  We prove 3-dimensional hyperbolic cone-manifolds are geometrically
inflexible: a cone-deformation of a hyperbolic cone-manifold determines a
bi-Lipschitz diffeomorphism between initial and terminal manifolds in the
deformation in the complement of a standard tubular neighborhood of the
cone-locus whose pointwise bi-Lipschitz constant decays exponentially in the
distance from the cone-singularity. Estimates at points in the thin part are
controlled by similar estimates on the complex lengths of short curves.
