We analyzed the crystal and electronic structures of Tl-based strong topological insulators TlSbTe₂,TlSbSe₂, TiBiTe₂ by using first-principles calculation results. The topological nature of these materials is characterized by a single Dirac cone at the [(Γ)] point. Aside from the latter robust surface state (SS), we find trivial SSs at (around) the Fermi level for large momenta as well as deep trivial SSs at (around) [(Γ)]. The calculated energy cuts show an isotropic shape of the Dirac cone and a simple spin structure of the cone. The strong dependence of electronic structure on both optimization of the chalcogenide atom position in bulk and surface relaxation, as well as the slow convergence of the Dirac cone with respect to the film thickness, are discussed. The situation in the thallides is contrasted with results for isostructural indium compounds InBiTe₂ and InSbTe₂, the latter not being topological insulators.