The aim of this study was to introduce high-resolution computed tomography (CT) of breast tumours using the diffraction-enhanced x-ray imaging (DEI) technique and to compare results with radiological and histo-pathological examinations. X-ray CT images of tumour-bearing breast tissue samples were acquired by monochromatic synchrotron radiation (SR). Due to the narrow beam and a large sample-to-detector distance scattering is rejected in the absorption contrast images (SR-CT). Large contrast enhancement is achieved by the use of the DEI-CT method, where the effects of refraction and scatter rejection are analysed by crystal optics. Clinical mammograms and CT images were recorded as reference material for a radiological examination. Three malignant and benign samples were studied in detail. Their radiographs were compared with optical images of stained histological sections. The DEI-CT images map accurately the morphology of the samples, including collagen strands and micro-calcifications of dimensions less than 0.1 mm. Histo-pathological examination and reading of the radiographs were done independently, and the conclusions were in general agreement. High-resolution DEI-CT images show strong contrast and permit visualization of details invisible in clinical radiographs. The radiation dose may be reduced by an order of magnitude without compromising image quality, which would make possible clinical in vivo DEI-CT with future compact SR sources.