  The uncertainty in the equilibration in heavy ion collisions due to the
choice of the value of the coupling is examined. The results of the
equilibration are indeed affected by this choice. In particular, a variation of
$\a_s$ from 0.3 to 0.5 reduces the parton phase of the plasma by as much as 4.0
fm/c and increasing coupling causes a reduction in the generated entropy. As
far as equilibration is concerned, larger coupling results in faster
equilibration both chemically and kinetically but improvements only happen to
the fermions. These are accompanied by more rapid cooling and therefore
shortened lifetime. In the light of these results, to choose $\a_s$ is almost
equivalent to choosing the results. Also because of consistency, any fixed
$\a_s$ is incompatible with an evolving plasma. The best choice is therefore
not to choose at all but let the system makes its own decision. We show a
simple recipe how this can be done. With an evolving coupling, equilibration is
accelerated with better results at the expense of the duration of the
deconfined phase.
