Computer-Aided Design is ubiquitous in todays world, as almost every manufactured object begins as a digital model across industries. At the same time, advances in 3D sensing have made point clouds a dominant form of raw 3D data. Recovering the CAD model of a physical object from its point cloud scan has two major applications: reverse engineering, where physical or hand-crafted prototypes need to be reconstructed automatically as editable digital models, and quality control, where recovering the CAD description of a manufactured object helps quantify and understand deviations introduced during the production process. Thus, converting unordered point clouds into structured CAD models is increasingly important for modern applications. Deep learning has enabled major progress in computer vision for both 2D and 3D data, and new datasets facilitate data-driven CAD reconstruction. Building on this foundation, we develop an end-to-end model that reconstructs CAD models from point clouds and introduce a segmentation approach that decomposes them into individual extrusions. These partial shapes increase data diversity, improving the generalization and robustness of deep learning models. Our strategy thereby provides a simple, yet effective way to increase reconstruction performance of deep learning models.