It is shown that the superconducting and structural properties of Tl2Ba2CuO6+δ depend on at least two defects. The Tl/Cu ratio used during synthesis determines the concentration of a defect that is likely to be Cu substitution on the Tl site, based on previously published work that proves the existence of such a defect. The structure exhibits a smaller orthorhombic strain, or tetragonal symmetry, for high concentrations of this defect. Tc tends to be lowered by this defect. An oxygen interstitial defect in the Tl-O double layer has a more pronounced effect on Tc, allowing the compound to be overdoped as the concentration of this defect increases. Features in the diffraction data also suggest the existence of a third defect which may involve the filling of oxygen vacancies at an oxygen site in the structure during early stages of oxygenation.