We have developed a second-order small-signal model for describing the nonlinear redistribution of noise in a saturated semiconductor optical amplifier. In this paper, the details of the model are presented. A numerical example is used to compare the model to statistical simulations. We show that the proper inclusion of second-order noise terms is required for describing the change in the skewness (third-order moment) of the noise distributions. The calculated probability density functions are described far out in the tails and can hence describe signals with very low bit error rate (BER). The work is relevant for describing the noise distribution and BER in, for example, optical regeneration.