  We consider the velocity distribution for a granular gas of inelastic hard
spheres described by the Boltzmann equation. We investigate both the free of
forcing case and a system heated by a stochastic force. We propose a new method
to compute the first correction to Gaussian behavior in a Sonine polynomial
expansion quantified by the fourth cumulant $a_2$. Our expressions are compared
to previous results and to those obtained through the numerical solution of the
Boltzmann equation. It is numerically shown that our method yields very
accurate results for small velocities of the rescaled distribution. We finally
discuss the ambiguities inherent to a linear approximation method in $a_2$.
