Although the international standard CityGML has five levels of detail (LODs), the vast majority of available models are the coarse ones (up to LOD2, ie block-shaped buildings with roofs). LOD3 and LOD4 models, which contain architectural details such as balconies, windows and rooms, nearly exist because, unlike coarser LODs, their construction requires several datasets that must be acquired with different technologies, and often extensive manual work is needed. We investigate in this paper an alternative to obtaining CityGML LOD3 models: the automatic conversion from already existing architectural models (stored in the IFC format). Existing conversion algorithms mostly focus on the semantic mappings and convert all the geometries, which yields CityGML models having poor usability in practice (spatial analysis is for instance not possible). We present a conversion algorithm that accurately applies the correct semantics from IFC models and that constructs valid CityGML LOD3 buildings by performing a series of geometric operations in 3D. We have implemented our algorithm and we demonstrate its effectiveness with several real-world datasets. We also propose specific improvements to both standards to foster their integration in the future.