Although the phylogeny of centipedes has found ample agreement based on morphology, recent analyses incorporating molecular data show major conflict at resolving the deepest nodes in the centipede tree. While some genes support the classical (morphological) hypothesis, others suggest an alternative tree in which the relictual order Craterostigmomorpha, restricted to Tasmania and New Zealand, is resolved as the sister group to all other centipedes. We combined all available data including seven genes (totalling more than 8 kb of genetic information) and 153 morphological characters for 24 centipedes, and conducted a sensitivity analysis to evaluate where the conflict resides. Our data showed that the classical hypothesis is obtained primarily when nuclear ribosomal genes exert dominance in the character data matrix (at high gap costs), while the alternative tree is obtained when protein-encoding genes account for most of the cladogram length (at low gap costs). In this particular case, the addition of genetic data does not produce a more stable hypothesis for deep centipede relationships than when analysing certain genes independently, but the overall conflict in the data can be clearly detected via a sensitivity analysis, and support and stability of shallow nodes increase as data are added.