To reason about observed behaviour of processes and their models, conformance checking techniques are rooted in the computation of artefacts. Related artefacts like alignments, multi-alignments and anti-alignments are defined over a distance function, most commonly Hamming or Levenshtein distances. In this paper we provide a new Partial MaxSAT encoding of these artefacts based on the Levenshtein distance and compare with their current state-of-the-art SAT encodings. We show a reduction in the resulting formula size for our proposed encoding, while also obtaining good performance results on the computation of the artefacts.