In contrast to LiDAR data provided by discrete return systems, full waveform LiDAR data (FWD) improve the quality of products and extend the possibilities of their application. Beside evident benefits, FWD imposes strong requirements on the sensor acquisition and storage hardware. At the moment, there is little effort reported on sensor level waveform data compression. Vendor specified waveform data formats are generally not published for the users and do not mention compression options. Since the recorded waveform is intrinsically noisy, there is less practical need to use lossless compression methods. As long as the properties of FWD are preserved, in other words, as long as it is possible to extract the same FWD features, and the compression noise is below or comparable to the noise of the signal, lossy compression methods are suitable. Such compression of FWD was studied in previous work where waveforms were compressed individually or in groups forming images, which is considered as 1D and 2D compression, respectively. This work presents a strategy for FWD compression that is based on multi-component transforms, which is included in JPEG-2000 Standard Part 2. This extension to JPEG-2000 Standard exploits the 3D correlation between waveform samples and allows compressing waveform cubes without organizing samples. The results of this study indicate that the removal of data redundancies in all three dimensions results in slightly better compression performance than using 1D or 2D approaches. More importantly, the user has the flexibility to decide on how much the data should be compressed or what level of the reconstruction error is allowed. Besides JPEG-2000 compression, this investigation includes experiments with additional data decorrelators, such as Karhunen-Loeve transform and wavelet transform. The conclusion of this study is that the JPEG-2000 Standard is an effective method for FWD compression of waveform cubes, resulting in high compression ratios and low data degradation.