The contrasting efficiency of erosion beneath cold glacier ice, beneath temperate glacier ice, and on ice-free mountain slopes is one of the key parameters in the development of relief during glacial periods. Detrital geochronology has been applied to the subglacial streams of the north face of the Mont-Blanc massif in order to estimate the efficiency of erosional processes there. Lithologically this area is composed of granite intruded at ~303 Ma within an older polymetamorphic complex. We use macroscopic features (on ~10,000 clasts) and U-Pb dating of zircon (~500 grains) to establish the provenance of the sediment transported by the glacier and its subglacial streams. The lithology of sediment collected from the surface and the base of the glacier is compared with the distribution of bedrock sources. The analysis of this distribution takes into account the glacier's surface flow lines, the surface areas beneath temperate and cold ice above and below the Equilibrium Line Altitude (ELA), and the extent of the watersheds of the three subglacial meltwater stream outlets located at altitudes of 2300 m, 1760 m and 1450 m. Comparison of the proportions of granite and metamorphics in these samples indicates that (1) glacial transport does not mix the clasts derived from subglacial erosion with the clasts derived from supraglacial deposition, except in the lower part of the ice tongue where supraglacial streams and moulins transfer the supraglacial load to the base of the glacier; (2) the glacial erosion rate beneath the tongue is lower than the erosion rate in adjacent non-glaciated areas; and (3) glacial erosion beneath cold ice is at least 16 times less efficient than erosion beneath temperate ice. The low rates of subglacial erosion on the north face of the Mont-Blanc massif mean that its glaciers are protecting "the roof of Europe" from erosion. A long-term effect of this might be a rise in the maximum altitude of the Alps.