Point clouds have been recognized as a crucial data structure for 3D content and are essential in a number of applications such as virtual and mixed reality, autonomous driving, cultural heritage, etc. In this paper, we propose a set of contributions to improve deep point cloud compression, i.e.: using a scale hyperprior model for entropy coding; employing deeper transforms; a different balancing weight in the focal loss; optimal thresholding for decoding; and sequential model training. In addition, we present an extensive ablation study on the impact of each of these factors, in order to provide a better understanding about why they improve RD performance. An optimal combination of the proposed improvements achieves BD-PSNR gains over G-PCC trisoup and octree of 5.50 (6.48) dB and 6.84 (5.95) dB, respectively, when using the point-to-point (point-to-plane) metric. Code is available at https://github.com/mauriceqch/pcc_geo_cnn_v2 .