Height models are a fundamental part of the geo-information required for various applications. The determination of height models by aerial photogrammetry, LiDAR or space images is time-consuming and expensive. For height models with large area coverage, UAVs are not economic. The freely available height models ASTER GDEM-3, SRTM, AW3D30 and TDM90 can meet various requirements. With the exception of ASTER-GDEM-3, which cannot compete with the other, the digital surface models SRTM, AW3D30 and TDM90 are analyzed in detail for accuracy and morphology in 4 test sites using LiDAR reference DTMs. The accuracy figures root mean square error, standard deviation, NMAD and LE90 are compared as well as the accuracy dependence on the terrain inclination. The analysis uses a layer for the open areas, excluding forest and settlement areas. Remaining elements that do not belong to a DTM are filtered. Particular attention is paid to systematic errors. The InSAR height models SRTM and TDM90 have some accuracy and morphological restrictions in mountain and settlement areas. Even so, the direct sensor orientation of TDM90 is better than for the other. Optimal results in terms of accuracy and morphology were achieved with AW3D30 corrected by TDM90 for the local absolute height level. This correction reduces the bias and also the tilt of the height models compared to the reference LiDAR DTM.