This paper contributes to the solution of the problem of transforming a process model with an arbitrary topology into an equivalent structured process model. In particular, this paper addresses the subclass of process models that have no equivalent well-structured representation but which, nevertheless, can be partially structured into their maximally-structured representation. The structuring is performed under a behavioral equivalence notion that preserves observed concurrency of tasks in equivalent process models. The paper gives a full characterization of the subclass of acyclic process models that have no equivalent well-structured representation but do have an equivalent maximally-structured one, as well as proposes a complete structuring method.