Case studies of four multiplets (vs-sensitive 1S7 and 1S8 and vp-sensitive 5S5 and 5S6) are considered to test the accuracy of normal mode constraints on aspherical structure at degrees above 2 (4, 6, 8). Analyses of misfit, along-branch consistency, and consistency with existing mantle models argue for the feasibility of constraints on higher structural degrees. Preliminary interpretation indicates a relative insensitivity of data misfits to dlnvp/dlnvs at degrees 6 and 8 in the lower mantle (perhaps due to inaccuracies in current Δvs models), and provides weak evidence of some decorrelation between Δvs and Δvp in the middle and lower mantle. ¿ American Geophysical Union 1995