  We introduce an improved form for the anisotropic hydrodynamics distribution
function which explicitly takes into account the free-streaming and
equilibrating contributions separately. We demonstrate that with this
improvement one can better reproduce exact results available in the literature
for the evolution of moments of the distribution function, in particular, for
moments which contain no powers of the longitudinal momentum in their
definition (m=0 moments). Using the resulting dynamical equations, we extract
the non-equilibrium attractor associated with our improved aHydro ansatz and
demonstrate that the improvement also allows one to better reproduce the exact
dynamical attractor obtained using kinetic theory in the relaxation time
approximation, particularly at early rescaled times and for m=0 moments.
