We show that the efficiency of single attosecond pulse generation
during atomic ionization by an intense few-optical-cycle laser
pulse can be enhanced dramatically when pre-excited electronic
states are used. This is due to the slowed-down spreading of the
laser-driven free-electron wave packet. We develop an analytical
approach to the treatment of the attosecond burst production due
to the electron recollision with a parent ion, assuming that the
atom is fully ionized during one optical cycle. Our analytical
and numerical simulations show that, when a hydrogen atom is
ionized from the 2s-state by an ultrashort pulse of a
Ti:sapphire (800\un{nm}) laser, the energy of the generated
attosecond pulse is several tens of times higher, its duration is
much shorter, and the spectral intensity of radiation in the VUV
and soft–X-ray range is several orders of magnitude superior to
that in the case of ionization from the ground state. We
determine the excited states preferable for experiments using the
fundamental or the second harmonic of a Ti:sapphire laser
