X-ray computed tomography (CT) data contains artefacts from many sources, with sufficient prominence to affect diagnostic utility when metal is present in the scans. These artefacts can be reduced, usually by the removal and in-filling of any sinogram data which has been affected by metal, and several such techniques have been proposed. Most of them are prone to introducing new artefacts into the CT data or may take a long time to correct the data. It is the purpose of this paper to introduce a new technique which is fast, yet can effectively remove most artefacts without introducing significant new ones. The new metal artefact reduction technique (RMAR) consists of an iterative refinement of the CT data by alternately forward- and back-projecting the part of the reconstruction near to metal. The forward-projection is corrected by making use of a prior derived from the reconstructed data which is independently estimated for each projection angle, and smoothed using a newly developed Bitonic filter. The new technique is compared with previously published (LI, NMAR, MDT) and commercial (O-MAR, IMAR) alternatives, quantitatively on phantom data, and qualitatively on a selection of clinical scans, mostly of the hip. The phantom data is from two recently published studies, enabling direct comparison with previous results. The results show an increased reduction of artefacts on the four phantom data sets tested. On two of the phantom data sets, RMAR is significantly better (p < 0.001) than all other techniques; on one it is as good as any other technique, and on the last it is only beaten by the Metal Deletion Technique (p < 0.001), which is significantly slower. On the clinical data sets, RMAR shows visually similar performance to MDT, with better preservation of bony features close to metal implants, but perhaps slightly reduced homogeneity in the far field. For typical CT data, RMAR can correct each image in 3–8 s, which is more than one hundred times faster than MDT. The new technique is demonstrated to have performance at least as good as MDT, with both out-performing other approaches. However, it is much faster then the latter technique, and shows better preservation of data very close to metal.