We explore the effect of applying tapered windows on atmospheric data to eliminate overestimation inherent in spectra computed from short time series. Some windows are more effective than others in correcting this distortion. The Hamming window gave the best results with experimental data. The Hanning window, which performed almost as well with the same data set, was used to demonstrate the effectiveness of the window in a numerical simulation of the process. We recommend that either of these windows be applied to short data samples prior to spectral analysis.