In order to reduce the power consumption after a transmitting electronic device in a wireless network has been detected, a receiving electronic device calculates transmit times of subsequent beacons from the transmitting electronic device based on a clock drift of the transmitting electronic device and the beacon period. Then, the receiving electronic device receives the subsequent beacon by opening scan windows that encompass the calculated transmit times. However, because the transmit times are more predictable after the transmitting electronic device has been detected (and the clock drift of the transmitting electronic device is known to the receiving electronic device), the receiving electronic device can reduce the width of the scan windows. In addition, the transmitting electronic device can further reduce the power consumption by increasing the beacon period.