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.