A Cox test with parametric bootstrap is developed to select between the linearized version of the First-Difference Almost Ideal Demand System (FDAIDS) and the Rotterdam model. A Cox test with parametric bootstrap has been shown to be more powerful than encompassing tests like those used in past research. The bootstrap approach is used with U.S. meat demand (beef, pork, chicken, fish) and compared to results obtained with an encompassing test. The Cox test with parametric bootstrap consistently indicates the Rotterdam model is preferred to the FDAIDS, while the encompassing test sometimes fails to reject FDAIDS.