Unlike those flexible functional forms which are local approximations, the ‘Constant Difference of Elasticities’ (CDE) function is globally well‐behaved. Due to its properties and parsimony in the number of parameters, the CDE functional form offers many potential applications. Two empirical applications are presented. First, aggregate CDE input demand functions are specified and estimated econometrically for the feed concentrate markets in Denmark, Ireland and the United Kingdom. The second empirical application illustrates how a matrix of compensated price elasticities can be obtained with only a priori knowledge of its direct and diagonal elements. The suggested approach exploits some of the properties of the Allen elasticities of substitution associated with the CDE functional