Long-branch attraction is a well-known source of systematic error that can mislead phylogenetic methods; it is frequently invoked post hoc, upon recovering a different tree from the one expected based on prior evidence. We demonstrate that methods that do not force the data onto a single tree, such as spectral analysis, Neighbor-Net, and consensus networks, can be used to detect conflicting signals within the data, including those caused by long-branch attraction. We illustrate this approach using a set of taxa from three unambiguously monophyletic families within the Pelecaniformes: the darters, the cormorants and shags, and the gannets and boobies. These three families are universally acknowledged as forming a monophyletic group, but the relationship between the families remains contentious. Using sequence data from three mitochondrial genes (12S, ATPase 6, and ATPase 8) we demonstrate that the relationship between these three families is difficult to resolve because they are separated by a short internal branch and there are conflicting signals due to long-branch attraction, which are confounded with nonhomogeneous sequence evolution across the different genes. Spectral analysis, Neighbor-Net, and consensus networks reveal conflicting signals regarding the placement of one of the darters, with support found for darter monophyly, but also support for a conflicting grouping with the outgroup, pelicans. Furthermore, parsimony and maximum-likelihood analyses produced different trees, with one of the two most parsimonious trees not supporting the monophyly of the darters. Monte Carlo simulations, however, were not sensitive enough to reveal long-branch attraction unless the branches are longer than those actually observed. These results indicate that spectral analysis, Neighbor-Net, and consensus networks offer a powerful approach to detecting and understanding the source of conflicting signals within phylogenetic data.