Using resonant inelastic x-ray scattering (RIXS) at the Cu L-absorption edge, we have observed intense, dispersive spin excitations in highly overdoped Tl2Ba2CuO 6+δ (superconducting Tc = 6 K), a compound whose normal-state charge transport and thermodynamic properties have been studied extensively and shown to exhibit canonical Fermi-liquid behavior. Complementary RIXS experiments on slightly overdoped Tl2Ba2CuO 6+δ (Tc = 89 K) and on Y1−xCaxBa2Cu3O 6+δ compounds spanning a wide range of doping levels indicate that these excitations exhibit energies and energy-integrated spectral weights closely similar to those of antiferromagnetic magnons in undoped cuprates. The surprising coexistence of Fermi-liquid-like charge excitations and high-energy spin excitations reminiscent of antiferromagnetic insulators in highly overdoped compounds poses a challenge to current theoretical models of the cuprates.High temperature superconductivity arises when the CuO 2 planes of layered copper-oxide compounds are doped with mobile charge carriers. When the number of mobile carriers per Cu atom, p, vanishes, the CuO 2 planes are antiferromagnetically ordered and exhibit conventional spin wave excitations with a total bandwidth of ∼ 300 meV. For hole doping p 0.05, the antiferromagnetic long-range order disappears, and the low-temperature ground state becomes superconducting. Inelastic neutron scattering (INS) experiments have demonstrated that dispersive spin excitations akin to antiferromagnetic spin waves persist in the superconducting state, although their low-energy spectral weight is progressively reduced with increasing p. According to current theories, these "paramagnon" excitations act as a key driving force for Cooper pairing [1]. Up to now, however, the INS studies have been largely limited to underdoped (0.05 p 0.15) [2-4] and lightly overdoped (0.15 p 0.2) cuprates, [5-7] where the spectral features attributable to paramagnons remain relatively sharp and intense. In the highly overdoped regime (p > 0.2), where the superconducting transition temperature, T c , and the superconducting energy gap are sharply reduced and eventually vanish, [8-10] INS experiments have thus far only been reported for a single cuprate family, La 2−x Sr x CuO 4 (La-214). [11, 12] They show progressive weakening of the spin excitations with energies E100 meV, continuing the trend already identified in the underdoped regime, but also indicate that excitations at higher E are less affected by doping. Since La-214 exhibits incommensurate magnetic order ("stripes") near optimal doping, and its T c is limited to ∼ 40 K, it is unclear whether these findings are generic for the cuprate superconductors. Recent resonant inelastic xray scattering (RIXS) experiments [13,14] allowed the detection of dispersive high-energy (E 100 meV) spin excitations in optimally doped cuprates with maximal T c ∼ 90 K, as well as in iron-based superconductors [15]. Although these high-energy paramagnons are strongly broadened by scattering from mobile carriers and thus diff...