Numerical optimization is a powerful method for identifying energy-efficient building designs. Automating the search process facilitates the evaluation of many more options than is possible with one-off parametric simulation runs. However, input data uncertainties and qualitative aspects of building design work against standard optimization formulations that return a single, so-called optimaldesign. This paper presents a method for harnessing a discrete optimization algorithm to obtain significantly different, economically viable building designs that satisfy an energy efficiency goal. The method is demonstrated using NREL's first-generation building analysis platform, Opt- E-Plus, and two example problems. We discuss the information content of the results, and the computationaleffort required by the algorithm.