A tomosynthesis apparatus for mammography has an x-ray source for emission of x-ray beams from different directions directed toward a detector, and a compression plate and a support plate arranged in the beam path between the x-ray source and the detector. A breast to be examined is positioned and compressed between the compression plate and the support plate. The compression plate exhibits a concave recess open in the direction of the support plate on the side of the compression plate facing toward the support plate.