The Burrows-Wheeler transform (BWT) is a popular method used for text compression. It was proved that BWT has optimal performance on standard words, i.e. the building blocks of Sturmian words. In this paper, we study the application of BWT on more general morphic words: the Thue-Morse word and to generalizations of the Fibonacci word to alphabets with more than two letters; then, we study morphisms obtained as composition of the Thue-Morse morphism with a Sturmian one. In all these cases, the BWT efficiently clusters the iterates of the morphisms generating prefixes of these infinite words, for which we determine the compression clustering ratio.

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