  In this paper, we want to control the geometry of some surface subgroups of a
cocompact Kleinian group. More precisely, provided any genus-2 quasi-Fuchsian
group $\Gamma$ and cocompact Kleinian group $G$, then for any $K>1$, we will
find a surface subgroup $H$ of $G$ that is $K$-quasiconformally conjugate to a
finite index subgroup $F<\Gamma$.
