Recent research has indicated that flexible forms do not always generate empirically credible elasticity estimates. In this paper we present a methodology from which we derive a new family of flexible functional forms (denoted by CES-GBC) that are richer in structure than the cost functions in current use. We use the CES-GBC form to estimate the demand for electricity under time-of-use pricing. The estimation results are encouraging. The elasticity estimates are very reasonable and the fit of the estimated equations is far superior than the more commonly used generalized Leontief, generalized square root quadratic, or any other member of the generalized Box-Cox family of cost functions.