Shear waves that traverse the lowermost mantle exhibit polarization anomalies and waveform complexities that indicate the presence of complex velocity structure above the core-mantle boundary. Synthetic seismograms for horizontally and vertically polarized shear waves (SH and SV, respectively) are computed using the reflectivity method for structures with low-velocity sheets (lamellae), and for comb-like models approximating long wavelength vertical transverse isotropy (VTI). Motivated by evidence for partial melt in the deep mantle, lamella parameter ranges include (1) δVP from -5 to -10%, δVS = 3δVP; (2) 100 to 300 km thickness of vertical stacks of lamella; (3) lamella spacing and thickness varying from 0.5 to 20 km; and (4) lamellae concentrated near the top, bottom, or throughout the D″ region at the base of the mantle. Such lamellae represent, in effect, horizontally emplaced dikes within D″. Excessively complex waveforms are produced when more than ~20% of D″ volume is comprised of low-velocity lamellae. Many lamellae models can match observed Sdiff splitting (1--10 s delays of SVdiff), but typically underpredict ScS splitting (1--4 s delays of ScSV). VTI model parameters are selected to address D″ observations, and include (1) 0.5 to 3% anisotropy; (2) discontinuous D″ shear velocity increases up to 3%; (3) D″ thicknesses from 100 to 300 km; and (4) VTI concentrated at the top, bottom, or throughout D″. VTI models readily match observed splits of ScS and Sdiff. We discuss lamellae and VTI model attributes in relationship to waveform complexities, splitting magnitude, triplications from a high-velocity D″ discontinuity, and apparently reversed polarity SVdiff onsets. The possible presence of melt-filled lamellae indicates that local chemical or thermal perturbations can produce regions that exceed the solidus within D″. Such melt could occur in the bulk of D″ because the melt is either close to neutral buoyancy, advective velocities exceed percolative velocities, or both.