The cross-directional control problem of web forming processes subject to input constraints is investigated. We focus our discussion on the analysis of the properties of a previously proposed anti-windup strategy specially tailored for cross-directional control systems. The strategy first seeks disturbance compensation in those control directions associated with the largest gains, as determined by a spatial frequency decomposition of the system's interaction matrix. Simulation results show that the attained steady state performance is superior to that achieved by traditional MIMO anti-windup schemes and is close to an optimal QP solution to the problem. In addition, the strategy presents a robust stabilizing feature, in the sense that it automatically disengages control in those directions where uncertainty in the sign of the gain can otherwise lead to instability.