In this paper, joint effect of transmitter and receiver IQ imbalance under insufficient and sufficient cyclic prefix (CP) is studied. The case of insufficient CP length results in interblock-interference (IBI) between the OFDM symbols. For compensation of this effect and other impairments, simultaneously, per-tone equalization (PTEQ) structure implementation is necessary. Regarding to the topology of this structure and required high length filters, the system computations will be very high, even using simplest adaptive algorithms. In this paper, firstly wavelet packet transform (WPT) is applied to branches of PTEQ structure to increase the convergence speed of adaptive algorithms. Then it is proposed to use the selective coefficient update (SCU) based on packets entropy on each branch of this structure to decrease the computations. In this way, not only the large amount of calculations will be eliminated but also systems operation will not be affected. Also, to further increase of convergence speed and computation reduction, using the data selective update (DSU) along with SCU is proposed. This kind of filtering (DSU) increases the algorithms convergence speed because of using adaptive noise dependent step size. Simultaneous using of two DSU and SCU methods besides the expedition and denoising characteristics of WPT makes suitable the proposed algorithm for using in real time systems. Simulation results show that this algorithm not only causes considerably reduction on the amount of calculations, but also does not affect the normal operation of algorithm. In addition, it is capable to compensate the joint channel and IQ imbalance distortions.