Ocean waves are known to be both random in time and nonlinear. Surface elevation time histories measured in the Gulf of Mexico during Hurricane Camille in 1969 are re-analyzed. The average shapes of large crests and deep troughs in time are shown to be close to symmetric around the instant when the maximum (or minimum) occurs, with only slight evidence of asymmetry from wave breaking in the time histories. There is considerable vertical asymmetry with higher and sharper crests and smaller and more rounded troughs. Overall, the analysis supports the use of a focused wave group based on the scaled autocorrelation function (NewWave) as proposed by Lindgren and Boccotti, with sum harmonic corrections. There is a very small second order difference setup for both large crests and troughs, consistent with considerable directional spreading in the hurricane sea-state. This spreading is likely to be larger than that usually assumed for nontropical winter storms. The spectral tail is shown to have a decay rate proportional to –4.5 power law midway between the classical JONSWAP (Phillips) –5 form and the –4 slope proposed by Battjes et al. (1987, “A Reanalysis of the Spectra Observed in JONSWAP,” J. Phys. Oceanogr., 17(8), pp. 1288–1295) as a correction to JONSWAP.