The extension of some immunization results to the framework of generalized s-convex orders is considered. A detailed study of the special case s=3 is undertaken. A portfolio strategy, which achieves immunization against 3-convex shift factors, necessarily matches durations and convexities. For some more general shift factors, we derive bounds on the change in portfolio value, which depend on the skewness increase between the liability and asset risks. A linear control of these immunization bounds is examined. For a specific minimax strategy these bounds can be reduced to a constant independently of the time horizon.