  This work is devoted to the study of deformations of hyperbolic cone
structures under the assumption that the lengths of the singularity remain
uniformly bounded over the deformation. Given a sequence $(M_{i}%, p_{i}) $ of
pointed hyperbolic cone-manifolds with topological type $(M,\Sigma) $, where
$M$ is a closed, orientable and irreducible 3-manifold and $\Sigma$ an embedded
link in $M$. If the sequence $M_{i}$ collapses and assuming that the lengths of
the singularity remain uniformly bounded, we prove that $M$ is either a Seifert
fibered or a $Sol$ manifold. We apply this result to a question stated by
Thurston and to the study of convergent sequences of holonomies.
