In order to diagnose the occurrence of a fault event in a Discrete-Event System (DES), it is first necessary to verify if the language of the system is diagnosable with respect to an observable event set and a fault event set. In some cases, the language of the system is also diagnosable even when a subset of the set of observable events under consideration is used as the actual observable event set. Among the benefits that such a reduction may bring we list the reduction in the number of sensors used in the diagnosis, therefore reducing the cost of the system, and the possibility to deploy the sensor redundancy to obtain a more reliable diagnosis decision. In this work, we propose two algorithms to find, in a systematic way, all minimal subsets of the observable event set that ensure the diagnosability of the DES (minimal diagnosis bases). The methods are based on the construction of verifiers and have lower computational complexity than another method recently proposed in the literature. (C) 2016 Elsevier Ltd. All rights reserved.