  For any irreducible representation of a surface group into
$\mathrm{SL}_2(\mathbb{C})$, we show that there exists a pants decomposition
where the restriction to any pair of pants is irreducible and where no curve of
the decomposition is sent to a trace $\pm 2$ element. We prove a similar
property for $\mathrm{SO}_3$-representations. We also investigate the type of
pants decomposition that can occur in this setting for a given representation.
This result was announced in a previous paper of the first and third named
authors, motivated by the study of the Azumaya locus of the skein algebra of
surfaces at roots of unity.
