Diagnosis of an active system (AS), an asynchronous and distributed discrete-event system, is typically abduction-based: given a temporal observation, the diagnoses, or candidates, are generated based on a complete model of the AS, where a candidate is a set of faults explaining the temporal observation. A critical problem, which is common to all approaches of model-based diagnosis, is a large number of candidates: this is a serious threat to diagnosticians, owing to the cognitive overload imposed by an overwhelming stream of information and, worse still, to the uncertainty raising from a large set of different diagnoses. This criticality is exacerbated by assuming that both the candidates and the relevant recovery actions, possibly performed by an artificial agent, are required in real time, like in a nuclear power plant or in a defense system. Since candidates with low cardinality are more probable than candidates with high cardinality, it seems appropriate to generate candidates in ascending order of cardinality, from most to least likely. This way, an agent is not required to wait for the complete generation of candidates to perform the recovery actions that are associated with the most probable diagnoses. A diagnosis technique for ASs with prioritization of candidates is presented. Evidence from experimental results shows that the diagnosis technique is not only sound and complete, inasmuch all and only correct candidates are generated, but also effective in providing the most likely candidates upfront.