This paper reports progress in work on CT reconstruction of incomplete X-ray (Radon) projection sets in situations where explicit object geometry and composition information is available. Previous work on this problem, reported in [1,2,3], addressed two major issues: 1.) appropriate compensation for missing projection data regarding flaws for which no explicit a priori data is available, and 2.) the scaling and geometric registration of explicit a priori component data. The first of these issues is addressed by restricting interest to the reconstruction of flaws which have high-contrast (high S/N) discontinuous boundaries. This restriction focuses attention on problems such as the inspection of monolithic material struc- tural components for cracks, porosity, inclusions, or dimensional abnormalities. It tends to exclude applications such as the imaging of slight density variations, or the imaging of diffuse boundary structures, such as might be encountered in medical applications. It was noted in the first year of this project that when reconstructing projection data from a compact support discontinuous boundary object, removal of a number of projections invariably increased the “size” of the reconstruction (i.e. increased the number of pixels above noise). This suggested that rather than setting the missing projection values to zero (12 norm minimization), it might be desirable to interpolate the missing projections such that the reconstructed object has a minimum size, i.e.minimum support. In a majority cases studied, this approach yields quite reasonable reconstructions of the object geometry, even in extreme cases where half the projection data is missing. When discrepancies between the true object and the reconstruction are significant due to extremely limited data, it was observed that support minimized reconstructions tend to be more intelligible than those of other methods, due to the straight-forward visual interpretation of the support minimized reconstruction.