A 3D X-ray device including an X-ray detector, an X-ray source and a computer. The X-ray detector and the X-ray source are moved about an object volume to be recorded on movement paths with a rotation of at least 185°. A number of X-ray projection images are recorded from different directions. X-rays irradiate the object volume in one of the irradiation directions and are captured by the detector. A 3D X-ray image of the object volume is calculated from the recorded X-ray projection images by a reconstruction method. The X-ray detector is arranged asymmetrically relative to a central axis through a center of rotation of the 3D X-ray device. A first fan beam and an opposite second fan beam rotated 180° form an overlap region. At least one X-ray filter is placed between the X-ray source and the object volume for attenuating an X-ray dose inside the overlap region.