Essentially related to the problem of spectrum estimation of random data by fast-Fourier-transform techniques is the problem of establishing efficient data windows or data-smoothing procedures for minimising leakage effects. Statistics of spectral estimates derived from finite data lengths indicate that the estimates are related to the true spectrum by a frequency convolution with a Fejer window. It is well known that leakage of power in the spectrum occurs from the nonnegligible sidelobes of this window. The paper presents an investigation into the application of data windows in spectral analysis. Consequent effects on the bias (amplitude) and the variance of the spectral estimates are analysed and compensating factors are specified. Criteria are further developed for comparing the increase in bandwidth of spectral analysis caused by different data-smoothing sequences. As the bandwidth of analysis is dependent on the bandwidth of the spectral window associated with a data window to the frequency tion of the window bandwidth leads to a measure of the loss of frequency resolution entailed by tapering the data. Although no universal definition exists for the bandwidth of a system or a time series, four different expressions are included for the bandwidth of a spectral window which relate the parameters of a data window to the frequency spread of its associated spectral window. Three families of data windows are considered, and computed results are presented which allow the choice of a data window as an optimum compromise between critical factors involved in the design of an efficient spectrum-estimation procedure.