Although active interference cancellation (AIC) is an appealing approach to reduce out-of-band radiation (OBR) in multicarrier systems without distorting data subcarriers, it usually requires a large number of reserved subcarriers to be effective. Introducing memory in AIC precoding may help alleviate this drawback in exchange for some increase in computational complexity. We propose a novel memory AIC precoder which, in contrast to previous schemes, minimizes OBR within a user-selectable frequency region and allows for controlling spectral overshoot.