We recall the simple statistical concept that non-Gaussian distribution peakedness results from the compounding of random processes. This idea is applied to observations and analysis of sea surface slopes as inferred using optical and microwave-scattering measurements. Our study emphasizes the importance of identifying and quantifying the distribution variance and kurtosis from observations. Data are shown to indicate consistently non-Gaussian peakedness, to indicate the need to report at least two parameters in an even order analysis, and to indicate near equivalence between radar and optical data. Physical interpretation for observed infrequent steep slopes is given via compounding statistical processes where normally distributed short-scale waves are modulated because of random fluctuations mainly associated with the underlying long wave field. Implications of non-Gaussian peakedness are provided for altimeter backscatter theory and for modeling wave-breaking probability. ¿ 2000 American Geophysical Union