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Lossless compression methods based on the Burrows-Wheeler transform (BWT) are regarded as an excellent compromise between speed and compression efficiency: they provide compression rates close to the PPM algorithms, with the speed of dictionary-based methods. Instead of the laborious statistics-gathering process used in PPM, the BWT reversibly sorts the input symbols, using as the sort key as many following characters as necessary to make the sort unique. Characters occurring in similar contexts are sorted close together, resulting in a clustered symbol sequence. Run-length encoding and Move-to-Front (MTF) recoding, combined with a statistical Huffman or arithmetic coder, is then typically used to exploit the clustering. A drawback of the MTF recoding is that knowledge of the character that produced the MTF number is lost. In this paper, we present a new, competitive Burrows-Wheeler posttransform stage that takes advantage of interpolative coding-a fast binary encoding method for integer sequences, being able to exploit clusters without requiring explicit statistics. We introduce a fast and simple way to retain knowledge of the run characters during the MTF recoding and use this to improve the clustering of MTF numbers and run-lengths by applying reversible, stable sorting, with the run characters as sort keys, achieving significant improvement in the compression rate, as shown here by experiments on common text corpora. K E Y W O R D S lossless compression, Burrows-Wheeler transform, move-to-front, interpolative coding This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.