Modern detectors used at synchrotron tomographic microscopy beamlines typically have sensors with more than 4–5 mega-pixels and are capable of acquiring 100–1000 frames per second at full frame. As a consequence, a data rate of a few TB per day can easily be exceeded, reaching peaks of a few tens of TB per day for time-resolved tomographic experiments. This data needs to be post-processed, analysed, stored and possibly transferred, imposing a significant burden onto the IT infrastructure. Compression of tomographic data, as routinely done for diffraction experiments, is therefore highly desirable. This study considers a set of representative datasets and investigates the effect of lossy compression of the original X-ray projections onto the final tomographic reconstructions. It demonstrates that a compression factor of at least three to four times does not generally impact the reconstruction quality. Potentially, compression with this factor could therefore be used in a transparent way to the user community, for instance, prior to data archiving. Higher factors (six to eight times) can be achieved for tomographic volumes with a high signal-to-noise ratio as it is the case for phase-retrieved datasets. Although a relationship between the dataset signal-to-noise ratio and a safe compression factor exists, this is not simple and, even considering additional dataset characteristics such as image entropy and high-frequency content variation, the automatic optimization of the compression factor for each single dataset, beyond the conservative factor of three to four, is not straightforward.