This paper argues that autonomic systems need to make their distributed monitoring adaptive in order to improve their “comprehensive” resulting quality; that means both the Quality of Service (QoS), and the Quality of Information (QoI). Thus, we propose a methodology to design monitoring adaptation based on high level objectives (goals) related to the management of quality requirements. One of the advantages of adopting a methodological approach, is that monitoring reconfiguration will be conducted through a consistent adaptation logic. Starting from a model-guided monitoring framework, we introduce our methodology to assist human administrators in eliciting the appropriate quality goals piloting the monitoring. Moreover, some monitoring adaptation patterns falling into reconfiguration dimensions are suggested and exploited in a cloud provider case-study illustrating the adaptation of Quality-Oriented monitoring.