We present two alternative algorithms for computing (all or some) solutions to the concept abduction problem: one algorithms is based on Reiter's hitting set tree algorithm, whereas the other on relies on a SAT encoding. In contrast to previous work, the algorithms do not rely on a refutation-based calculus and, hence, can be used also with efficient reasoners for tractable DLs such as EL and its extensions. An adaptation to other forms of (logic-based) abduction, e.g., to ABox abduction, is also possible.