X-ray absorption spectra on the overdoped high-temperature superconductors Tl2Ba2CuO6+δ and La2-xSrxCuO4±δ reveal a striking departure in the electronic structure from that of the underdoped regime. The upper Hubbard band, identified with strong correlation effects, is not observed on the oxygen K edge, while the lowest-energy prepeak gains less intensity than expected above p∼0.21. This suggests a breakdown of the Zhang-Rice singlet approximation and a loss of correlation effects or a significant shift in the most fundamental parameters of the system, rendering single-band Hubbard models inapplicable. Such fundamental changes suggest that the overdoped regime may offer a distinct route to understanding in the cuprates. © 2009 The American Physical Society.