  Let $\rho$ be a representation of the fundamental group of a punctured
surface into $\mathrm{PSL}_2 (\mathbb{C})$ that is not Fuchsian. We prove that
there exists a Fuchsian representation that strictly dominates $\rho$ in the
simple length spectrum, and preserves the boundary lengths. This extends a
result of Gueritaud-Kassel-Wolff to the case of $\mathrm{PSL}_2
(\mathbb{C})$-representations. Our proof involves straightening the pleated
plane in $\mathbb{H}^3$ determined by the Fock-Goncharov coordinates of a
framed representation, and applying strip-deformations.
