A new demand system, related to the Almost Ideal Demand System (AIDS) of Deaton and Muellbauer, is developed and illustrated. This Inverse AIDS (IAIDS) retains all of the desirable theoretical properties of the AIDS model with the exception of, consistent aggregation. An empirical issue is whether a linear approximation will work as well for the IAIDS as it has for the AIDS model, since quantities are not as highly correlated as prices. An application to US meat demand demonstrates that the linear approximation of the IAIDS is excellent, which enhances the ease and range of application.