3D Kirchhoff theory is used to calculate synthetic short-period (1 s) seismograms for the reflection PcP at the core-mantle boundary (CMB). The CMB models have sinusoidal topography of wavelength L and and amplitude E. E values of 0.5 and 1 km are assumed, in agreement with results of PKP-precursor studies, and L ranges from 600 to 10 km. The corresponding PcP amplitude-distance curves in the range 22--81¿ are compared with the smooth curve for a spherical CMB (E=0). For L≥100 km pronounced amplitude variations around the reference curve occur, corresponding to PcP focusing by lows and defocusing by highs of the CMB. For L≤50 km the amplitude curve is smooth again, but with lower values than on the reference curve: part of the energy is deflected from the specular PcP ray of the reference model by diffuse reflection. These results are in qualitative agreement with seismological observations of (1) strong scatter in PcP amplitudes and (2) generally very low PcP amplitudes at distances beyond 70¿. ¿ American Geophysical Union 1989