  The free evolution of inelastic particles in one dimension is studied by
means of Molecular Dynamics (MD), of an inelastic pseudo-Maxwell model and of a
lattice model, with emphasis on the role of spatial correlations. We present an
exact solution of the 1d granular pseudo-Maxwell model for the scaling
distribution of velocities and discuss how this model fails to describe
correctly the homogeneous cooling stage of the 1d granular gas. Embedding the
pseudo-Maxwell gas on a lattice (hence allowing for the onset of spatial
correlations), we find a much better agreement with the MD simulations even in
the inhomogeneous regime. This is seen by comparing the velocity distributions,
the velocity profiles and the structure factors of the velocity field.
