The spectral analysis of a signal from a randomly sampled time series is discussed. Spectral estimates derived from the direct transform of this series are compared with those obtained by the correlation method of analysis discussed earlier by the authors (Gaster & Roberts 1975). As found previously, additional variability arises from the random character of the sampling instants. An expression for this variability is derived, and predictions based on it are compared, over a wide range of sampling rates and bandwidths, with computed values obtained from simulated data. The relation between variability and sampling rate is used to find an optimum rate at which this variability is a minimum for a given amount of computation. By this means analysis of a simulated record is carried out over three and a half decades of frequency in one-third octave steps. The relative merits of forming spectral estimates by the direct transform of the data are compared with those of transforming the autocorrelation function. It turns out that although the computational effort is in general less with the technique investigated here, a greater quantity of data is needed to achieve a given level of variability.