We address the problem of recovering a CT image from partial fan-beam data and prior knowledge. The method used is that of convex projections also known as the method of projections onto convex sets (POCS). We consider several incomplete-data geometries including those associated with limited source travel and beam-blocking internal opacities. To enable the recovery we use several prior-knowledge constraints including one associated with the directivity of the image vector. The overall recovery algorithm can be practically implemented by exploiting the Toeplitz structure of key operators.