We measured absolute P'P'df as well as differential P'P'bc-P'P'df and P'P'ab-P'P'df travel time residuals for earthquakes in Alaska and the Aleutians recorded at NORSAR array (Norway). For such paths, P'P'df samples two regions of the inner core which have been identified as strongly anisotropic (~3.5%), respectively beneath the Central Pacific and Africa, and should arrive some ~6s earlier than predicted by a standard model. Absolute and differential travel times do not appear to be anomalous. A very complex texture and/or heterogeneity of the top ~400 km of the inner core, or a significant contribution from the strongly heterogeneous D″, is required to explain this discrepancy. ¿ 2000 American Geophysical Union