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Statistical reconstruction (SR) of X-ray CT data may lead to images that are seriously affected by edge artifacts that are not present in filtered back projection (FBP) images. These artifacts appear as interference patterns and as severe overshoots in the areas of sharp intensity transitions. We attribute this inherent property of iterative reconstructions to discretization errors. A fundamental solution to the problem is to perform the reconstructions on an image grid that is finer than typically employed for FBP reconstruction, followed by a downsampling of the resulting image to a granularity normally used for display. We show that such a procedure strongly suppresses the edge artifacts and is a much more effective solution than post-filtering of the reconstructions.