High-harmonic generation (HHG) by a zero-range atom illuminated by a l
inearly polarized laser pulse in the presence of an additional static
electric field is investigated theoretically. It is shown that the cut
off of the harmonic spectrum can be controlled with the help of the st
atic field. The plateau can be extended far beyond the usual cutoff en
ergy of \E-0\ + 3.17U(p). In some cases, a second plateau appears that
extends to still higher energies. The cutoff energies of the first as
well as the second plateau are correctly predicted by a classical mod
el. However, the static field strengths required for these manipulatio
ns of the HHG cutoff are much larger than experimentally available.