Electrons have been accelerated from solid target surfaces by sub-10-fs laser pulses of 120 microJ energy which were focused to an intensity of 2x10;{16} W/cm;{2}. The electrons have a narrow angular distribution, and their observed energies exceed 150 keV. We show that these energies are not to be attributed to collective plasma effects but are mainly gained directly via repeated acceleration in the transient field pattern created by incident and reflected laser, alternating with phase-shift-generating scattering events in the solid.