An x-ray system for imaging a breast of an upright patient comprising: a breast immobilization unit configured to immobilize a breast of an upright patient between two facing compression surfaces; an x-ray source on one side of the breast immobilization unit and an x-ray imaging receptor on another side of the immobilization unit, said source selectively emitting an imaging beam of x-rays and said receptor receiving said imaging beam after passage thereof through the immobilization unit, and said source and receptor being mounted for selective movement about the breast immobilization unit; an x-ray data acquisition unit coupled with said source and receptor and configured to selectively operate said system in a CT mode in which the source and receptor move rotationally about the breast immobilization unit and thus a breast of an upright patient immobilized therein, over a CT source trajectory angle of at least 180° and the receptor generates image data for a plurality of projection images CTp of the breast taken at different angles within said CT angle, wherein the rotation for CT imaging excludes positions of the source in a sector or segment that is sufficient to clear the patient's head position while taking x-ray CT data over a sufficient angle of rotation for reconstruction of high quality CTr images; an image processing unit configured to receive and computer-process at least some of said image data for said images CTp to thereby generate reconstructed images CTr representing slices of the breast having selected thicknesses and orientations, and to produce display slice images CTrd based thereon; and a display unit receiving said selectively displaying said display images CTrd for viewing. a breast immobilization unit configured to immobilize a breast of an upright patient between two facing compression surfaces; an x-ray source on one side of the breast immobilization unit and an x-ray imaging receptor on another side of the immobilization unit, said source selectively emitting an imaging beam of x-rays and said receptor receiving said imaging beam after passage thereof through the immobilization unit, and said source and receptor being mounted for selective movement about the breast immobilization unit; an x-ray data acquisition unit coupled with said source and receptor and configured to selectively operate said system in a CT mode in which the source and receptor move rotationally about the breast immobilization unit and thus a breast of an upright patient immobilized therein, over a CT source trajectory angle of at least 180° and the receptor generates image data for a plurality of projection images CTp of the breast taken at different angles within said CT angle, wherein the rotation for CT imaging excludes positions of the source in a sector or segment that is sufficient to clear the patient's head position while taking x-ray CT data over a sufficient angle of rotation for reconstruction of high quality CTr images; an image processing unit configured to receive and computer-process at least some of said image data for said images CTp to thereby generate reconstructed images CTr representing slices of the breast having selected thicknesses and orientations, and to produce display slice images CTrd based thereon; and a display unit receiving said selectively displaying said display images CTrd for viewing.