Usual methods of spectrum estimation allow very strong frequencies to affect the spectrum estimates at distant frequencies, because the weighting function (spectrum window) cannot be made identically zero over the rejected range of frequencies. To give bounds for this error, a pair of windows, one with positive side lobes (Bartlett), the other with negative side lobes (modified Bartlett), are used simultaneously. Thus we demonstrate the error reduction achieved by detrending and prewhitening an example economic time series. The details of the spectrum windows, and a discussion of confidence limits for the spectrum, are given in the appendix. A program for the IBM 650 is available.