The current document is directed to methods and systems that employ distributed-computer-system metrics collected by one or more distributed-computer-system metrics-collection services, call traces collected by one or more call-trace services, and attribute values for distributed-computer-system components to identify attribute dimensions related to anomalous behavior of distributed-computer-system components. In a described implementation, nodes correspond to particular types of system components and node instances are individual components of the component type corresponding to a node. Node instances are associated with attribute values and node are associated with attribute-value spaces defined by attribute dimensions. Using attribute values and call traces, attribute dimensions that are likely related to particular anomalous behaviors of distributed-computer-system components are determined by decision-tree-related analyses and are reported to one or more computational entities to facilitate resolution of the anomalous behaviors.