The direct phase-contrast X-ray tomography, which reconstructs tomograms directly from projection phase-contrast images without the phase retrievals, finds many interesting applications for detection of interfaces for different tissues. In this work we explore and clarify the contrast mechanism of the direct phase-contrast tomography, and show that the direct phase-contrast tomogram is a mixture of three components: the 3D map of the imaged object's linear attenuation coefficients, the map of the rescaled 3D Laplacians of its refraction indices, and artifacts related to the global distribution of the attenuation coefficients and refraction indices. The need of phase retrieval for accurate and quantitative tomography for medical applications is pointed out. A phase tomography reconstruction formula for soft tissue imaging, which requires just a single phase-contrast image per projection for reconstruction, is presented. © 2008 Elsevier Ireland Ltd. All rights reserved.