Several studies of the 2004 Parkfield earthquake have linked the spatial distribution of the event’s aftershocks to the mainshock slip distribution on the fault. Using geodetic data, we find a model of coseismic slip for the 2004 Parkfield earthquake with the constraint that the edges of coseismic slip patches align with aftershocks. The constraint is applied by encouraging the curvature of coseismic slip in each model cell to be equal to the negative of the curvature of seismicity density. The large patch of peak slip about 15 km northwest of the 2004 hypocenter found in the curvature-constrained model is in good agreement in location and amplitude with previous geodetic studies and the majority of strong motion studies. The curvature-constrained solution shows slip primarily between aftershock “streaks” with the continuation of moderate levels of slip to the southeast. These observations are in good agreement with strong motion studies, but inconsistent with the majority of published geodetic slip models. Southeast of the 2004 hypocenter, a patch of peak slip observed in strong motion studies is absent from our curvature-constrained model, but the available GPS data do not resolve slip in this region. We conclude that the geodetic slip model constrained by the aftershock distribution fits the geodetic data quite well and that inconsistencies between models derived from seismic and geodetic data can be attributed largely to resolution issues.