The presence of a thin polymer layer on the surface of a colloidal particle can have a profound effect on its electrophoretic mobility. The model developed here treats the hydrodynamics of the polymer layer as a distribution of Stokes resistance centers within a thin diffuse layer; fixed charge may reside on the surface of the particle core or throughout the layer. The theory is semianalytical in that asymptotic methods are used to simplify the equations but several integrals must be evaluated numerically. Special attention is paid to the effects of polarization and relaxation. It is shown that distributing immobile charge throughout the layer produces a response where the particle's mobility exceeds that found when the same amount of charge is spread uniformly over the surface of the rigid core. Increasing the drag due to the fuzzy layer always diminishes the mobility. In either case, the hydrodynamic permeability of the layer has a strong influence on particle movement. Results are also given for the dipole coefficient in the expression for the conductivity of a dilute suspension.