Free-electron laser sources now under construction are intended to attain r
adiative intensities higher than 10(16) W cm(-2) at photon energies up to 3
0 eV. We investigate the over-the-barrier mechanism of ionization of heavy
atoms by such a source. We find that, for valence electrons, this mode of i
onization is suppressed in the regime where the electric field and photon e
nergy of the laser are comparable, respectively, to atomic electric fields
and binding energies. Ionization of inner-shell electrons is still possible
, but some kind of 'two-fluid' model is necessary to describe this phenomen
on.