Experimentally observed narrowing of spectral holes in a glass under hydros
tatic pressure confirms our theoretical finding that the external pressure,
in addition to increasing the frequencies of soft localized modes, also re
duces their number. This occurs because the majority of soft localized mode
s in glasses is shown to have a negative cubic anharmonicity. For that reas
on the applied pressure not only enhances the stiffness of these modes, but
also transforms a fraction of them into tunneling two-level systems, where
as the simultaneous reverse transformations of some other two-level systems
into soft localized modes are less numerous.