Terrorism is tightly connected to the Muslim minority in the West, and this could lead to counterterrorism measures targeting Muslims specifically. This paper uses a unique survey experiment fielded in the US, France, Finland, and Norway to study the levels of support for targeting groups that vary in both their majority versus minority status and in their connection to terrorism. Threatening news stories are used to investigate whether or not the level of support is affected by right-wing extremist and Islamist terrorism. Finally, the moderating effect of attitudes toward immigration is studied. People support counterterrorism measures that target threatening groups (Islamists and right-wing extremists) more than those that do not (Muslims), but this is not the case for those people who are against immigration. When people read threatening news stories, there is an increase in support for counterterrorism measures in general, even measures that target groups unrelated to the stories.