The existence of seismic discontinuities within the continental upper mantle has long been recognized, with more recent studies often indicating an association with elastic anisotropy. Their near-vertical sampling renders teleseismic P and S waves suitable for characterization of mantle discontinuities, but computationally efficient methods of calculating synthetic seismograms are required for structures that exhibit lateral variability. We consider lithospheric models consisting of planar, homogeneous anisotropic layers with arbitrary dip. We adopt the traveltime equation of Diebold for dipping, plane-layered media as the basis for a high-frequency asymptotic method that does not require ray tracing. Traveltimes of plane waves in anisotropic media are calculated from simple analytic formulae involving the depths of layers beneath a station and the vertical components of phase slowness within the layers. We compute amplitudes using the reflection and transmission matrices for planar interfaces separating homogeneous anisotropic media. Modelling indicates that upper-mantle seismic responses depend in a complex fashion on both layer dip and anisotropy, particularly in the case of converted phases. Azimuthal anisotropy generally displays a distinctive 180° backazimuthal periodicity in Ps conversion amplitude, as opposed to the 360° symmetry produced by dip. In contrast, anisotropy with a steeply plunging axis may under certain conditions be difficult to distinguish from interface dip, as both exhibit a 360° symmetry. We demonstrate the application of the method on Ps and Sp conversion data from the Yellowknife Array, which show evidence for both dipping and anisotropic layering, attributed to layers of anisotropi c fabric in the upper mantle associated with ancient subducted slabs.