Digital spectrum analysis of harmonic signals can result in amplitude estimates in error as much as 3.92 dB. The corresponding frequency estimates are not exact. The paper presents a general method for obtaining significantly improved estimates of amplitude and frequency. Criteria are given which allow specification of an error limit. Specific equations are given for sample signals that are unmodified (open window) and for signals modified by a Hanning data window. The phenomenon called ’’leakage’’ is shown to result from discontinuities imposed by the computation process at the periodically extended ’’ends’’ of a sample signal and not, as is often supposed, by discontinuities presumed to (but do not) exist at the ’’ends’’ of the open window. Criteria for window selection to reduce leakage are discussed. Calibration is specifically treated. When any data window other than the open window is used, a different calibration must be applied to periodic and random components in a signal. Although discussion is limited to a single harmonic signal, the method can be applied in a straightforward way to signals with multiple harmonics. Subject Classification: 10.60; 60.10; 30.80; 40.60; 50.85, 60.50; 85.32, 85.84.