Active interference cancellation (AIC) is known to be a very effective technique for reducing the interference of OFDM sidelobes to primary licensed users in cognitive OFDM systems. However, AIC has some shortcomings such as high computational complexity and spectrum overshoot on the cancellation subcarriers. Spectrum overshoot is mainly caused due to unconstrained or unbalanced power allocation to the cancellation tones used in AIC. In this paper, we propose an improved AIC technique in which the problem of spectrum overshoot is tackled. We show that by a modification to the solution of the optimization problem involved in AIC, we can obtain a trade-off between the amount of spectrum overshoot and sidelobe suppression without increasing the system complexity. In particular, spectrum overshoot can be completely eliminated. Furthermore, simulations prove that with this modification, the peak spectral interference at the primary band is less than that of the AIC technique with a single power constraint.