Flexure mechanisms are widely utilized in precision mechanisms, but their practical use is limited by three major factors, namely restricted range of motion, parasitic motion, and significant reduction in support stiffness when deflected. To address this limitation, in this research the potential of variable thickness flexures in minimizing the aforementioned issues is evaluated. Two novel parametrizations are utilized to optimize these variable thickness flexures, which are then compared to their commonly used constant thickness counterparts. Furthermore, initially curved flexures have been found to be promising in optimizing mechanisms with high performance in terms of parasitic motion and stiffness tuning. Three novel designs are proposed and optimized in this research for improved performance. As variable thickness showed promising results, these newly designed mechanisms are further optimized by incorporating variable thickness into the initially curved flexure mechanisms. The outcomes of this study demonstrate a significant enhancement in terms of support stiffness and range of motion without compromising other important factors.