The possibility of achieving maximally stable, low-sidelobe spectral estimates, without the need for overlapping or temporal weighting, is investigated both theoretically and via simulation. In particular, the (frequency domain) power spectral estimates of each of a sequence of abutting rectangularly gated time data segments are averaged, and then Fourier transformed into the lag (or correlation) domain. This correlation estimate is then reshaped, by dividing out the undesirable triangular autocorrelation of the rectangular temporal weighting, and by multiplying by a desirable lag-weighting function with low sidelobes. Another Fourier transform yields the final spectral estimate of interest. This technique includes, as special cases, the Blackman-Tukey technique and the weighted overlapped segment-averaging FFT technique. The general method has been analyzed in terms of the mean and variance of the spectral estimate, thereby revealing the fundamental dependence of its performance on the temporal weighting, lag weighting, amount of overlap, number of pieces, available data record length, and desired frequency resolution. The mean spectral estimate is equal to the convolution of the true spectrum with an effective window. In the case of lag reshaping, the effective window corresponds directly with the desirable lag-weighting function above, with its low sidelobes. More generally, the effective window is equal to the convolution of the lag window with the magnitude-squared temporal window. Analytic results for the variance of the spectral estimate with rectangular temporal weighting indicate that if the length of the temporal weighting is selected to be somewhat larger than the length of the lag weighting, the variance is at a near minimum. Furthermore, in this situation, the possibly deleterious sidelobes of the temporal weighting can be exactly compensated by proper choice of lag weighting, resulting in low sidelobes and good decay of the overall effective spectral window. Simulation results that confirm all these effects predicted theoretically are presented. The possibility of detecting a weak tonal via lag reshaping is demonstrated, both for a nearby frequency as well as a distant tonal.