Digital hologram sequences have great potential for the recording of 3D scenes of moving macroscopic objects as their numerical reconstruction can yield a range of perspective views of the scene. Digital holograms inherently have large information content and lossless coding of holographic data is rather inefficient due to the speckled nature of the interference fringes they contain. Lossy coding of still holograms and hologram sequences has shown promising results. By definition, lossy compression introduces errors in the reconstruction. In all of the previous studies, numerical metrics were used to measure the compression error and through it, the coding quality. Digital hologram reconstructions are highly speckled and the speckle pattern is very sensitive to data changes. Hence, numerical quality metrics can be misleading. For example, for low compression ratios, a numerically significant coding error can have visually negligible effects. Yet, in several cases, it is of high interest to know how much lossy compression can be achieved, while maintaining the reconstruction quality at visually lossless levels. Using an experimental threshold estimation method, the staircase algorithm, we determined the highest compression ratio that was not perceptible to human observers for objects compressed with Dirac and MPEG- 4 compression methods. This level of compression can be regarded as the point below which compression is perceptually lossless although physically the compression is lossy. It was found that up to 4 to 7.5 fold compression can be obtained with the above methods without any perceptible change in the appearance of video sequences.