Stoneley modes are a special subset of normal modes whose energy is confined along the core–mantle boundary (CMB). As such, they offer a unique glimpse into Earth structure at the base of the mantle. They are often observed through coupling with mantle modes due to rotation, ellipticity and lateral heterogeneity, though they can be detected without such coupling. In this study, we explore the relative sensitivities of seismic spectra of two low-frequency Stoneley modes to several factors, taking as reference the fully coupled computation up to 3 mHz in model S20RTS. The factors considered are (i) theoretical, by exploring the extent to which various coupling approximations can accurately reproduce reference spectra and (ii) model-based, by exploring how various Earth parameters such as CMB topography, attenuation and S- and P-wave structures, and the seismic source solution may influence the spectra. We find that mode-pair coupling is insufficiently accurate, but coupling modes within a range of ±0.1 mHz produces acceptable spectra, compared to full coupling. This has important implications for splitting function measurements, which are computed under the assumption of isolated modes or at best, mode-pair or group coupling. We find that uncertainties in the P-wave velocity mantle model dominate compared to other model parameters. In addition, we also test several hypothetical models of mantle density structure against real data. These tests indicate that, with the low-frequency Stoneley mode spectral data considered here, it is difficult to make any firm statement on whether the large-low-shear-velocity-provinces are denser or lighter than their surroundings. We conclude that better constraints on long wavelength elastic mantle structure, particularly P-wave velocity, need to be obtained, before making further statements on deep mantle density heterogeneity. In particular, a dense anomaly confined to a thin layer at the base of the mantle (less than ∼100–200 km) may not be resolvable using the two Stoneley modes tested here, while the ability of higher frequency Stoneley modes to resolve it requires further investigations.