A model simplification technique is required to control the level of detail (LOD) of a three-dimensional (3D) computer-aided design (CAD) model. In particular, to simplify a B-rep model, volume decomposition operations are performed to decompose the model into volumes, and the decomposed volumes are then sequentially removed according to their importance. Volume decomposition operations can be categorized into wrapping and cutting decompositions, depending on the type of the acquired delta volume. If both wrapping and cutting decompositions can be applied to the same region, a criterion should be established for selecting the appropriate operation for that region. In this paper, we propose selective and iterative volume decomposition that combines four wrapping and two cutting decomposition operations. In addition, we propose volume and area ratios as the selection criteria for wrapping and cutting. We conducted experiments involving two part models and two assembly models to validate the proposed method. The experimental results showed that the proposed method produces a larger number of decomposed volumes with various volume distributions compared to previous methods. In summary, the proposed method is a highly effective approach for achieving incremental model simplification and obtaining multi-resolution models. (C) 2019 Elsevier Ltd. All rights reserved.