Homogeneous Tl₂Ba₂CuOₓ ceramics were synthesized by a novel route allowing tight control of thallium losses, starting from Tl₂Ba₂O₅ precursors and using high gas pressures. Annealing followed by fast quenching into gallium allowed us to map the critical temperature (0 to 92 K) and the crystal symmetry (orthorhombic or tetragonal) in the (T;p(O₂)) plane. The orthorhombic phase is found to be stoichiometric, whereas the tetragonal phase has a homogeneity domain in the thallium concentration. The critical temperature, determined by the oxygen concentration, is not sensitive to the crystal structure. Selected physical properties of Tl₂Ba₂CuOₓ compounds are presented.