We study changes in political discourse during campaigns, using a novel dataset of candidate websites for U.S. House elections, 2002-2016, and manifestos for French parliamentary and local elections, 1958-2022. We find that candidates move to the center in ideology and rhetorical complexity between the first round (or primary) and the second round (or general election). This convergence reflects candidates’ strategic adjustment to their competitor, as predicted by Downsian models of competition: Using an RDD, we show that candidates converge to the platform of opponents who narrowly qualified for the last round, as opposed to those who narrowly failed to qualify.