In this paper we develop a sound and complete type and behaviour inference algorithm for a fragment of CML (Standard ML with primitives for concurrency). Behaviours resemble terms of a process algebra and yield a concise representation of the communications taking place during execution; types are mostly as usual except that function ypes and ‘delayed communication types’ are labelled by behaviours expressing the communications that will take place if the function is applied or the delayed action is activated. The development of the present paper improves a previously published algorithm in achieving completeness as well as soundness; this is due to an alternative strategy for generalising over types and behaviours.