Data-domain elastic wavefield tomography is an effective method for updating multiparameter elastic models that exploits much of the information provided by observed multicomponent data. However, poor illumination of the subsurface by P- and S-waves often prevents reliable updates of the model parameters. Moreover, differences in illumination, amplitude, and wavelength between P- and S-waves can distort the intrinsic physical relationships between the reconstructed model parameters. We have developed a method for elastic isotropic wavefield tomography that explicitly constrains the relationship between P- and S-wave velocities. By incorporating a model constraint term in the objective function, we confine P- and S-velocity updates to a physical area defined by prior information, for example, by laboratory measurements or well logs. We have determined that this physical constraint yields models that are more physically plausible, compared with models obtained using only the data misfit objective function.