It is shown that some recent data on the crest-to-trough heights of sea waves are fitted just as well as by the one-parameter Rayleigh distribution as by the two-parameter Weibull distribution, provided that the rms amplitude ? is taken as 0.925(2m0)1/2, where m0 is the lowest moment of the frequency spectrum. Reasons why the ratio ?/(2m0)1/2, should differ from unity are discussed. It is shown that the effect of finite wave steepness would be to increase the radio by a factor <1+1/2(ak)2 approximately, contrary to observation. The effect of finite band width is estimated from a model assuming low background noise superposed linearly on a delta function spectrum. For narrow band widths one obtains the formula ?2/2m0=1-0.734v2, where v is the rms spread of the noise about the mean frequency. Values of v2 corresponding to Pierson-Moskowiez spectra give results in close agreement with observation.