Political scientists have long asserted that populists use simpler language than their mainstream rivals to appeal to ordinary people and distance themselves from elites. However, there is little comparative evidence in support of that claim. In this study, we investigate the linguistic simplicity of four right-wing populists compared to their principal opponents in the United States, France, United Kingdom, and Italy. We do so by analysing a corpus of approximately one million words from leaders’ speeches, using a series of linguistics measures for evaluating simplicity. Contrary to expectations, we find that Donald Trump was only slightly simpler than Hillary Clinton, while Nigel Farage in the UK and Marine Le Pen in France were more complex than their main rivals, and Italy’s Matteo Salvini was simpler on some measures but not others. We conclude that the simple language claim is not borne out and that other aspects of the received wisdom about populism should be re-examined.