An interface circuit in an electronic device (such as an access point) may provide a targeted wake-up time (TWT) service period (SP) schedule to a recipient electronic device. During operation the interface circuit may receive a TWT setup request associated with the recipient electronic device, where the TWT setup request includes non-availability information specifying one or more times when the recipient electronic device will be unavailable. For example, the non-availability information may include one or more times when the recipient electronic device has limited ability to transmit and/or receive. The interface circuit may provide a TWT setup response for the recipient electronic device, where the TWT setup response includes information specifying the TWT SP schedule for the recipient electronic device that includes at least one of: a TWT SP start time, a TWT SP duration, or an interval between TWT SPs.