  The order of high harmonics emitted by an atom in an intense laser field is
limited by the so-called cutoff frequency. Solving the time-dependent
Schr\"odinger equation, we show that this frequency can be increased
considerably by a parabolic confining potential, if the confinement parameters
are suitably chosen.
  Furthermore, due to confinement, the radiation intensity remains high
throughout the extended emission range. All features observed can be explained
with classical arguments.
