I shall show how to generate models for the pi-calculus as free algebras for an equational theory; where the theory has separate components for name creation, communication of names over channels, and nondeterminism. This provides a modular characterisation of pi-calculus models, full abstraction for bisimulation congruence, a Moggi-style computational monad, and the bonus of an accompanying modal logic. The only tricky part is that it all has to be done within the functor category Set^I, using some general results of Power and Plotkin about enriched Lawvere theories.