Traditionally, conodont intrarelationships have been reconstructed following the evolutionary palaeontology paradigm, which lacks a formal methodology, renders hypotheses unrepeatable and takes little account of the imperfect nature of the fossil record. Cladistics provides a prescriptive approach to phylogeny reconstruction and, it is argued, a rigorous method of character analysis that is not incompatible with the aims of evolutionary palaeontology. To demonstrate this, we use the Silurian family Kockelellidae as an example of how cladistics can be used to reconstruct relative relationships, and how such hypotheses can be converted to phylogenies. We follow traditional, cladistic approaches to assessing the completeness of the fossil record and find that failure to conduct this within a milieu of absolute, rather than merely relative, relationships leads to spurious inferences of gaps in the fossil record. This appears to be a problem that is widespread in theory, but peculiar to species in practice, and parallels the observation that cladograms of fossil species tend to exhibit poorer correlation to stratigraphy than do cladograms of fossil higher taxa. We conclude that cladistics provides the only appropriate framework within which to conduct character analysis; phylogenies can be developed from cladograms but very often this additional inferential step is entirely superfluous to the aims of evolutionary studies.