  We show the propagation of regularity, uniformly in time, for the scaled
solutions of the inelastic Maxwell model for small inelasticity. This result
together with the weak convergence towards the homogenous cooling state present
in the literature implies the strong convergence in Sobolev norms and in the
$L^1$ norm towards it depending on the regularity of the initial data. The
strategy of the proof is based on a precise control of the growth of the Fisher
information for the inelastic Boltzmann equation. Moreover, as an application
we obtain a bound in the $L^1$ distance between the homogeneous cooling state
and the corresponding Maxwellian distribution vanishing as the inelasticity
goes to zero.
