We reexamine the possibility of resolving 3D density structure in the mantle, by performing test inversions using a dataset of well constrained degree 2 splitting coefficients. We show that degree 2 in Vs and Vp can be resolved, and confirm that dlnVs/dlnVp>2.5 at depths >2000km, indicating a chemical component to large scale heterogeneity. Models with &rgr; positively correlated with Vs in the deepest mantle fit the data at least as well as those in which density and velocities are anti-correlated. However, some rough bounds on dln&rgr;/dlnVs can be inferred. Models obtained from geodynamic considerations are acceptable, in contrast to models with large negative (0.6)dln&rgr;/dlnVs throughout the lower mantle. The most robust feature is a marked increase in dln&rgr;/dlnVs at the top of the lower mantle reaching a maximum around 1500 km. ¿ 2001 American Geophysical Union