We analyze short-period PKP precursor wave trains recorded at Global Digital Seismograph Network stations in the distance range 120¿<Δ<140¿ to infer the nature of inhomogeneities near the core-mantle boundary. Travel times and particle motions are consistent with predictions of single-scattered waves near the CMB. The dominant frequencies are aroung 1 Hz. The regions best sampled are beneath Indonesia, North America, Central Africa, and South America. Based on first-order scattering theory, the characteristics of the wave number spectrum of the structural inhomogeneities are obtained for two hypotheses: volume inhomogeneities and topographic irregularities. For the range of wavelengths sampled by these data (between 10 and 70 km), the spectrum of inhomogeneities is best represented by a power law of index 5.3 for volume inhomogeneities and 6.8 for topographic irregularities. If the scattering is due only to volumetric inhomogeneities, we estimate the strength of the structural variations to be about 0.5% in P wave velocity for a 200-km-thick layer. If the scattering is due only to topographic irregularities, the topography has an rms height of 280 m. At present we can not distinguish between these two types of inhomogeneities. ¿ American Geophysical Union 1988