A better estimation of the power spectrum of a time series formed with unequally spaced observations may be obtained by means of a data-compensated discrete Fourier transform. This transform is defined so as to include the uneven spacing of the dates of observation and weighting of the corresponding data. The accurate determination of the peak heights allows one to design harmonic filters and thus to make a more certain choice among peaks of similar height and also to discriminate peaks that are just aliases of other peaks. The theory is applied to simulated time series and also to true observational data.