1. Cephalometric conventions today may have little basis in either biology or biometrics. 2. There is no theory of cephalometrics, only conventions which involve landmarks and straight lines only. These fail to capture the curving of form and its changes, exclude proper measures of size for bent structures, and misrepresent growth, portraying it as vector displacement rather than a generalized distortion. 3. Conventional cephalometric procedures misinform by fabrication of misleading geometric quantities, by camouflage, particularly of remodeling, by confusion about what is happening (analysis of rotations, treating shape separately from size, and registering angles on landmarks as vertices), and by subtraction as a representation of growth. 4. We suggest that the present systems offer little real hope of improvement sufficient to meet our needs in craniofacial growth research. We call attention to three possible techniques to be included in future cephalometric conventions: (1) tangents and curvatures, (2) Blum's medial axis ("skeleton"), and (3) biorthogonal grids.