Relationships among Neoaves, a group comprising approximately 95% of all extant birds, are difficult to resolve because of multiple short internodes presumably created by a rapid evolutionary radiation around the K/Pg boundary. This difficulty has plagued both morphological and molecular studies. Compared with molecular studies with extensive taxon and character sampling, morphological datasets have largely failed to provide insight into the phenotypic evolutionary transitions of the neoavian radiation. Extinct neoavian taxa remain an understudied but critical key to resolving relationships among these problematic stem lineages and understanding evolutionary changes in structure and function. Adzebills (Aptornis), some of the most phylogenetically controversial fossil neoavians, are extinct terrestrial birds endemic to New Zealand since at least the early Miocene. Past morphological studies have placed adzebills as a sister taxon to the flightless Kagu of New Caledonia (Rhynochetos jubatus) or to the land- and waterfowl group Galloanseres. Recent molecular studies reveal the Kagu and Sunbittern (Eurypyga helias) to be sister taxa, whereas adzebills have been postulated to be within Rallidae (rails, gallinules, and coots) or the sister taxon of Sarothruridae (flufftails) or Ralloidea (finfoots, flufftails, and rails). To better resolve the position of adzebills and begin constructing a fine-scale total evidence phylogenetic dataset for the base of Neoaves, we constructed a new and more comprehensive morphological dataset of 368 discrete osteological characters for 38 extant and two extinct taxa that includes extensive sampling of nearly all neoavian stem lineages. We then combined this dataset with 32 DNA sequences of the slowly evolving nuclear RAG1 and RAG2 genes. Morphological results place adzebills as the sister taxon of trumpeters (Psophia) within core Gruiformes and confirm strong support for a Kagu+Sunbittern sister group (99% bootstrap value). Results for analyses of the combined data were identical, and the adzebill+trumpeter clade was supported by a 99% Bayesian clade credibility value. Although the Kagu+Sunbittern sister group is consistent with recent molecular hypotheses, the adzebill+trumpeter group is novel.