Several new liquid-crystalline indene and pseudoazulene systems are reported. These molecules give rise to either columnar hexagonal mesophases and/or columnar plastic phases. The unique nature of these compounds stems from their non-classical discotic structure. Although the molecules have rigid aromatic cores, they lack terminal tails and instead the polarizable atoms (S, halogens) or polar groups (CN, CO) act as unusual soft parts. On the basis of many structurally related materials, we conclude that for this type of compound molecular stacking in the solid state is a prerequisite for the appearance of a columnar mesophase, although other intermolecular interactions within the layers are also important in establishing liquid-crystalline order. The behavior reported for these mesomorphic molecules opens up new possibilities in the search for related molecular interactions that might be useful for the construction of supramolecular architectures with particular properties.