Public discourse is increasingly concerned with the way that politicians communicate. This is fuelled by a new generation of politicians, such as Donald Trump, Boris Johnson, and representatives of populist parties, who evidently communicate less sophisticated than mainstream politicians. However, the question of whether and how linguistic styles affect citizens is largely unexplored. We argue that both citizens and politicians might benefit from simple political communication. First, mechanically, citizens should have a better chance to understand political positions if political discourse is less sophisticated. Second, linguistic simplicity can function as a heuristic for citizens by signaling that politicians are among the "people" instead of being part of the "elites". We test our arguments using a pre-registered three-wave vignette survey experiment in Germany (N = 5,800). Our findings show that simple messages (as compared to sophisticated messages) indeed increase citizens' comprehension of political positions. Moreover, we find that citizens use language sophistication as a heuristic to fill informational gaps about politicians. Politicians who communicate less sophisticated are perceived to have rather modest socioeconomic backgrounds. As a result, the use of simple language can benefit politicians' claims to belong to the people instead of the elite. Our findings add important new insights to our understanding of the effects of political communication in contemporary democracies.