Dense record sections from deep earthquakes in Fiji and Argentina recorded on hundreds of short-period stations in California at distances of 81¿ to 85¿ are used to investigate the detailed P wave velocity structure above the core-mantle boundary (CMB). In the Fiji data a secondary phase arriving 2 to 4 s after the direct P is identified as a precursor to PcP. This phase provides good evidence for a reflection off the top of a thin low-velocity layer above the CMB. Comparisons to synthetic seismograms indicate a layer thickness of 10 km and a velocity reduction of 5%--10% compared to the overlying mantle. A record section from an Argentina event does not show the PcP precursor, indicating that the low-velocity layer is not a global feature. This thin low-velocity layer is in the same place as a much larger S wave velocity anomaly in the lower mantle and is probably indicative of a boundary layer just above the CMB under the mid-Pacific. ¿ American Geophysical Union 1995