  Let $G$ be a group acting on a tree $T$ with finite edge stabilizers of
bounded order. We provide, in some very interesting cases, upper bounds for the
complexity of the intersection $H\cap K$ of two tame subgroups $H$ and $K$ of
$G$ in terms of the complexities of $H$ and $K$. In particular, we obtain
bounds for the Kurosh rank $Kr(H\cap K)$ of the intersection in terms of Kurosh
ranks $Kr(H)$ and $Kr(K)$, in the case where $H$ and $K$ act freely on the
edges of $T$.
