We performed Raman scattering experiments on superconductivity-induced features in Bi2Sr2(Ca1-xYx)Cu2O8+delta (Bi-2212), YBa2Cu3O6+x (Y-123), and Tl2Ba2CuO6+delta (Tl-2201) single crystals. The results in combination with earlier ones enable us to systematically analyze the spectral features in the doping range 0.07⩽p⩽0.24. In B2g (xy) symmetry, we find universal spectra and the maximal gap energy Δ₀ to scale with the superconducting transition temperature Tc. The B1g (x2−y2) spectra in all three compounds show an anomalous increase of the intensity toward overdoping. The energy scale of the corresponding peak is neither related to the pairing energy nor to the pseudogap, but possibly stems from a symmetry breaking transition at the onset point of superconductivity at psc2≃0.27.