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The problem of obtaining information on the molecular properties of non-cylindrically symmetric solute molcules in liquid crystals is examined. Nitrobenzene, tetrafluoro-p-benzoquinone and pyridine have been investigated in various nematic solvents at a series of temperatures using proton, fluorine and deuterium NMR where relevant. The ordering matrices for these essentially rigid molecules have been determined as a function of temperature. The predictions of a mean field theory for solutes deviating from cylindrical symmetry are considered. The relative importance of polarizability, steric forces and specific interactions in determining orientational ordering is discussed.