A theoretical investigation of the equalization-enhanced phase noise (EEPN) and its mitigation is presented. We show with a frequency domain analysis that the EEPN results from the non-linear inter-mixing between the sidebands of the dispersed signal and the noise sidebands of the local oscillator. It is further shown and validated with system simulations that the transmission penalty is mainly due to the slow optical frequency fluctuations of the local oscillator. Hence, elimination of the frequency noise below a certain cut-off frequency significantly reduces the transmission penalty, even when frequency noise would otherwise cause an error floor. The required cut-off frequency increases linearly with the white frequency noise level and hence the linewidth of the local oscillator laser, but is virtually independent of the symbol rate and the accumulated dispersion.