A mammography system using a tissue exposure control relying on estimates of the thickness of the compressed and immobilized breast (20 and 22) and of breast density (26, 28, 30 and 32) to automatically derive one or more technic factors (24). The system further uses a tomosynthesis arrangement that maintains the focus of an anti-scatter grid (12d) on the x-ray source (12a) and also maintains the field of view of the x-ray receptor (12c). Finally, the system finds an outline that forms a reduced field of view (48) that still encompasses the breast in the image (46), and uses for further processing, transmission or archival storage the data within said reduced field of view (48).