A major problem we humans have in the engineering of complex, computer-based systems is understanding and defining how the required behaviour of a whole system is to be achieved by its components, without becoming lost in component-centric details such as internal state machines and intercomponent messages. This paper proposes and illustrates a modelling methodology for overcoming such problem that proceeds, in a systematic and traceable manner, from UCM models (use case maps), to MSC models (message sequence charts), to ROOM-style communicating-state-machine models. For concreteness in a limited space, the method is illustrated by a simple example that is not representative of the complex kinds of systems we have in mind.