The Southworth hypothesis predicts that inframarginal food stamp recipients should choose the same bundle of goods, whether they receive coupons or cash. Empirical research has contradicted this prediction. Here, we present a model that retains some attractive features of the Southworth hypothesis, while relaxing the key assumption that appears to be incorrect. In particular, we allow different forms of benefits to have distinct effects on desired, or unrestricted food spending. Two categories of previously commonly used empirical models are evaluated as special cases of our more general model. We estimate this model using data from two cash-out experiments.