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A method is presented for quantitative polychromatic cone-beam phase-contrast tomographic imaging of a single-material object from few projections. This algorithm exploits the natural combination of binary tomography with a phase-retrieval method that makes explicit use of the single-material nature of the sample. Such consistent use of a priori knowledge reduces the number of required projections, implying significantly reduced dose and scanning time when compared to existing phase-contrast tomography methods. Reconstructions from simulated data sets are used to investigate the effects of noise and establish a minimum required number of projections. An experimental demonstration is then given, using data from a point-projection X-ray microscope. Here, the complex distribution of refractive index in a sample containing several nylon fibers with diameters between 100 μm and 420 μm is reconstructed at a …