  We compute the shear viscosity, $\eta$, at general temperatures $T$, in a
BCS-BEC crossover scheme which is demonstrably consistent with conservation
laws. The study of $\eta$ is important because it constrains microscopic
theories by revealing the excitation spectra. The onset of a normal state
pairing gap and the contribution from pair degrees of freedom imply that $\eta$
at low $T$ becomes small, rather than exhibiting the upturn predicted by most
others. Using the local density approximation, we find quite reasonable
agreement with just-published experiments.
