A game of herding with capacity constraints is studied experimentally. Differences between Level-k strategies depend on the cost of choosing an alternative that has reached capacity, with a maximum difference between Level-1 and higher levels when the cost is high. This design makes Level-1 behavior relatively easy to identify. Though strategies consistent with higher levels are also found, a substantial proportion of observed strategies are consistent with Level-1. Within-subject correlations across settings suggest that Level-1 thinking can explain overweighting of private information in herding games. In addition, evidence of a correlation between cognitive ability and level of thinking is found.