Shear distortion has been a popular formal and informal measure, whether used quantitatively or visually, in assessing the quality of mappings or the shape of elements in a quad mesh. Nevertheless, well-known energies such as conformal- and isometric-based energies do not directly target lowering shear distortion but only bound it. Consequently, the shear distortion can be unnecessarily high.We introduce a new shear energy and offer an efficient way to incorporate it in the latest state-of-the-art optimization framework. The resultant mapping has substantially lower shear distortion, and the cost is a reasonably low addition of conformal or isometric distortion. The energy is minimized efficiently, and the run time of an iteration is of the same order of optimizing other popular energies. We also introduce a new scale-invariant, second-order smoothness energy that when combined with the shear energy, leads to smooth anisotropic mappings with low shear distortion.We demonstrate these energies and compare with the state of the art in the application of seamless parametrization, where the quality of mapping a checkerboard pattern is paramount since it directly affects the quality of an extracted quad mesh.