We introduce a type system for the π-calculus which is designed to guarantee that typable processes are well-behaved, namely they never produce a run-time error and, even if they may diverge, there is always a chance for them to łfinish their workž, i.e., to reduce to an idle process. The introduced type system is based on non-idempotent intersections, and is thus very powerful as for the class of processes it can capture. Indeed, despite the fact that the underlying property is Π 0 2-complete, there is a way to show that the system is complete, i.e., that any well-behaved process is typable, although for obvious reasons infinitely many derivations need to be considered.