  We study type III contractions of Calabi-Yau threefolds containing a ruled
surface over a smooth curve. We discuss the conditions necessary for the image
threefold to by smoothable. We describe the change in Hodge numbers caused by
this contraction and smoothing deformation. A generalization of a fomula for
calculating Hodge numbers of hypersurfaces in $\mathbb{P}^4$ with ordinary
double and triple points is presented. We use these results to construct new
Calabi-Yau threefolds of Picard rank two arising from a family of quintic
threefolds containing a cone.
