Fahlman and Ulrych (1982) describe a method for estimating the power and phase spectra of gapped time series, using a maximum-entropy reconstruction of the data in the gaps. It has proved difficult to apply this technique to solar oscillations data, because of the great complexity of the solar oscillations spectrum. A means for avoiding this difficulty is described, and the results of a series of blind tests of the modified technique are reported. The main results of these tests are: (1) gap filling gives good results, provided that the signal-to-noise ratio in the original data is large enough, and provided the gaps are short enough. For low-noise data, the duty cycle of the observations should not be less than about 50 percent. (2) the frequencies and widths of narrow spectrum features are well reproduced by the technique. (3) The technique systematically reduces the apparent amplitudes of small features in the spectrum relative to large ones.