The paper deals with the behavior of an MPC for the control of a level of a tank, whose inflow is subject to persistent plantwide disturbances. It is shown that the response of an industrial MPC can be aggressive and oscillatory in such situations. The result is that the disturbance propagates further. The reason is the assumption made by the industrial MPCs regarding the future evolution of the disturbance. To improve the response in presence of plantwide disturbances, an MPC with disturbance forecasting is proposed. Such MPC is able to handle tight constraints and still reduce the movement of the outflow of the tank, therefore reducing the disturbance propagation. To compare the MPC with prediction forecasting with other two strategies used in industrial practice to handle measured disturbances, the paper uses sinusoidal disturbances and real disturbances coming from a refinery.