An understanding of spin excitations in cuprates is essential since the mechanism of high-TC superconductivity might be linked to spin fluctuations. Band calculations for ‘one-dimensional' unit cells of La2CuO4 show larger coupling (spin–phonon coupling, SPC) between anti-ferromagnetic spin waves and O-phonons than for Cu- or La-phonons. When this result is applied to a two-dimensional, free-electron like band, it leads to an ‘hourglass' shape of the spin excitation spectrum, as in recent experiments. Isotope shifts and doping dependences of the excitations are discussed.