Because of its nearly global coverage, the Shuttle Radar Topographic Mission (SRTM) topography is a promising data set for estimating mountain glacier volume changes. But, first, its absolute accuracy must be thoroughly investigated in a glacial environment. We use topographic data available in the French Alps to assess the usefulness of SRTM for the monitoring of glacier volume variations. We observe clear biases with altitude both on ice-free and glacier-covered areas. At high altitudes, SRTM elevations are underestimated by up to 10 m. These biases can have a significant impact on any estimate of glacier volume changes. If SRTM is the most recent of the two compared topographies, the volume loss is overestimated (and vice versa). We cannot conclude definitively on the origin of these biases and whether they affect all high-mountain areas but our findings invite reconsideration of previous estimates of glacier wastage based on SRTM.