With TDX-EDEM (EDEM), AW3D30, SRTM and ASTER GDEM-3 (GDEM) global or nearly global free elevation models are available, which are in several countries more accurate than the Digital Elevation Models (DEMs) of the national survey administrations. All these DEMs have a point spacing of 1 arcsecond, which corresponds to ~31 m at the equator. EDEM, based on the TanDEM-X satellite combination, is the latest one, available since 2024. All named DEMs were analysed against reference aerial LiDAR DEMs in four test areas – Mountain, Rolling, Flat and City to gain an overview of their characteristics and accuracy. All these DEMs exhibit systematic errors that depend on the type of data acquisition and the terrain slope. Using ICESat-2 elevation profiles, these systematic errors can be reduced, thus improving the DEMsTo exclude areas with high vegetation, built-up areas, and water surfaces, an exclusion layer is required. The major improvement by ICESat-2 can be reached through a Z-shift of the DEMs determined by comparing the DEMs with ICESat-2 data. Only in few cases a correction by tilt or higher order systematic errors was justified. The best results were achieved with EDEM; only in steep mountainous and in built-up areas, AW3D30, corrected by ICESat-2, has advantages. SRTM and GDEM DEMs are not as good and should no longer be used.