  Let $S$ be any closed hyperbolic surface and let $\lambda$ be a maximal
geodesic lamination on $S$. The amount of bending of an abstract pleated
surface (homeomorphic to $S$) with the pleating locus $\lambda$ is completely
determined by an $(\mathbb{R}/2\pi\mathbb{Z})$-valued finitely additive
transverse cocycle $\beta$ to the geodesic lamination $\lambda$. We give a
sufficient condition on $\beta$ such that the corresponding pleating map
$\tilde{f}_{\beta}:\mathbb{H}^2\to\mathbb{H}^3$ induces a quasiFuchsian
representation of the surface group $\pi_1(S)$. Our condition is genus
independent.
