An accurate and efficient design optimization method is developed for hypersonic vehicles. For flow analysis, the axisymmetric Navier-Stokes and finite-rate chemical reaction equations are solved implicitly using Newton's method. A gradient-based method is implemented for numerical optimization. Sensitivities are evaluated using the discrete adjoint method. Bezier curves are used for geometry parameterization. The objective of design is to minimize drag while keeping aerodynamic heating below initial values. Although the ablation analysis is excluded in the design process, the noncharring ablation characteristics of the baseline and optimized geometries are compared. An implicit method is developed for the analysis of carbon ablation. The surface thermochemistry and axisymmetric heat conduction equations are solved simultaneously. A thermochemical equilibrium assumption is employed at the surface. Results are demonstrated for a simple sphere-cone geometry.