<p>We use sensitivity analysis to design <i>bounding-focused</i> discretization (cutting-surface) methods for the global optimization of nonconvex semi-infinite programs (SIPs). We begin by formulating the optimal bounding-focused discretization of SIPs as a max-min problem and propose variants that are more computationally tractable. We then use parametric sensitivity theory to design an effective heuristic approach for solving these max-min problems. We also show how our new iterative discretization methods may be modified to ensure that the solutions of their discretizations converge to an optimal solution of the SIP. We then formulate optimal bounding-focused <i>generalized</i> discretization of SIPs as max-min problems and design heuristic algorithms for their solution. Numerical experiments on standard nonconvex SIP test instances from the literature demonstrate that our new bounding-focused discretization methods can significantly reduce the number of iterations for convergence relative to a state-of-the-art feasibility-focused discretization method.</p>