The role of the confinement potential symmetry on the electronic and optical properties of quantum mires is systematically studied. In a wide class of quantum mires with mirror symmetry we evidence a new set of optical transitions resulting both from band mixing and Ct, symmetry breaking at zone center. Several kinds of quasi-one-dimensional excitons are predicted as well as their specific dipole coupling. Even for ultralow C-1 symmetry we find independent excitons with distinct polarization selection rules.