Two advanced group-based voice services, known as Push-to-Conference (P2C) and Push-to-Message (P2M) services are provided by a real-time exchange (RTX) that interfaces to the wireless network. The RTX provides a full-duplex Push-to-Conference (P2C) session between an initiator and two or more other participants, wherein the P2C session comprises a full-duplex conference call, and both the real time exchange and handsets participating in the P2C session communicate with each other using call setup and in-band signaling within the wireless network. The realtime exchange may be coupled to and work with a Push-to-Message (P2M) server to deliver multimedia messages in a non-real time manner from an originator to one or more recipients, without establishing voice paths between the originator and recipients, wherein the P2M server, and an optional Voice Mail Server, provide a message storage facility for the multimedia messages. Additionally, a technique based on handset speech buffering permits zero delay call set-ups to be achieved.