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Newly discovered fossils from the Silurian and Devonian periods are beginning to challenge embedded perceptions about the origin and early diversification of jawed vertebrates (gnathostomes). Nevertheless, an explicit cladistic framework for the relationships of these fossils relative to the principal crown lineages of the jawed vertebrates (osteichthyans: bony fishes and tetrapods; chondrichthyans: sharks, batoids, and chimaeras) remains elusive. We critically review the systematics and character distributions of early gnathostomes and provide a clearly stated hierarchy of synapomorphies covering the jaw-bearing stem gnathostomes and osteichthyan and chondrichthyan stem groups. We show that character lists, designed to support the monophyly of putative groups, tend to overstate their strength and lack cladistic corroboration. By contrast, synapomorphic hierarchies are more open to refutation and must explicitly confront conflicting evidence. Our proposed synapomorphy scheme is used to evaluate the status of the problematic fossil groups Acanthodii and Placodermi, and suggest profitable avenues for future research. We interpret placoderms as a paraphyletic array of stem-group gnathostomes, and suggest what we regard as two equally plausible placements of acanthodians: exclusively on the chondrichthyan stem, or distributed on both the chondrichthyan and osteichthyan stems.