  We have studied the effect of thermal annealing on electron dephasing times
$\tau_\phi$ in three-dimensional polycrystalline metals. Measurements are
performed on as-sputtered and annealed AuPd and Sb thick films, using
weak-localization method. In all samples, we find that $\tau_\phi$ possesses an
extremely weak temperature dependence as $T \to 0$. Our results show that the
effect of annealing is non-universal, and it depends strongly on the amount of
disorder quenched in the microstructures during deposition. The observed
"saturation" behavior of $\tau_\phi$ cannot be easily explained by magnetic
scattering. We suggest that the issue of saturation can be better addressed in
three-dimensional, rather than lower-dimensional, structures.
