Insufficient price variation seriously hampers many applications of consumer demand models. This paper examines the empirical performance of a potential remedy for this problem that was suggested by [Lewbel, A., 1989. Identification and estimation of equivalence scales under weak separability. Review of Economic Studies 56, 311-316], the construction of individual specific price indices for bundles of goods. These individual specific price indices allow for a population with heterogeneity in preferences for goods within a given bundle of goods. We confine ourselves to heterogeneous Cobb Douglas within bundle preferences, while between bundles, we allow for several parametric and even general nonparametric specifications. In a variety of settings, we show that such prices produce superior empirical results than the ones obtained through the traditional practice of using aggregate price indices. Our empirical analysis is based on the British Family Expenditure Survey data, and uses several categories of food. Both in parametric as well as nonparametric models, we obtain higher precision of estimates for parameters or functions, as well as economically more plausible results.