Communication complexity---the minimum amount of communication required---of computing a function of data held by several parties is studied. A communication model where silence is used to convey information is introduced. For this model the worst-case and average-case complexities of symmetric functions are studied. For binary-input functions the average- and worst-case complexities are determined and the protocols achieving them are described. For functions of non-binary inputs one-round communication, where each party is restricted to communicate in consecutive stages, is considered and the extra amount of communication required by one- over multi-round communication is analyzed. For the special case of ternary-input functions close lower and upper bounds on the worst-case one-round complexity are provided and protocols achieving them are described. Protocols achieving the average-case one-round complexity for ternary-input functions are also described. These protocols can be generalized to inputs of arbitrary size.