Consumers generally prefer scarce products, which has been related to their exclusiveness. Currently scarce products, however, are not necessarily exclusive, but could be scarce because many other consumers previously bought them. We propose that consumers also prefer scarce products in this situation, which an appeal to uniqueness cannot explain. Three experiments support our predictions and reveal that scarcity effects even occur when consumers only see traces of others' behavior through emptied shelf space. Furthermore, this bandwagon effect disappears when uniqueness is threatened due to others in close spatial distance.