Summary: The investigation of the extremal case of the Burrows-Wheeler transform leads to study the words \(w\) over an ordered alphabet \(A=\{a_{1},a_{2},\cdots ,a_k\}\), with \(a_{1}<a_{2}<\cdots <a_k\), such that \(\text{bwt}(w)\) is of the form \(a^{n_k}_ka^{n_{k-1}}_{k-1}\cdots a^{n_2}_2a^{n_1}_1\), for some non-negative integers \(n_{1},n_{2},\cdots ,n_k\). A characterization of these words in the case \(|A|=2\) has been given in [S. Mantaci, A. Restivo, and M. Sciortino, “Burrows-Wheeler transform and Sturmian words”, Inf. Process. Lett. 86, No. 5, 241–246 (2003; Zbl 1162.68511)], where it is proved that they correspond to the powers of conjugates of standard words. The case \(|A|=3\) has been settled in [J. Simpson and S. J. Puglisi, “Words with simple Burrows-Wheeler transforms”, Electron. J. Comb. 15, No. 1, Research Paper R83, 17 p. (2008; Zbl 1183.68446)], which also contains some partial results for an arbitrary alphabet. In the present paper we show that such words can be described in terms of the notion of “palindromic richness”, recently introduced in [A. Glen, J. Justin, St. Widmer and L. Q. Zamboni, “Palindromic richness”, Eur. J. Comb. 30, No. 2, 510–531 (2009; Zbl 1169.68040)]. Our main result indeed states that a word \(w\) such that \(\text{bwt}(w)\) has the form \(a^{n_k}_ka^{n_{k-1}}_{k-1}\cdots a^{n_2}_2a^{n_1}_1\) is strongly rich, i.e. the word \(w^{2}\) contains the maximum number of different palindromic factors.