We tackle this question in the context of Mexico's "war on drugs". In three experimental studies, we assess the presence of human costs in a military operation against a drug lord and present arguments either justifying or condemning these costs. We consistently find that, even in successful operations, Mexicans’ support for militarization decreases when military operations involve civilian casualties, but not when casualties are cartel-related. This finding holds both for victims and non-victims of cartel-related violence. These and other findings shed light on the public opinion side of the militarization of security debate, with important implications for security policy reform and democratic politics in Latin America and beyond.