Data from the Jason-2 calibration/validation mission phase are analyzed to identify the correlation between the measurement errors of sea-surface height (SSH) and significant wave height (SWH). A cross-spectral analysis indicates that the SSH and SWH errors are nearly white and coherent at scales from 12 km to 100 km, consistent with the hypothesized error source, the waveform retracker. Because of the scale separation between the SWH signal and noise, it is possible to correct the SSH data by removing the noise correlated with the SWH noise. Such a correction has been developed using data from the calibration orbit phase and applied to independent data from other phases of the Jason-1 mission. The efficacy of the correction varies geographically, but variance reductions between 1.6 cm^2 and 2.2 cm^2 have been obtained, corresponding to reductions of 20% to 27% in the noise floor of along-track spectra. The corrections are obtained from, and applied to, conventional, 1 Hz, altimetry data, and lead to improvements in the signal-to-noise for identification of short-wavelength features, such as the internal tides.