The fact that so many different kinds of coordination models and languages have been proposed suggests that no one single approach will be the best for all coordination problems. Different coordination styles exhibiting different properties may be more suitable for some problems than others. Like other architectural styles, coordination styles can be expressed in terms of components, connectors and composition rules. We propose an approach in which coordination styles are expressed as “component algebras”: components of various sorts can be combined using operators that realize their coordination, yielding other sorts of components. We show how several coordination styles can be defined and applied using Piccola, a small language for composing software components. We furthermore show how glue abstractions can be used to bridge coordination styles when more than one style is needed for a single application.