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The quality of pictures which are generated by X-ray scanners is limited essentially by the inter-dependence of patient dose, contrast and spatial resolution. When the collection of scan data is restricted to a region of medical interest, the skin dose can be reduced or the resolution can be improved. Two methods are presented which produce excellent pictures of the region from restricted scan data to be collected by a rotation-only scanner. The first method, SVIS, makes use of additional data outside the region, which are scanned at an X-ray intensity which is reduced by means of an absorber in front of the X-ray tube. The second method, SRACS, requires no X-ray data outside the region and replaces the missing data by artificial data which are calculated from the slice outline. This is determined by optical means. Pictures are shown which are reconstructed from true scan data of a body slice, where the data restriction is simulated on a computer and the Convolution method is used as the reconstruction technique.