Organizations are struggling to move and manage their IT Services and/or IT-enabled Services to the Cloud, slowing the adoption of Cloud services. In our research we intend to help organizations adopt Cloud services and demystify fears and concerns. In order to accomplish this, we propose a method based on the Outsourcing Lifecycle and the continuous approach of the Capability Maturity Model Integrated (CMMI) models, resulting in a Cloud Maturity Model. The model allows organizations to know which processes need to be performed, and how they should be improved when moving and managing services in the Cloud. To evaluate the Cloud Maturity Model we performed a set of twelve semi-structured interviews with seven Cloud clients and five suppliers. Although some changes were suggested, the interviews allowed us to conclude that the model was accepted by the interviewees.