First-order theory predicts that zero-crossing wave should have a Rayleigh distribution, but measured waves are slightly smaller than the theoretical prediction. Suggested explanations for this discrepancy have included the nonlinearity of the wave surface, limitations on height as a result of breaking, and the effect of spectral width. In a recent paper, Tayfun (1981b) showed that the shape of the spectrum influences the height distribution because the wave envelope has different amplitudes at the time of the crest and trough. We have compared the distribution developed by Tayfun to simulated waves with different spectral shapes as well as to observations and found excellent agreement. The theoretical, simulated, and measured wave height distributions agree to within 1% in height. This result reinforces the conclusion that linear Gaussian simulations can reporduce many features of ocean waves.