Literature on censorship in competitive authoritarian regimes identifies a simple tradeoff: muffling an opposition media outlet can reduce voters’ exposure to anti-incumbent news content, but may also erode the incumbent’s own ability to communicate. This characterization neglects indirect benefits and costs of censoring an opposition media outlet: collateral censorship. By weakening competition in media markets, the incumbent allows allied media outlets to further bend their editorial lines in his favor. But voters may punish the incumbent for restricting access to valued programming. We formalize this trade-off in a stylized Bayesian persuasion model that guides our analysis of the Venezuelan case. When the government of Hugo Chávez revoked the broadcast license of a major television station, voters without cable lost access. Using new data and a difference-in-differences design, we find that these voters punished Chávez at the polls—suggesting that the electoral cost of taking away popular programs exceeded the electoral benefits of restricting access to media criticism among voters without cable. But the decision may have helped Chávez in the electorate as a whole, by inducing favorable shifts in the editorial lines of other outlets. Our findings underscore the relevance of collateral censorship—indirect consequences of targeting opposition outlets—for media freedom in competitive authoritarian regimes.