Orthogonal frequency division multiplexing (OFDM) is a spectral efficient multi-carrier modulation technique which offers many advantages in wireless as well as wired communication systems. Major issues of OFDM implementation are its high peak to average power ratio (PAPR) and extreme sensitivity to carrier frequency offset (CFO). In this paper, we propose a new scheme named optimum null swapping for combined PAPR reduction and CFO estimation in OFDM systems by using one training symbol (pilot) with some null subcarriers embedded in it. We exploit certain number of nulls in the pilot symbol for swapping with some data subcarriers of the data block in such a way as to reduce PAPR. By the proper allocation of null subcarriers based on some specific sequences at the transmitter, CFO is estimated at the receiver using the same pilot OFDM symbol. The computational complexity of the new objective function for the proposed joint optimum null swapping scheme is made significantly low by using the Tabu search algorithm. Moreover, the proposed method demands less side information to be send to the receiver for the reverse swapping of nulls in order to retrieve original data symbols. Simulation results show that the proposed joint scheme offers substantial reduction in PAPR apart from CFO estimation without any additional bandwidth overhead. © 2015, Springer Science+Business Media New York.