Pli selon pli is Boulez’s richest encounter with Mallarmé. As a ‘portrait’ of the poet which sets three of his sonnets, it can be associated not only with other composers – Ravel, Debussy – who set Mallarmé, but also with the poet’s own views on music, and his radical yet tradition-conscious formal practices. Structural and poetic aspects of the fourth movement of the work, ‘Improvisation III’, are examined in detail, highlighting Boulez’s increasing concern with matters of formal coherence. This suggests a strengthening resistance to modernism as fragmentation and the embrace of a modern classicism which shuns the fixed hierarchies of tonal classicism as well as the parodistic juxtapositions of neoclassicism. At the same time, however, the multiple resonances on which modern classicism depends for its coherence ensure that certain aspects of Mallarmé-inspired narrative – concerning shipwrecks and sirens, among other things – cannot be entirely suppressed in present-day critical commentary.