We present a detailed investigation of the structural and superconducting properties of Tl2Ba2CuOx compounds as a function of oxygen pressure and annealing temperature prior to quenching. The crystal structure depends both on the oxygen concentration and on thallium deficiency. At the stoichiometric cation composition Tl:Ba:Cu=2:2:1, the parameters p(O2) and Tquench uniquely define the structure and the superconducting Tc. With adequate heat treatment sequences, reversible transitions from the tetragonal to the orthorhombic phase have been observed.