The regular perturbation (RP) series used to analytically approximate the solution of the nonlinear Schrodinger equation has a serious energy-divergence problem when truncated to the first order. The enhanced RP (ERP) method can improve the accuracy of the first-order RP approximation by solving the energy divergence problem. In this paper, we propose an ERP-based nonlinearity compensation technique, referred to as ERP-NLC, to compensate for the fiber nonlinearity in a polarization-division multiplexed dispersion unmanaged optical communication system. We also propose a modified perturbation-based NLC (PB-NLC) technique by simple phase-rotation (PR) of the nonlinear coefficient matrix, referred to as the PR-PB-NLC. The PR-PB-NLC can be considered as a by-product of the ERP-NLC technique. We show through numerical simulation that, for a 256 Gb/s single-channel system, the proposed ERP-NLC technique improves the Q-factor performance by ∼1.2 dB and ∼0.6 dB when compared to the electronic dispersion compensation (EDC) and the PB-NLC techniques, respectively, at a transmission distance of 2800 km. Also, the result for a 1.28 Tb/s wavelength-division multiplexed five-channel transmission system at the same transmission distance shows that the Q-factor performance of the ERP-NLC technique is improved by ∼0.6 dB and ∼0.4 dB when compared to the EDC and the PB-NLC techniques, respectively. The simulation results for the PR-PB-NLC technique for a single-or five-channel transmission system show an improved Q-factor performance when compared to the EDC and PB-NLC techniques. Finally, we show that the proposed performance enhancement comes with a negligible increase in the computational complexity for the ERP-NLC and PR-PB-NLC techniques when compared to the PB-NLC technique.