We extend full-waveform inversion by Wavefield Reconstruction Inversion by including convex constraints on the model. Contrary to the conventional adjoint-state formulations, Wave-field Reconstruction Inversion has the advantage that the Gauss-Newton Hessian is well approximated by a diagonal scaling, which allows us to add convex constraints, such as the box- and the edge-preserving total-variation constraint, on the square slowness without incurring significant increases in computational costs. As the examples demonstrate, including these constraints yields far superior results in complex geological areas that contain high-velocity high-contrast bodies (e.g. salt or basalt). Without these convex constraints, adjoint-state and Wavefield Reconstruction Inversion get trapped in local minima for poor starting models.