Empirical studies have shown that terrorists' policy goals are rarely achieved, leading some to conclude that terrorism doesn't work. We theorize that terrorism works, but for its supporters rather than for the terrorists themselves. Because supporters are willing to contribute resources to a terrorist organization, thereby increasing the terrorist organization's ability to launch attacks, this will coerce the targeted government to revise its policies in accordance with the supporters' preferences. Targeted governments respond with concessions in order to erode support and thereby render the terrorists easier to defeat. Support can be rational even when, as is empirically likely, supporters' ideal policies are closer to those of the government than to those of the terrorists. We examine six campaigns generally regarded as unambiguous failures of terrorism. For each, we show that governments made concessions that placated the supporters but not the terrorists, and that this was followed by successful suppression of the weakened terrorists.