This paper proposes a novel approach to phase-noise compensation. The basic idea is to approximate the phase-noise statistics by a finite number of realizations, i.e., a phase-noise codebook. The receiver then uses an augmented received signal model, where the codebook index is estimated along with other parameters. The realization of the basic idea depends on the details of the air interface, the phase-noise statistics, the propagation scenario and the computational constraints. In this paper, we will focus on a MQAM-OFDM system with pilot sub-carriers within each OFDM symbol. The channel is frequency selective, fading and unknown. A decision-feedback method is employed to further enhance performance of the system. Simulation results are shown for uncoded and coded systems to illustrate the performance of the algorithm, which is also compared with previously employed methods. Our simulations show that for a 16-QAM coded OFDM system over a frequency selective Rayleigh fading channel affected by phase noise with root-mean-square (RMS) of 14.4 degrees per OFDM symbol, the proposed algorithm is 1.5dB from the ideal phase-noise free case at a BER of $10^{-4}$. The performance of the best reference scheme is 2.5dB from the ideal case at BER of $10^{-4}$. The proposed scheme is also computationally attractive.