We present a mitochondrial (mt) genome phylogeny inferring relationships within Neuropterida (lacewings, alderflies and camel flies) and between Neuropterida and other holometabolous insect orders. Whole mt genomes were sequenced for Sialis hamata (Megaloptera: Sialidae), Ditaxis latistyla (Neuroptera: Mantispidae), Mongoloraphidia harmandi (Raphidioptera: Raphidiidae), Macrogyrus oblongus (Coleoptera: Gyrinidae), Rhopaea magnicornis (Coleoptera: Scarabaeidae), and Mordella atrata (Coleoptera: Mordellidae) and compared against representatives of other holometabolous orders in phylogenetic analyses. Additionally, we test the sensitivity of phylogenetic inferences to four analytical approaches: inclusion vs. exclusion of RNA genes, manual vs. algorithmic alignments, arbitrary vs. algorithmic approaches to excluding variable gene regions and how each approach interacts with phylogenetic inference methods (parsimony vs. Bayesian inference). Of these factors, phylogenetic inference method had the most influence on interordinal relationships. Bayesian analyses inferred topologies largely congruent with morphologically-based hypotheses of neuropterid relationships, a monophyletic Neuropterida whose sister group is Coleoptera. In contrast, parsimony analyses failed to support a monophyletic Neuropterida as Raphidioptera was the sister group of the entire Holometabola excluding Hymenoptera, and Neuroptera + Megaloptera is the sister group of Diptera, a relationship which has not previously been proposed based on either molecular or morphological data sets. These differences between analytical methods are due to the high among site rate heterogeneity found in insect mt genomes which is properly modelled by Bayesian methods but results in artifactual relationships under parsimony. Properly analysed, the mt genomic data set presented here is among the first molecular data to support traditional, morphology-based interpretations of relationships between the three neuropterid orders and their grouping with Coleoptera.