Most models of lower crust/mantle viscosity inferred from postearthquake relaxation assume one or two uniform-viscosity layers. A few existing models possess apparently significant radially variable viscosity structure in the shallow mantle (e.g., the upper 200 km), but the resolution of such variations is not clear. We use a geophysical inverse procedure to address the resolving power of inferred shallow mantle viscosity structure using postearthquake relaxation data. We apply this methodology to 9 years of GPS-constrained crustal motions after the 16 October 1999 M = 7.1 Hector Mine earthquake. After application of a differencing method to isolate the postearthquake signal from the “background” crustal velocity field, we find that surface velocities diminish from ∼20 mm/yr in the first few months to ≲2 mm/yr after 2 years. Viscoelastic relaxation of the mantle, with a time-dependent effective viscosity prescribed by a Burgers body, provides a good explanation for the postseismic crustal deformation, capturing both the spatial and temporal pattern. In the context of the Burgers body model (which involves a transient viscosity and steady state viscosity), a resolution analysis based on the singular value decomposition reveals that at most, two constraints on depth-dependent steady state mantle viscosity are provided by the present data set. Uppermost mantle viscosity (depth ≲ 60 km) is moderately resolved, but deeper viscosity structure is poorly resolved. The simplest model that explains the data better than that of uniform steady state mantle viscosity involves a linear gradient in logarithmic viscosity with depth, with a small increase from the Moho to 220 km depth. However, the viscosity increase is not statistically significant. This suggests that the depth-dependent steady state viscosity is not resolvably different from uniformity in the uppermost mantle.