The state of American politics would be improved, many argue, if more moderate and qualified people served in government. We investigate what draws such individuals to run, focusing on a dimension of politics that has received scant attention within the candidate-entry literature—the ability of candidates, once elected, to exercise meaningful influence over policy. In a conjoint experiment, we find that the opportunity to wield greater authority differentially increases moderates’ interest in seeking office, and that more qualified people express more interest in running for offices with greater authority, lower thresholds for passing legislation, and higher staff support. These findings have implications for political representation, government effectiveness, and the relationship between institutional reform and mass politics.