  Compton scattering of short and ultra short (sub-cycle) laser pulses off
mildly relativistic electrons is considered within a QED framework. The
temporal shape of the pulse is essential for the differential cross section as
a function of the energy of the scattered photon at fixed observation angle.
The partly integrated cross section is sensitive to the non-linear dynamics
resulting in a large enhancement of the cross section for short and, in
particular, for ultra-short flat-top pulse envelopes which can reach several
orders of magnitude, as compared with the case of a long pulse. Such effects
can be studied experimentally and must be taken into account in
Monte-Carlo/transport simulations of %$e^+e^-$ pair production in the
interaction of electrons and photons in a strong laser field.
