Point cloud representation is an emerging visual data technology, targeting immersive 3D experiences in the context of multiple applications scenarios, notably entertainment, geographical information systems, medicine, architecture, and robotics. Since a point cloud may easily involve millions of points, and thus an enormous amount of data, its effective storage and transmission critically asks for efficient coding solutions. With this purpose in mind, several point cloud coding (PCC) solutions have been proposed in the literature; special emphasis is due to the recent MPEG standards, which target interoperability in this domain, notably the MPEG V-PCC standard. The objective of this paper is to improve the V-PCC standard compression efficiency by proposing novel solutions for the V-PCC packing module without compromising in any way the V-PCC stream (syntax and semantics) and decoder compliance. In this context, several patch packing solutions are proposed, including new packing algorithms and associated sorting and positioning metrics; for the metrics, both absolute and relative approaches are proposed. The RD performance results show BD-Rate savings up to 0.8% for the best packing solution regarding the V-PCC benchmark. Moreover, the packing map size reductions can go up to 12%, on average.