  Diffusive shock acceleration at collisionless shocks remains the most likely
process for accelerating particles in a variety of astrophysical sources. While
the standard prediction for strong shocks is that the spectrum of accelerated
particles is universal, $f(p)\propto p^{-4}$, numerous phenomena affect this
simple conclusion. In general, the non-linear dynamical reaction of accelerated
particles leads to a concave spectrum, steeper than $p^{-4}$ at momenta below a
few tens of GeV/c and harder than the standard prediction at high energies.
However, the non-linear effects become important in the presence of magnetic
field amplification, which in turn leads to higher values of the maximum
momentum $p_{max}$. It was recently discovered that the self-generated
perturbations that enhance particle scattering, when advected downstream, move
in the same direction as the background plasma, so that the effective
compression factor at the shock decreases and the spectrum becomes steeper. We
investigate the implications of the excitation of the non-resonant streaming
instability on these spectral deformations, the dependence of the spectral
steepening on the shock velocity and the role played by the injection momentum.
