  Nonlinear single Compton scattering has been thoroughly investigated in the
literature under the assumption that initially the electron has a definite
momentum. Here, we study a more general initial state, and consider the
electron as a wave-packet. In particular, we investigate the energy spectrum of
the emitted radiation and show that in typical experimental situations some
features of the spectra shown in previous works are almost completely washed
out. Moreover, we show that at comparable relative uncertainties, the one in
the momentum of the incoming electron has a larger impact on the photon spectra
at a fixed observation direction than the one on the laser frequency.
