  The hyperfine splittings in heavy quarkonia are studied using new
experimental data on the di-electron widths. The smearing of the spin-spin
interaction is taken into account, while the radius of smearing is fixed by the
known $J/\psi-\eta_c(1S)$ and $\psi(2S)-\eta'_c(2S)$ splittings and appears to
be small, $r_{ss} \approx 0.06$ fm. Nevertheless, even with such a small radius
an essential suppression of the hyperfine splittings ($\sim 50%)$ is observed
in bottomonium. For the $nS b\bar b$ states $(n=1,2,...6)$ the values we
predict (in MeV) are 28, 12, 10, 6, 6, and 3, respectively. In single-channel
approximation for the $3S$ and $4S$ charmonium states the splittings 16(2) MeV
and 12(4) MeV are obtained.
