To allow realistic policy simulations in a changing environment, inverse demand systems must remain regular over substantial variations in quantities. The distance function is a convenient vehicle for generating such systems. While its use directly yields Hicksian inverse demand functions, those functions will not usually have an explicit representation in terms of the observable variables. However, this problem need not hinder estimation and can be solved by using a numerical inversion estimation approach. This article develops the formal theory for using distance functions in this context and demonstrates the operational feasibility of the method.