  Let M be a closed, orientable, irreducible, non-simply connected 3-manifold.
We prove that if M admits a sequence of Riemannian metrics whose sectional
curvature is locally controlled and whose thick part becomes asymptotically
hyperbolic and has a sufficiently small volume, then M is Seifert fibred or
contains an incompressible torus. This result gives an alternative approach for
the last step in Perelman's proof of the Geometrisation Conjecture for
aspherical 3-manifolds.
