In order to improve constraints on deep mantle vp, we use generalized spectral fitting (GSF) and data from 12 recent large earthquakes to measure normal mode structure coefficients for a set of 7 vp sensitive multiplets (7S6, 5S7, 5S8, 6S9, 6S10, 5S11, 5S12). This set includes three different classes of strong sensitivity to vp heterogeneity as a function of frequency. We have significantly improved resolution of this part of the spectrum because the use of GSF allows us to provide the first measurements of 6S9 and 5S11, which are strongly coupled to multiplets of the 7S overtone branch, while the use of an expanded data set permits refined measurements of the other multiplets. Our results are consistent with prior measurements, but reveal an inconsistency between the data and model predictions that previously had not been apparent. Recent mantle models that fit most long-wavelength data overestimate the amplitude of degree 2 splitting coefficients for multiplets with two different types of sensitivity to vp heterogeneity. This observation implies that the strong degree 2 component of existing models of the correlation and scaling of δ ln vs and δ ln vp will need to be adjusted significantly in much of the mantle.