A conceptually simple method for power estimation in maximum entropy spectral analysis, based on evaluation of complex residues of the spectral density estimator, is suggested. Numerical integration of the peaks of the power density function is thus avoided. The agreement in simple cases with conventional estimates is demonstrated, and the explicit performance is analyzed in detail in a series of examples. The close connection between the residue power estimate and the estimate proposed recently by Pisarenko is pointed out. The method is particularly suitable for spectral decomposition of low noise time series with several harmonic components, because it allows a direct listing of frequency and power estimates, provides an indication of the purity of the obtained harmonic components and enhances the resolution of the maximum entropy spectral density estimator. Computing facilities with modern program libraries are required for efficient use of the method.