Loose coupling is often quoted as a desirable property of systems architectures. One of the main goals of building systems using Web technologies is to achieve loose coupling. However, given the lack of a widely accepted definition of this term, it becomes hard to use coupling as a criterion to evaluate alternative Web technology choices, as all options may exhibit, and claim to provide, some kind of "loose" coupling effects. This paper presents a systematic study of the degree of coupling found in service-oriented systems based on a multi-faceted approach. Thanks to the metric introduced in this paper, coupling is no longer a one-dimensional concept with loose coupling found somewhere in between tight coupling and no coupling. The paper shows how the metric can be applied to real-world examples in order to support and improve the design process of service-oriented systems.