Often political races are not really competitive, and the path to reelection is smooth for many incumbents. In two-candidate races for office we suggest the introduction of a new re-election rule, which we call the “Score-replication Rule.” This rule requires that, to be reelected, any incumbent has to obtain a percentage of votes that is at least as high as the highest vote-share he/she obtained in any previous election (reduced by some margin). Such a delimiter would restrain negative “incumbency advantages,” and render reelection competitive again. It could also reduce polarization in the United States Congress. Moreover, we suggest how history-bound reelections could be used in European-style proportional election systems.