This paper presents an optimization methodology for designing radiant enclosures containing specularly-reflecting surfaces. The optimization process works by making intelligent perturbations to the enclosure geometry at each design iteration using specialized numerical algorithms. This requires far less time than the forward "trial-and-error" design methodology, and the final solution is near optimal. In this application, the radiant enclosure is analyzed using a Monte Carlo technique based on exchange factors, and the design is optimized using the Kiefer-Wolfowitz method. This design methodology is demonstrated by solving two industrially-relevant design problems involving two-dimensional enclosures that contain specular surfaces.