  We argue that the phenomenologically inferred ratio of shear viscosity to
entropy density of the quark-gluon plasma, $\eta/\s < 0.5$ near the
deconfinement temperature $T_c$, can be understood from perturbative QCD. To
rebut the widespread, opposite view we first show that, and why, the existing
leading order result in (fixed) coupling should not be further expanded in
logarithms. Emphasizing then that the resummation mandatory for screening also
settles the often neglected question of scale setting for the running coupling,
we establish a temperature dependence of $\eta/\s$ which agrees well with
constraints from hydrodynamics.
