Abductive inference provides consistent expla- nations for observable effects and has been of special interest in the context of diagnosis. The abduction problem is in general NP-hard, thus, there is a high motivation to derive solutions efficiently for practical instances. In this pa- per, we focus on propositional abduction in the framework of model-based diagnosis. We re- view four algorithms to compute explanations: one employs an ATMS to derive diagnoses and the others are conflict-directed methods based on an unsatisfiable reformulation of the abduc- tive system description. In an empirical eval- uation we compare the different approaches on practical examples. Our experiments indicate that the ATMS provides the best performance results for the majority of problems.