In early 1976 the Homer phased-array radar was used to study the spectra of radio-auroral echoes. Good temporal resolution was obtained by using very short data segments. These were analyzed by the maximum entropy method (MEM) of spectra analysis, in a form suitable for treating multiple segments of data. The use of a relatively new method of spectra analysis to obtain spectral estimates of such a short data sample raises a number of questions concerning the reliability of the results. A variety of tests using synthetic time series have demonstrated both the reliability of the spectra estimates and the superiority of MEM for the analysis of Homer radar data. In particular, line-splitting or shifting does not seem to be a problem for spectra with sufficiently broad spectral peaks such as those of the radio aurora. Also, although the widths of the peaks in MEM spectra are highly variable, they average to give the true width. Analysis of the widths of spectral peaks in the Homer radio-auroral data indicates that more than one scattering mechanism may be involved, and that the auroral electrojet is probably quite irregular.