The primary goal of NASA's Ice, Cloud, and land Elevation Satellite (ICESat) mission was to detect centimeter-level changes in global ice sheet elevations at the spatial scale of individual ice streams. Confidence in detecting these small signals requires careful validation over time to characterize the uncertainty and stability of measured elevations. A common validation approach compares altimeter elevations to an independently characterized and stable reference surface. Using a digital elevation model (DEM) from geodetic surveys of one such surface, the salar de Uyuni in Bolivia, we show that ICESat elevations at this location have a 0.0-cm bias relative to the WGS84 ellipsoid, 4.0-cm (1-sigma) uncertainty overall, and 1.8-cm uncertainty under ideal conditions over short (50 km) profiles. We observe no elevation bias between ascending and descending orbits, but we do find that elevations measured immediately after transitions from low to high surface albedo may be negatively biased. Previous studies have reported intercampaign biases (ICBs) between various ICESat observation campaigns, but we find no statistically significant ICBs or ICB trends in our data. We do find a previously unreported 3.1-cm bias between ICESat's Laser 2 and Laser 3, and we find even larger interlaser biases in reanalyzed data from other studies. For an altimeter with an exact repeat orbit like ICESat, we also demonstrate that validation results with respect to averaged elevation profiles along a single ground track are comparable to results obtained using reference elevations from an in situ survey.