The Burg spectral estimator (BSE) exhibits better peak resolution than conventional linear spectral estimators, particularly for short data records. Based on this property, the quality of the BSE is investigated with the available data record segmented and the relevant parameters or functions associated with each segment averaged. Averaging of autoregressive coefficients, reflection coefficients, or spectral density functions is used with the BSE and the corresponding performances are studied. Approximate expressions for the mean and variance of these modified Burg spectral estimators are derived. Lower bounds for the mean and variance of reflection coefficients are also deduced. Finally, the variance of the estimation errors associated with the modified power spectral density estimators is compared against the theoretical Cramer-Rao lower bound.