Non-linear cascade scattering of intense, tightly focused laser pulses by
relativistic electrons is studied numerically in the classical approximation
including the radiation damping for the quantum parameter hwx-ray/E<1 and an
arbitrary radiation parameter Kai. The electron energy loss, along with its
side scattering by the ponderomotive force, makes the scattering in the
vicinity of high laser field nearly impossible at high electron energies. The
use of a second, co-propagating laser pulse as a booster is shown to solve this
problem