Use cases are a powerful and widely recognised tool for functional requirements elicitation and specification of prospective software applications. However, there still are major problems and misunderstandings about the use case approach. One of these is the troublesome notion of use case interleaving which is discussed in this work. Interleaving is still present in the current UML specification. A. Simons correctly realised that interleaving compares with goto/comefrom semantics that were already judged harmful by Dijkstra at the emergence of the Structured Programming era. Simons, thus, has requested the explicit dropping of interleaving semantics. The authors give further support for Simons’ request by showing that interleaving causes severe inconsistencies within UML and contradicts other proven and practically relevant use case concepts such as Goal-Based Use Cases of A. Cockburn, and contractual specifications of use cases expressed by pre- and postcondition approaches. Significant fixes to UML are proposed, in addition to those suggested by Simons. These will dramatically clarify prevailing problems and confusion with use cases and use case relationships among both practitioners and researchers.