  Photoelectron spectra obtained from the ab initio solution of the
time-dependent Schr\"odinger equation can be in striking disagreement with
predictions by the strong-field approximation (SFA) not only at low energy but
also around twice the ponderomotive energy where the transition from the direct
to the rescattered electrons is expected. In fact, the relative enhancement of
the ionization probability compared to the SFA in this regime can be several
orders of magnitude. We show for which laser and target parameters such an
enhancement occurs and for which the SFA prediction is qualitatively good. The
enhancement is analyzed in terms of the Coulomb-corrected action along analytic
quantum orbits in the complex-time plane, taking soft recollisions under the
Coulomb barrier into account. These recollisions in complex time and space
prevent a separation into sub-barrier motion up to the "tunnel exit" and
subsequent classical dynamics. Instead, the entire quantum path up to the
detector determines the ionization probability.
