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It has long been observed that accuracy in spectral estimation greatly affects the quality of enhanced speech. A small decrease in the bias and variance of the estimator can greatly reduce the amount of residual noise and distortion in the recovered speech. To date, however, there has been little interest in a rigorous analysis quantifying such observations. In this paper, we analyze the effect of spectral estimate variance on enhanced speech as measured by quantitative and qualitative means. The performance analysis is derived for the signal subspace and the minimum mean square error short-time spectral amplitude estimators. Error is defined as the random function of frequency given by the difference between the estimated and the true power spectral density (PSD) functions. It is measured by its variance as a fraction of the clean speech PSD squared: a norm called the variance quality factor (VQF). The error VQF is derived in terms of the VQF of measurable quantities such as noisy speech and noise alone. It is shown that reducing the PSD estimate variance reduces significantly the VQF of the enhancement error. We provide analytical derivations to establish the results and accompanying simulations to confirm the theoretical analysis. Simulations test the periodogram, Blackman-Tukey, Bartlett-Welch, and Multitaper spectral estimation methods.