Occlusion culling and level-of-detail rendering have become two powerful tools for accelerating the handling of very large models in real-time visualization applications. We present a framework that combines both techniques to improve rendering times. Classical occlusion culling algorithms compute potentially visible sets (PVS), which are supersets of the sets of visible polygons. The novelty of our approach is to estimate the degree of visibility of each object of the PVS using synthesized coarse occluders. This allows to arrange the objects of each PVS into several Hardly-Visible Sets (HVS) with similar occlusion degree. According to image accuracy and frame rate requirements, HVS provide a way to avoid sending to the graphics pipeline those objects whose pixel contribution is low due to partial occlusion. The image error can be bounded by the user at navigation time. On the other hand, as HVS offer a tighter estimation of the pixel contribution for each scene object, it can be used for a more convenient selection of the level-of-detail at which objects are rendered. In this paper, we describe the new framework technique, provide details of its implementation using a visibility octree as the chosen occlusion culling data structure and show some experimental results on the image quality.