A method is described for using a limited number (typically 10-50) of low-dose radiographs to reconstruct the three-dimensional (3D) distribution of x-ray attenuation in the breast. The method uses x-ray cone-beam imaging, an electronic digital detector, and constrained nonlinear iterative computational techniques. Images are reconstructed with high resolution in two dimensions and lower resolution in the third dimension. The 3D distribution of attenuation that is projected into one image in conventional mammography can be separated into many layers (typically 30-80 1-mm-thick layers, depending on breast thickness), increasing the conspicuity of features that are often obscured by overlapping structure in a single-projection view. Schemes that record breast images at nonuniform angular increments, nonuniform image exposure, and nonuniform detector resolution are investigated in order to reduce the total x-ray exposure necessary to obtain diagnostically useful 3D reconstructions, and to improve the quality of the reconstructed images for a given exposure. The total patient radiation dose can be comparable to that used for a standard two-view mammogram. The method is illustrated with images from mastectomy specimens, a phantom, and human volunteers. The results show how image quality is affected by various data-collection protocols.