We have studied the effect of thermal annealing on electron dephasing times τ φ 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 τ φ possesses an extremely weak temperature dependence as T → 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 τ φ cannot be easily explained by magnetic scattering. We suggest that the issue of saturation can be better addressed in three-dimensional, rather than lowerdimensional, structures.