Seismic estimates of sharpness of the mantle discontinuities are important for constraining models of composition and temperature in the deep Earth but these data are difficult to obtain. We explore a possibility to determine sharpness of the major mantle discontinuities (those at depths around 400 and 650 km) from the broad-band records of phases converted from P to S underneath the receiver. Our estimates are obtained from a comparative analysis of waveforms of the converted phases and those of the P waves in the teleseismic records of BRV (Kazakhstan), GRF (Germany), NREO (Norway) and YKW (Canada). The data indicate that the shape of the pulse converted at the 400-km discontinuity is close to that of the P wave whereas the pulse of the 650-km conversion is substantially broader. We infer from this comparison that the 400-km discontinuity is sharp (width of the transition zone is less than 5--7 km). The 650-km transition is modelled by a linear gradient zone 20--30 km thick. ¿ American Geophysical Union 1993