1. A method for generating a digital tomosynthetic 3D X-ray image of an examination object, comprising the steps of: moving an X-ray tube through a plurality of projection angles relative to an examination object, and irradiating the examination object with X-rays from said X-ray tube at each of said projection angles, and detecting X-rays attenuated by the examination object with a digital X-ray detector, to generate respective images of the examination object at said projection angles, said projection angles including a first of said projection angles at a starting position of movement of said X-ray tube; only at said first of said projection angles, irradiating the examination object with X-rays from the X-ray tube at a dose that is lower than a dose employed at others of said projection angles, to generate a preliminary image of the examination object; automatically electronically evaluating said preliminary image to identify at least one operating parameter for said X-ray tube for generating a remainder of said images, and operating said X-ray tube with said at least one operating parameter to generate said remainder of said images; and computationally reconstructing a digital tomosynthetic 3D X-ray image of the examination object at least from said remainder of said images.