Early vertebrate evolution involved a series of drastic structural reorganisations as new features were added and elaborated. The fossil record illuminates this evolutionary history more directly than inferences from the diversity of living forms, but the fossils usually consist only of bones whereas many of the most important and interesting changes occurred in the soft anatomy. Traditional approaches to reconstructing the musculature and other soft tissues of fossil vertebrates rely on subjective tools, like the visual identification of rough bone textures thought to indicate muscle attachments, and generally leave a lot to be desired. Here I propose a wholly novel and radically more objective approach to the identification of soft-tissue contacts, using holotomographic synchrotron CT at sub-micron resolutions to identify these contacts by the three-dimensional micro-architecture of the bone. A pilot study has already shown that such scans (performed at the ESRF synchrotron facility in Grenoble) are capable of imaging key features such as arrested growth surfaces and probable Sharpey s fibres in 380 million year old fossils. We will undertake a systematic review of the three-dimensional bone micro-architectures associated with different soft-tissue contacts in living vertebrates, and the use this as a key to reconstruct the soft-tissue contacts on fossil bones with unprecedented accuracy. This will permit us to produce far more reliable reconstructions of the soft anatomy than has hitherto been possible. Our findings will inform other areas of palaentology, particularly functional morphology, and will also be of great importance to evolutionary developmental biology.