Previous studies have shown that postseismic relaxation following the 2004 Mw6.0 Parkfield, CA, earthquake is dominated by afterslip. However, we show that some fraction of the afterslip inferred from kinematic inversion to have occurred immediately below the seismically ruptured area may in fact be a substitute for viscous postseismic deformation of the lower crust. Using continuous GPS and synthetic aperture radar interferometry, we estimate the relative contribution of shallow afterslip (at depth less than 20km) and deeper seated deformation required to account for observed postseismic surface displacements. Exploiting the possible separation in space and time of the time series of displacements predicted from viscoelastic relaxation, we devise a linear inversion scheme that allows inverting jointly for the contribution of afterslip and viscoelastic flow as a function of time. We find that a wide range of models involving variable amounts of viscoelastic deformation can fit the observations equally well provided that they allow some fraction of deep-seated deformation (at depth larger than ∼20 km). These models require that the moment released by postseismic relaxation over 5 years following the earthquake reached nearly as much as 200% of the coseismic moment. All the models show a remarkable complementarity of coseismic and shallow afterslip distributions. Some significant deformation at lower crustal depth (20-26 km) is required to fit the geodetic data. The condition that postseismic deformation cannot exceed complete relaxation places a constraint on the amount of deep seated deformation. The analysis requires an effective viscosity of at least ∼1018 Pa s of the lower crust (assuming a semi-infinite homogeneous viscous domain). This deep-seated deformation is consistent with the depth range of tremors which also show a transient postseismic response and could explain as much as 50% of the total postseismic geodetic moment (the remaining fraction being due to afterslip at depth shallower than 20 km). Lower crustal postseismic deformation could reflect a combination of localized ductile deformation and aseismic frictional sliding.