A number of studies have confirmed the global existence of a transition zone discontinuity at 410 km depth by aligning large numbers of long-period seismograms on a surface reflection phase before stacking. In particular, SS and PP precursors from the 410-km discontinuity (termed P410P and S410S) have revealed long-wavelength topography of this discontinuity. Here we extend these techniques to examine the reflection coefficient of the 410-km discontinuity. Using our measurements of P410P and S410S amplitudes, we constrain the impedance contrasts across the 410-km discontinuity. We also show lateral variations in the P wave impedance contrast at 410 km, which is typically low under North America and China and higher beneath the North Pacific. The S wave impedance contrast shows less variability on the regional scale. However, analysis of P410P and S410S amplitudes over smaller areas (by binning traces into spherical caps) shows that the S wave reflection coefficient varies over much shorter scale lengths than that for P waves. The different patterns of variation for P410P and S410S reflection amplitudes could be due to the presence of melt, water, or other chemical heterogeneities in the transition zone. Other factors such as temperature or mantle olivine content variations could also influence precursor amplitudes, but they would be expected to lead to correlated variations, and so they cannot explain all the variation that we observe.