In many democracies, parties and their voters rely on competitive primary elections to choose nominees for the general election. Competitive primaries may help parties select higher quality candidates and advertise these candidates to voters, but they also run the risk of exposing nominees' flaws, offending losing candidates' supporters, and making the party look weak to general-election voters. Do longer, more competitive primaries help or harm parties in the general election? The existing literature on so-called divisive primaries comes to mixed conclusions, likely because of chronic issues of omitted variable bias and reverse causation. In this paper, we address these problems by taking advantage of U.S. states that use runoff primaries, second-round elections which, when triggered, create longer, more contentious primaries. Using a regression discontinuity design in primary elections close to the runoff threshold, we find large and negative effects of runoffs on the party's general-election fortune in the U.S. House and Senate. We estimate that going to a runoff decreases the party's general election vote share by 6-9 percentage points, on average, and decreases the probability that the party wins the general election by roughly 21 percentage points, on average. In U.S. state legislatures, in contrast, runoff primaries do not hurt, and in competitive contexts may in fact help, parties in the general election. The results suggest that divisive primary elections are highly damaging when salience is high but beneficial when salience is low, a pattern we argue is driven by the opposing effects of information in high vs. low salience primary elections.