Summary: We show how the standard failures/divergences model for CSP can be extended by adding to each process' representation the set of all infinite traces it can perform. This allows a full and compositional treatment of unboundedly non-deterministic constructs such as \(\sqcap S\) and \(P\backslash X\) for infinite \(S\) and \(X\). By allowing unbounded non- determinism we lose two of the main properties of semantics we have become used to: completeness of the model and continuity of the language constructs. Thus the existence and analysis of fixed points required for recursion becomes much less straightforward than we are used to. A novel technique is used to demonstrate the existence of the fixed points: an operational semantics is constructed for unboundedly non-deterministic CSP and proved congruent to the denotational one. A corollary to this proof is the existence of the required fixed points. It also demonstrates that the least fixed point remains the natural denotation of a recursion, even though recursions no longer reach their fixed points in \(\omega\) iterations from \(\perp\).