An electronic device (such as an access point) that selectively provides a probe response is described. During operation, the electronic device receives a probe request from the second electronic device. Then, the electronic device determines whether one or more response criteria are met or achieved. For example, based at least in part on an identifier of the second electronic device, the electronic device may determine when the one or more response criteria are met by accessing a probe-activity history of the second electronic device that is stored in memory. If the one or more response criteria are met, the electronic device provides the probe response. Otherwise, the electronic device does not provide the probe response and the probe request may be dropped.