A theoretical expression for the joint distribution of wave period and amplitude, which was previously derived for a Gaussian record with a narrow spectrum, is restated in simple form. According to this distribution the variability of wave periods, for waves of a given height, is inversely proportional to the wave height, so that that higher waves tend to be more regular. The distribution is found to agree well with some observations of wave periods and amplitudes from the Gulf of Mexico, as given by Bretschneider (1959).