A method is disclosed that enables the transmission of a digital message along with a corresponding media information signal, such as audio or video. A telecommunications device that is processing the information signal from its user, such as a speech signal, encodes the information signal by using a model-based compression coder. One such device is a telecommunications endpoint. Then, based on an evaluation of the perceptual significance of each encoded bit, or on some other meaningful characteristic of the signal, the endpoint's processor: (i) determines which encoded bits can be overwritten; and (ii) intersperses the digital message bits throughout the encoded signal in place of the overwritten bits. The endpoint then transmits those digital message bits as part of the encoded information signal. In this way, no additional bits are appended to the packet to be transmitted, thereby addressing the issue of compatibility with existing protocols and firewalls.