A tool for investigating P-wave (Vp) structure at the base of the mantle is presented. SKS waves at distances around 107¿ are incident upon the core-mantle boundary (CMB) with a slowness that allows for coupling with diffracted P-waves (Pd) at the base of the mantle. The P-wave diffraction occurs at both the SKS entrance and exit locations of the outer core. The resulting phase, SPdKS, arrives slightly later in time that SKS, having a wave path through the mantle and core very close to SKS. The difference time between SKS and SPdKS most strongly depends on Vp at the base of the mantle near SKS core entrance and exit points. Digitized long-period (5--15s) observations from deep focus Tonga events recorded by North American WWSSN and Canadian Seismographic Network stations, and South American events recorded by European and Eurasian WWSSN stations exhibit anomalously large SPdKS-SKS difference times. SKS and the later arriving SPdKS are separated by several seconds more than predictions made by the global average PREM model. Models having a pronounced low-velocity zone in Vp at the base of the mantle best predict the observations. These models are perturbations of the PREM model, whereby the lowermost 50--100 km of the D' layer has a negative Vp gradient, with the mantle-side CMB Vp reduced from PREM by 5% (to 13.0 km/s) at the base of the mantle. ¿ American Geophysical Union 1993