The importance of including uncertainties in the design process of aerospace systems is becoming increasingly recognized, leading to the recent development of many techniques for optimization under uncertainty. Most existing methods represent uncertainties in the problem probabilistically; however, in many real life design applications it is often difficult to assign probability distributions to uncertainties without making strong assumptions. Existing approaches for optimization under different types of uncertainty mostly rely on treating combinations of statistical moments as separate objectives, but this can give rise to stochastically dominated designs. Horsetail matching is a flexible approach to optimization under any mix of probabilistic and interval uncertainties that overcomes some of the limitations of existing approaches. The formulation delivers a single, differentiable metric as the objective function for optimization. It is demonstrated on algebraic test problems and the design of a flying wing using a coupled aero-structural analysis code.