The largest phylogenetic analysis of ichthyosaurs to date is presented, with 114 ingroup taxa coded at species level. Completeness of the taxa included varied from >98% to <2%; ten taxa were removed a priori using Concatabominations, due to incompleteness and taxonomic uncertainty. The data were analysed using three widely used optimisation criteria: maximum parsimony, maximum likelihood, and Bayesian inference; while similar, each criterion produced different topologies, support, and levels of resolution. Maximum parsimony found a well-resolved consensus tree with minor improvement from a posteriori pruning of unstable taxa; however, general support remains low. Tree resolution was reduced more by taxa that lacked codings from phylogenetically important regions of the tree, rather than by those that simply lacked many codings. Resolution present in the most likely tree is poorly supported; sister relationships cannot be confirmed, although similarities are found to the most parsimonious tree. Bayesian inference found poorly resolved consensus trees. While more resolved, an equal-distribution rate prior is significantly worse than the null gammadistribution rate prior for morphological data, but suggests rate heterogeneity across ichthyosaur phylogeny. Tree comparisons under each analytical criterion failed to select a single best tree, however, the Bayesian inference tree with gamma-distribution rate prior is selected as the best tree based on recent analyses showing improved accuracy using this criterion. Unequivocally resolved clades include Ichthyopterygia, Ichthyosauria, Shastasauria, Euichthyosauria, Parvipelvia, and Neoichthyosauria, but with variation in their taxonomic components. Mixosauridae and Ophthalmosauridae are similarly recovered, but their definitions are modified to stem-based definitions to prevent substantial variation of included taxa. Several genera are not monophyletic: Brachypterygius,