In order to make accurate estimates of anisotropy in D″, as measured from observations of Sdiff(Sd) it is necessary to correct the observed waveforms for anisotropy outside of the deepest mantle as well as side refraction along the path, and to pick arrivals of SVd and SHd as accurately as possible. We show that corrections based on estimates of upper mantle anisotropy inferred from SKS/SKKS splitting measurements are sometimes insufficient and propose a master event method to directly obtain more accurate corrections on specific source-station paths. Our study illustrates the complexity of structure that needs to be taken into account when addressing issues of D″ properties using seismic body wave methods. We also describe a method to accurately measure the arrival time of the corrected SVd wave. ¿ 1998 American Geophysical Union