We propose a TCP window-size delegation method for TXOP Exchange applicable to the downlink in wireless access networks. In TXOP Exchange, the compliant stations (STAs) cooperatively use their available bandwidth in accordance with their required QoSs. TXOP Exchange was previously validated for the uplink. The proposed delegation method enables STAs to delegate their bandwidth for the downlink as well without requiring any modifications to the legacy access point or the STAs. Simulation demonstrated that this method works well.