A search is made for lateral heterogeneity in the earth's inner core by analyzing the differential travel times between PKP-DF, PKP-CD and PKP-Cdiff. These are P waves that are respectively transmitted through, reflected by, and diffracted around the inner core. From this data, heterogeneity in and near the inner core is found to be small. Residuals from PREM in the 134¿ to 157¿ range are bounded by ¿0.8 sec., consistent with a ¿0.9% variation in P velocity in the upper 200 km. of the inner core. The region pattern of velocity variation inferred from the differential times is consistent with those obtained from global inversions of absolute PKP-DF times.