Minimal Hitting Set (MHS) is a well-known and complete method to compute all explanations of an ABox abduction problem. MHS is NP-complete and widely recognized as inefficient. MergeXplain (MXP), on the other hand, is fast, but does not guarantee to find all explanations. MHS-MXP is a hybrid algorithm which adopts the divide-and-conquer heuristics of MXP and combines it with MHS. MHS-MXP is complete and – at least on a part of the inputs – more efficient than MHS. We describe a favourable class of inputs for the hybrid algorithm. We describe an experimental implementation which enables us to perform first preliminary empirical evaluation on this class of inputs.