To date, essentially only two structural models have been proposed and debated in detail for explaining the liquid state order of triglycerides, and both invoke a form of thermotropic liquid crystalline order in triglyceride melts. These are the paralamellar model of Larsson et al. (J. Am. Oil Chem. Soc. 1992, 69, 835) and the nematic model of Cebula et al. (J. Am. Oil Chem Soc. 1992, 69, 130). An alternative discotic model is proposed here that adequately accounts for the broad small-angle X-ray diffraction peak often observed in the liquid state of fats and oils. In this alternative model, triglyceride molecules exist in the liquid state with fully splayed chains, approximating "Y"-shapes (Y-conformers). These are loosely bound within discs that stack into flexible, relatively short cylindrical rods of colloidal dimension, which in turn assemble into rod-packings with short-range order akin to disordered versions of thermotropic discotic liquid crystalline phases in other lipidic systems.