  We generalize the notion of tight geodesics in the curve complex to tight
trees. We then use tight trees to construct model geometries for certain
surface bundles over graphs. This extends some aspects of the combinatorial
model for doubly degenerate hyperbolic 3-manifolds developed by Brock, Canary,
and Minsky during the course of their proof of the Ending Lamination Theorem.
Thus we obtain uniformly Gromov-hyperbolic geometric model spaces equipped with
geometric $G-$actions, where $G$ admits an exact sequence of the form $$1 \to
\pi_1(S) \to G \to Q \to 1.$$ Here $S$ is a closed surface of genus $g > 1$ and
$Q$ belongs to a special class of free convex cocompact subgroups of the
mapping class group $MCG(S)$.
