One of the most intriguing facts about communication using quantum states is that these states cannot be used to transmit more classical bits than the number of qubits used, yet in some scenarios there are ways of conveying information with exponentially fewer qubits than possible classically [3, 26]. Moreover, these methods have a very simple structure--they involve only few message exchanges between the communicating parties. We consider the question as to whether every classical protocol may be transformed to a "simpler" quantum protocol--one that has similar efficiency, but uses fewer message exchanges. We show that for any constant k, there is a Supported by the EU 5th framework program QAIP IST