Using weak-motion recordings of aftershocks of the 1989 Loma Prieta earthquake recorded in Oakland, California, near the failed Nimitz Freeway, two methods have been applied to estimate the site response of an alluvium site and three mud-over-alluvium sites. The first estimate is the traditional spectral ratio, and the second utilizes the cross spectrum. Recordings obtained at a nearby bedrock site are used as estimates of the sediment site input motions. While the two site response estimates produce similar peaks and troughs, there is an approximate factor of 2 difference in amplitudes. This discrepancy is evidence that there is a much greater level of noise than would be expected from the pre-event ambient noise. We interpret this as signal-generated noise produced by scattering from heterogeneities, which causes the true sediment site input to differ significantly from the bedrock site recording. Given this level of noise, the cross-spectrum estimate suffers a severe downward bias (by a factor of 2 in this study) and should probably not be used when the input motion is estimated from a bedrock site recording. The spectral-ratio estimates are relatively unbiased, but the level of noise introduces a large degree of uncertainty. Therefore, inferences about site response from individual spectral ratios should probably be avoided. On the other hand, ensemble averages of the estimates significantly reduce the scatter to reveal resonances that agree quite well in frequency and overall shape with those of one-dimensional models whose parameters were determined independently. A discrepancy of higher observed amplitudes than predicted by theory remains unexplained but most likely results from the effects of boundary layer topography, which are not accounted for by the simple one-dimensional models.