In robotic teleoperation, the knowledge of the state of the remote environment in real-time is a paramount. Advances in the development of highly accurate 3D cameras able to provide high quality point clouds appear to be a feasible solution for generating live, up-to-date virtual environments. Unfortunately, the exceptional accuracy and high density of this data represents a burden for communications requiring a large bandwidth affecting setups where the local and remote systems are geographically distant, particularly. This paper presents a multiple level-of-detail (LoD) compression strategy for 3D data based on tree-like codification structures capable of compressing a single data frame at multiple resolutions using dynamically-configured parameters. The level of compression (resolution) of objects is prioritise based on: i) placement on the scene and ii) type of object. For the former, classical point cloud fitting and segmentation techniques are implemented; for the latter, user-defined prioritisation is considered. The results obtained are compared using a single LoD (whole-scene) compression technique previously proposed by the authors. Results showed a considerable improvement to the transmitted data size and update frame rate while maintaining low distortion after decompression.