Many of the 3D city models offered by the German federal states were created using a model-driven approach based on airborne laser scanning point clouds. The method consists of dividing the building footprint into small regions, for each of which a parameterized standard roof shape is chosen from a catalog in such a way that it best matches the point cloud of the corresponding roof area. A model-based approach usually means that small structures such as dormers are lost. However, these structures affect the gradient and position of the model roof segments. To obtain more accurate main roof facets that can be used as the basis for adding higher level of detail objects, a correction is required. The best plane equation of each roof facet of the given model is estimated from the point cloud using the Random Sampling Consensus (RANSAC) algorithm. If a model facet needs to be adjusted, its boundary polygon has to be recalculated. This is done with a mixed integer linear program, which changes the positions of the vertices so that they lie on as many roof planes as possible. Vertices on the cadastral footprint are allowed to be moved only on the footprint, other vertices have to stay within the (not necessarily convex) footprint polygon. In this paper, such a program is presented and applied to city models of North Rhine-Westphalia.