Dominant theories of counterinsurgency suggest that state forces must win over citizens to identify insurgents among them. Yet even where state forces are losing, polling shows consistently strong support for counterinsurgents. How can we explain this discrepancy? Dominant theories of counterinsurgency could be incorrect, or, as we posit, individuals systematically may falsify their reported preferences. This study builds on the intuition that individuals feel pressure to report consistently strong support for the military when asked directly, perhaps especially when they rely on an illegal organization or economy. We argue that this pressure decreases when individuals are asked indirectly, in a way that allows them to conceal their response. To assess, we randomize whether support for the military is measured directly and indirectly in a survey experiment in Colombia. We find lower rates of support with the indirect measure, and the difference is most pronounced in areas of insurgent control.