Anticipatory anti-windup compensation involves activation of the anti-windup compensator before the physical saturation limits on the control signals are reached; the anti-windup compensator is activated in anticipation of actuator saturation occurring. Existing studies, which have used a pseudo-LPV representation for compensator synthesis, have proposed convex but somewhat complicated and opaque synthesis routines. This paper offers an alternative method of synthesising anticipatory anti-windup compensators, involving the exploitation of a "non-square" sector condition associated with a combination of deadzone nonlinearities. This method leads to an anticipatory compensator synthesis routine which is close to that associated with standard immediately activated anti-windup compensators. A numerical example and comments on the use of anticipatory anti-windup are also given.