Parameters that both distinguish fricatives in a given language, and characterize normal and disordered productions would be useful. Various parametrizations have been tried since the 1950s with only partial success. Forrest etal. [J. Acoust. Soc. Am. 84, 115–123 (1988)] defined spectral moments of speech power spectra, but found that these failed to distinguish the voiceless English fricatives. They have however proven useful for distinguishing sibilants, and for characterizing long‐term place changes of sibilants in disordered speech. As discussed in this paper, other changes, and nonsibilants, are not so easily characterized. Relative amplitude differences have to date not been incorporated in spectral moment methodology. The quality of the spectral estimate (whether consistent, unbiased) affects the variability of the moments, and means of obtaining a good estimate usually involve assuming stationarity or ergodicity. Finally, moments capture little that is known about fricative production. Modern techniques for consistent PSD estimation (e.g., multitaper and wavelet analysis) have been examined; their suitability in analyzing fricatives is discussed. While these modern PSD estimation methods may improve the performance of spectral moments, they also lend themselves to new parametric methods which do not rely on assumptions of ergodicity or stationarity. [Research supported by EPSRC.]