We use thermodynamically self-consistent and hybrid methods to analyze the correlation of important physical parameters (e.g. bulk density, elastic moduli) with bulk Mg# and modal composition in mantle peridotites at upper mantle conditions. Temperature (anharmonic and anelastic), pressure and compositional derivatives for all these parameters are evaluated. The results show that the widely used correlations between Vp/Vs and Mg# in peridotites are strictly valid only for garnet-bearing assemblages at temperatures < 900 °C. The correlation breaks down when: i) spinel is the stable Al-rich phase in the assemblage and ii) when anelastic attenuation of seismic velocities becomes important (T ≳ 900 °C). This implies that the range of applicability of published Vp/Vs-Mg# correlations for the upper mantle is limited to a depth interval between the spinel-garnet phase transition and the 900 °C isotherm. We use numerical simulations to show that this depth interval is virtually nonexistent in lithospheres thinner than ∼ 140 km and can comprise up to ∼ 50% of the lithospheric mantle in thick (> 220 km) lithospheric domains. In addition, we show that for most of the upper mantle the expected Δ(Vp/Vs) values associated with compositional variations are smaller than the resolution limit of current seismological methods. All these considerations suggest that the Vp/Vs ratio is not a reliable measure of compositional variations and that for large parts of the upper mantle compositional anomalies cannot be separated from thermal anomalies on the basis of seismological studies only. We further confirm that the only reliable indicator of compositional anomalies in a peridotitic mantle is the ratio of density to shear wave velocities (ρ/Vs). Our results demonstrate that geophysical-petrological models (forward or inverse) that model these two fields (i.e. density and Vs) self-consistently within a robust thermodynamic framework are necessary for characterizing the small-scale thermal and compositional structure of the lithosphere and sublithospheric upper mantle.