We describe how to construct a model space for a geometrically tame indecomposible hyperbolic 3-manifold, based on a set of end invariants for the simply degenerate ends. We construct a lipschitz map from the model into the hyperbolic manifold, and show that the lift to the universal covers is a quasi-isometry. In this way, we give another proof of Thurston's Ending Lamination Conjecture for indecomposible manifolds. Many of our constructions are similar to those of the original proof by Minsky, Brock and Canary, and are based on tight geodesics in the curve graph. The logical structure however is somewhat different, and some of the more technical material is simplified. Much of the argument is set in the context of a doubly degenerate group, in which case the lipschitz and quasi-isometry constants depend only only the topological type of the surface.
First draft: August 2005. Revised: October 2006.