Abstract Electronic structures of Tl-based copper-oxide superconductors were examined by performing tight-binding band calculations on the Tl 2 O 4 double layers of Tl 2 Ba 2 Ca n−1 Cu n O 2n+4 and on the TlO 3 single layers of TlBa 2 Ca n−1 Cu n O 2n+3 . When the distortion of their Tl-O sheets is taken into consideration, the Tl 2 O 4 double layers are found to have the bottom of the Tl 6s-block bands significantly below the Fermi level so that they have a large electron pocket to remove electrons from the x 2 - y 2 bands of the CuO 2 layers. In sharp contrast, however, the Tl 6s-block bands of the TlO 3 single layers are found to lie well above the Fermi level, regardless of whether or not the distortions in their Tl-O sheets are taken into consideration. Unlike the Tl 2 O 4 double layers, therefore, the TlO 3 single layers do not remove electrons from the x 2 − y 2 bands of the CuO 2 layers. This is consistent with the observation that stoichiometric TlBa 2 Ca n−1 Cu n O 2n+3 already has a high formal oxidation state (2n+1)/n for (e.g., + 3.00, + 2.50, and + 2.33 for n =1,2, and 3, respectively), and hence further hole generation to produce superconductivity does not seem necessary.