In the stationary Gaussian model of a sea state the ratio between mean zero-upcrossing wave amplitude and rms free surface displacement is always less than (&pgr;/2)1/2, approaching it when the bandwidth tends to zero (narrow band). This is a further argument for a recent explanation given by Longuet-Higgins of a discrepancy between wave data from the Gulf of Mexico and predictions through the narrow band Gaussian model.