From the perspective of Enterprise Shared Services, the definition of the Cloud as a standard three-layered service model (IaaS, PaaS, SaaS) to describe cloud computing, with each layer defined in terms of the operational control capabilities it offers to its consumers, is not optimal. Shared services have unique characteristics around ownership, funding and operations, and they span SaaS and PaaS layers. This article proposes a refinement to the three-layered Cloud categorization scheme that suits better the needs of Enterprise Shared Services.