We have investigated the speed of compressional waves in a polythermal glacier by, first, predicting them from a simple three-phase (ice, air, water) model derived from a published ground-penetrating radar study, and then comparing them with field data from four orthogonally orientated walkaway vertical seismic profiles (VSPs) acquired in an 80 m deep borehole drilled in the ablation area of Storglaciären, northern Sweden. The model predicts that the P-wave speed increases gradually with depth from 3700ms–1 at the surface to 3760ms–1 at 80m depth, and this change is almost wholly caused by a reduction in air content from 3% at the surface to <0.5% at depth. Changes in P-wave speed due to water content variations are small (<10 ms–1); the model’s seismic cold–temperate transition surface (CTS) is characterized by a 0.3% decrease downwards in P-wave speed (about ten times smaller than the radar CTS). This lack of sensitivity, and the small contrast at the CTS, makes seismically derived water content estimation very challenging. Nevertheless, for down-going direct-wave first arrivals for zero- and near-offset VSP shots, we find that the model-predicted travel times and field observations agree to within 0.2 ms, i.e. less than the observational uncertainties.