DISA vs. G729 CoDec

I have configured my asterisk- PBX system with DISA. It works fine ONLY if the caller uses a G711 CoDec. With a G729 CoDec, the caller will hear nothing even though the incoming line is registered with the G729 CoDec as its default CoDec. Does anyone know if DISA will work with a G729 CoDec?