An electronic device is described. This electronic device may associate with a second electronic device (such as an access point) in a WLAN. While associating or associated with the second electronic device, the electronic device may receive, from the second electronic device, an AID corresponding to the electronic device for use when communicating frames in the WLAN. Moreover, while associated with the second electronic device, the electronic device may obtain a second AID corresponding to the electronic device for use when communicating second frames in the WLAN, where the associating includes replacing the AID with the second AID. Note that obtaining the second AID may include: the electronic device selecting the second AID from a predefined set of AIDs, which were previously received from the second electronic device; or the electronic device receiving, from the second electronic device, the second AID.