The almost Gaussian nature of OFDM (Orthogonal Frequency Division Multiplexing) signals with high number of subcarriers N is widely employed to characterize nonlinearly distorted OFDM signals and to evaluate the corresponding performance. In this paper we study the accuracy of the Gaussian approach when evaluating nonlinear effects in OFDM signals with finite number of subcarriers, showing the strengths and limitations of this approach. It is shown that the decomposition in useful and self-interference components is valid even for a reduced number of subcarriers. The Gaussian approximation of the nonlinear self-interference at the subcarrier level is very accurate provided that N^2 is high. However, the nonlinear distortion levels slightly lower than the ones obtained with the Gaussian approximation, with relative errors dropping with 1/N, leading to somewhat pessimistic SIR levels (Signal to Interference Ratio).