  The Compton scattering of X-ray photons, assisted by a short intense optical
laser pulse, is discussed. The differential scattering cross section reveals
the interesting feature that the main Klein-Nishina line is accompanied by a
series of side-lines forming a broad plateau where up to ${\cal O} (10^3)$
laser photons participate simultaneously in a single scattering event. An
analytic formula for the width of the plateau is given. Due to the non-linear
mixing of X-ray and laser photons a frequency dependent rotation of the
polarization of the final state X-ray photons relative to the scattering plane
emerges. A consistent description of the scattering process with short laser
pulses requires to work with X-ray pulses. An experimental investigation can be
accomplished, e.g., at LCLS or the European XFEL in the near future.
