We constructed models of the 410-km discontinuity, in which the shape and width of the velocity and density increase were constrained by mineral physics data on the &agr;-&bgr; transition in (Mg, Fe)2SiO4. The transition was represented as cubic functions of depth, and its width was estimated to range between 8--24 km. Reflection coefficients were calculated for these models for competing estimates of the percentage of olivine in the mantle, using synthetic seismograms that include the finite-frequency effects of the distributed transition. Comparing the synthetic reflectivities with the average reflectivity observed in previous analyses of ScS reverberations, we conclude that the mantle composition is close to that of pyrolite (55 vol. % olivine). Furthermore, much of the range of reflectivity can be explained by temperature variation in a pyrolite mantle. An olivine-poor composition (35 vol. % olivine) marginally satisfies the seismic data only if the transition thickness averages less than 10 km. ¿ 1999 American Geophysical Union