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A distributed system-level diagnosis algorithm allows the fault-free nodes of a system to diagnose the state of all nodes in the system. Diagnosis has been successfully employed for dependable network fault management. In this paper we present a new hierarchical adaptive distributed system-level diagnosis algorithm, Hi-ADSD with Detours which has latency at most log2 2N, but requires less tests and less diagnostic information than other hierarchical diagnosis algorithms. Nodes running the new algorithm are grouped in clusters. If a tested node is faulty, instead of executing more tests, the tester tries to obtain information about the rest of the cluster from nodes tested fault-free outside the cluster, such that the diagnosis of the system is not delayed. Each such alternative path to a cluster is called a detour. An extra test is executed on a given cluster only when no detour is available. The worst case of the algorithm's latency is formally proved. Simulation results are presented.