  The spectra of Compton radiation emitted during electron scattering off an
intense laser beam are calculated using the framework of strong-field quantum
electrodynamics. We model these intense laser beams as finite length
plane-wave-fronted pulses, similar to Neville and Rohrlich [Phys. Rev. D {\bf
3}, 1692 (1971)], or as trains of such pulses. Expressions for energy and
angular distributions of Compton photons are derived such that a comparison of
both situations becomes meaningful. Comparing frequency distributions for both
an isolated laser pulse and a laser pulse train, we find a very good agreement
between the results for long pulse durations which breaks down however for
ultrashort laser pulses. The dependence of angular distributions of emitted
radiation on a pulse duration is also investigated. Pronounced asymmetries of
angular distributions are found for very short laser pulses, which gradually
disappear with increasing the number of laser field oscillations. Those
asymmetries are attributed to asymmetries of the vector potential describing an
incident laser beam.
