A new, reduced complexity algorithm is proposed for compensating the Inter-Carrier Interference (ICI) caused by severe PHase Noise (PHN) and Residual Frequency Offset (RFO) in OFDM systems. The algorithm estimates and compensates the most significant terms of the frequency domain ICI process, which are optimally selected via a Minimum Mean Squared Error (MMSE) criterion. The algorithm requires minimal knowledge of the phase process statistics, the estimation of which is also considered. The scheme outperforms previously proposed compensation methods of similar complexity, when severe phase impairments are present.