People with extreme political opinions are alternatively characterized as being relatively unthinking or as confident consumers and practitioners of politics. In three studies, we tested these competing hypotheses using cognitive anchoring tasks (total N = 6,767). Using two different measures of political extremity, we found that extremists were less influenced than political moderates by two types of experimenter-generated anchors (Studies 1–3) and that this result was mediated by extremists’ belief superiority (Study 2). Extremists and moderates, however, were not differentially influenced by self-generated anchors (Study 2), which suggests that extremists differentiated between externally and internally generated anchors. These results are consistent with the confident-extremist perspective and contradict the unthinking-extremist perspective. The present studies demonstrate the utility of adopting a basic cognitive task to investigate the relationship between ideology and cognitive style and suggest that extremity does not necessarily beget irrationality.