We present results from forward modelling to study the feasibility of using S-to-P converted phases to image the seismic discontinuity structure of the crust and upper mantle. We show that a significant level of P-wave energy arriving before the direct S-wave arrival can interfere with the S-to-P converted phases of interest and may result in Sp receiver function phases that do not represent true earth structure. The source of this P-wave energy is attributable to a number of phases, including those that have undergone multiple reflections off the Earth's surface. For deep focus earthquakes (300-600 km deep), a significant amount of P-wave energy is observed from pPPP, pPPPP and sPPPP phases, and arrives within the same time window as predicted for S-to-P converted phases from the direct S phase arrival. Furthermore, for earthquakes at all depths, interfering P-wave energy arrives within the same time window as predicted for S-to-P converted phases from the SKS phase arrival, limiting the usefulness of SKSp receiver functions for upper mantle imaging. To isolate true Sp receiver function phases from contamination due to other P-wave phases, we find it necessary to stack receiver functions from a range of epicentral distances and depths in order to aid the suppression of noise and other unwanted phases. We provide constraints on the noise levels to be expected as a function of epicentral distance and earthquake depth. We find that the lowest noise levels are achievable by restricting epicentral distance to less than 75 degrees and the depth of earthquakes used to less than 300 km.