The relative amplitudes and travel times of ScS and S phases are utilized to place constraints on the shear-wave velocity gradient above the core-mantle boundary. A previously reported long-period ScSH/SH amplitude ratio minimum in the distance range 65¿ to 70¿ is shown to be a localized feature, apparently produced by an amplitude anomaly in the direct S phase, and therefore need not reflect the velocity gradient at the base of the mantle. The amplitude ratios that are free of this anomaly are consistent with calculations for the JB model or models with mild positive or negative velocity gradients in the lowermost 200 km of the mantle. ScSV arrivals are particularly sensitive to the shear velocity structure just above the core-mantle boundary. The apparent arrival time of the peak of ScSC is as much as 4 s greater than that of ScSH in the distance range 75¿ to 80¿ for Sea of Okhotsk events recorded in North America. This can be explained by interference effects by a localized high velocity layer or strong positive S wave velocity gradient in the lowermost 20 km of the mantle. A velocity increase of about 5% is required to explain the observed shift between ScSH and ScSH. This thin, high velocity layer varies laterally, as it is not observed in similar data from Argentine events. Refined estimates of the outermost core P velocity structure are obtained by modeling SKS signals in the distance range 75¿ to 85¿.