Employing nonlinear functions in audio DSP algorithms requires attention as they generally introduce aliasing. Among others, antiderivative antialiasing proved to be an effective method for static nonlinearities and gave rise to a number of variants, including our AA-IIR method. In this paper we introduce an improvement to AA-IIR that makes it suitable for use in stateful systems. Indeed, employing standard antiderivative antialiasing techniques in such systems alters their frequency response and may cause stability issues. Our method consists in cascading a digital filter after the AA-IIR block in order to fully compensate for unwanted delay and frequency-dependent effects. We study the conditions for such a digital filter to be stable itself and evaluate the method by applying it to the diode clipper circuit.