Temperature dependent weak localization is measured in metallic nanowires in a previously unexplored size regime down to width w = 5 nm. The dephasing time, tau(phi), shows a low temperature T dependence close to quasi-1D theoretical expectations (tau(phi) approximately T(-2/3)) in the narrowest wires, but exhibits a relative saturation as T-->0 for wide samples of the same material, as observed previously. As only sample geometry is varied to exhibit both suppression and divergence of tau(phi), this finding provides a new constraint on models of dephasing phenomena.