribus, controlling for substantive issue positions, parliamentary experience and position in government. Concurrently, the effects of particular normalisation strategies and their specific calibration varied for the radical right and left. The findings deepen our comparative understanding of diverse anti-establishment strategies used in party competition.