The new Dutch national digital elevation model (DEM), acquired with laser altimetry, is almost complete. The Dutch Survey Department fulfils an intermediary function between laser data suppliers and final users of the DEM. One of the most important tasks of the Survey Department is to guarantee the quality of the delivered laser DEMs to the users. For this purpose, a new height error description scheme is developed, allowing to quantify error effects at different scales. Such a new error description scheme was necessary because the former quality description of DEMs was insufficient. The error behaviour of laser altimetry data, acquired by a complex system of different sensors, cannot be expressed by solely two parameters: a bias and a standard deviation. The former and the new error description scheme will be addressed together with methods to quantify the differently scaled error components. Among them are cross correlation techniques, empirical covariance function analysis from geostatistics and 1d strip adjustment. The contractual demands for maximal allowed error amplitudes, derived from real data, will be presented. The benefit of the error description scheme for DEM users will be illustrated by propagating the error components to the height precision of derived products. Summarizing, it can be stated that this paper deals with the height precision of laser altimetry DEMs and the effects of the different error components on the measured heights. This paper does however not aspire to give methods for eliminating or minimizing these errors.