Polyelectrolyte multilayers were constructed from poly(styrenesulfonate), PSS, and poly(diallyldimethylammonium) with regularly interspersed layers of deuterated PSS. Annealing, by salt, of the fuzzy internal layering within this multilayer was followed using neutron reflectometry. A "limited source" diffusion model fit the data well and showed that polyelectrolyte migrates much more slowly within the bulk of a multilayer than at the surface. Enhanced surface mobility and a nonlinear increase in diffusion rate with salt concentration were explained by a salt doping model, where correlated short lengths of polyelectrolyte move by exchange with counterions ("extrinsic charge") doped into the ultrathin film of polyelectrolyte complex on exposure to solutions of high ionic strength.