In recent years, UML has become a standard language for modeling software requirements and design. In this paper we investigate the suitability of UML as a semiformal requirements specification language. Using the Teleservices and Remote Medical Care (TRMCS) case study as an example, we identify and demonstrate various problems and deficiencies of UML, particularly concerning use case models and system decomposition. We also investigate whether and how the deficiencies can be overcome and how potential alternatives could look.