A technique communicates data between a first client device and a second client device. The technique involves establishing a regular communications pathway from the first client device to the second client device through a communications server, and establishing a highly confidential communications pathway from the first client device to the second client device. The highly confidential communications pathway circumvents the communications server. The technique further involves, after the regular communications pathway and the highly confidential communications pathway are established, conveying highly sensitive information from the first client device to the second client device only through the highly confidential communications pathway to avoid exposing the highly sensitive data to the communications server through the regular communications pathway.