  We discuss corrections to the ratio of shear viscosity to entropy density
$\eta/s$ in higher-derivative gravity theories. Generically, these theories
contain ghost modes with Planck-scale masses. Motivated by general
considerations about unitarity, we propose new boundary conditions for the
equations of motion of the graviton perturbations that force the amplitude of
the ghosts modes to vanish. We analyze explicitly four-derivative perturbative
corrections to Einstein gravity which generically lead to four-derivative
equations of motion, compare our choice of boundary conditions to previous
proposals and show that, with our new prescription, the ratio $\eta/s$ remains
at the Einstein-gravity value of $1/4\pi$ to leading order in the corrections.
It is argued that, when the new boundary conditions are imposed on six and
higher-derivative equations of motion, $\eta/s$ can only increase from the
Einstein-gravity value. We also recall some general arguments that support the
validity of our results to all orders in the strength of the corrections to
Einstein gravity. We then discuss the particular case of Gauss-Bonnet gravity,
for which the equations of motion are only of two-derivative order and the
value of $\eta/s$ can decrease below $1/4\pi$ when treated in a nonperturbative
way. Our findings provide further evidence for the validity of the KSS bound
for theories that can be viewed as perturbative corrections to Einstein
Gravity.
