A method for communication includes, during a call conducted among two or more subscribers in a circuit-switched network, which operates in accordance with a first communication protocol that manages calls among the subscribers by exchanging discrete events among elements of the circuit-switched network, receiving from the circuit-switched network a sequence of the events related to the call. Based on the sequence of the events, at least one emulated communication session is generated in a packet-switched network that operates in accordance with a second communication protocol. Multiple call services are provided to the call conducted in the circuit-switched network from the packet-switched network by cascading multiple service sessions, each providing a respective one of the call services, in the packet-switched network responsively to the emulated communication session.