An existing conjunctive use optimization model of the Mississippi River Valley alluvial aquifer was used to evaluate the effect of selected constraints and model variables on ground-water sustainable yield. Modifications to the optimization model were made to evaluate the effects of varying (1) the upper limit of ground-water withdrawal rates, (2) the streamflow constraint associated with the White River, and (3) the specified stage of the White River. Upper limits of ground-water withdrawal rates were reduced to 75, 50, and 25 percent of the 1997 ground-water withdrawal rates. As the upper limit is reduced, the spatial distribution of sustainable pumping increases, although the total sustainable pumping from the entire model area decreases. In addition, the number of binding constraint points decreases. In a separate analysis, the streamflow constraint associated with the White River was optimized, resulting in an estimate of the maximum sustainable streamflow at DeValls Bluff, Arkansas, the site of potential surface-water withdrawals from the White River for the Grand Prairie Area Demonstration Project. The maximum sustainable streamflow, however, is less than the amount of streamflow allocated in the spring during the paddlefish spawning period. Finally, decreasing the specified stage of the White River was done to evaluate a hypothetical river stage that might result if the White River were to breach the Melinda Head Cut Structure, one of several manmade diversions that prevents the White River from permanently joining the Arkansas River. A reduction in the stage of the White River causes reductions in the sustainable yield of ground water.