1. A method for recording images of a definable region of an examination object using an x-ray diagnostics facility for producing computed tomography recordings, comprising: providing an image recording facility having at least one radiation source and at least one radiation detector of the type which generates images of objects by rotating about a center of rotation definable as an isocenter with respect to the object; recording images of the entire examination region by rotating the image recording facility about a first isocenter, wherein the first isocenter is the center of rotation of the recording facility, with a first measuring field, a first resolution and a first dose, and generating an overview image of the examination object; defining a region in the examination object based on the overview image and defining a second isocenter at a location different from the first isocenter based upon a feature of the region, wherein the feature is selected from the group consisting of the location of the region, the geometry of the region, and a combination thereof; re-positioning the image recording facility to displace the center of rotation of the facility with respect to the object from the first isocenter to the second isocenter without requiring movement of the examination object from a fixed position on a support; recording images of the region by rotating the image recording facility about the second isocenter; and generating a region image showing the region.