Design optimization methods using high-fidelity computational fluid dynamics simulations are becoming increasingly popular in the area of aerodynamic design, sustaining the desire to make these methods more computationally efficient. Such design strategies typically define the aerodynamic product using a parametric model of the geometry, but this can often require a large number of design variables, increasing the computational cost. This thesis proposes that a parametric model of aerodynamic flow features, rather than geometry, can be a parsimonious method of representing designs, giving a reduction in the number of design parameters required for optimization. The parameterization of flow features is coupled with inverse design, in order to recover the corresponding geometry. While an expensive analysis code is used in evaluating design performance, computational cost is reduced by using a low-fidelity code in the inverse design process. This newly presented method is demonstrated using four case studies in 2-D airfoil design, in which the parameterized flow feature is the surface pressure distribution, and two case studies for 3-D wing design, in which the spanwise loading distribution is parameterized. These strategies are consistently compared against a benchmark design search method which uses a conventional parameterization of the geometry. The two methods are described in detail, and their relative performance is analysed and discussed. The newly presented method is found to converge towards the optimum design significantly more quickly than the benchmark method, providing designs with greater performance for a given computational expense. A parameterization of flow features can generate designs with higher quality and detail than a geometry-based method of the same dimensionality.