Gradient-orthogonal representations of aspheric shapes give a more effective and intuitive characterization that also copes with increasingly complex surfaces. Further, we have seen a range of applications where standard design codes (including CodeV® and Zemax®) can find systems with better optical performance when optimized in this representation. The examples presented here include a system with no global axis of symmetry and another with freeform surfaces. In all these particular cases, the end results can be retro-fitted in terms of conventional representations, but the optimizers fail to find the superior solutions unless an orthogonal basis is employed during the design process. Because the communication of shape is so much more effective in terms of a gradient-orthogonal description, our results give added motivation for the communities of design, fabrication, and testing to gain more experience with this new convention.