  It is known that many Calabi-Yau manifolds form a connected web. The question
of whether all Calabi-Yau manifolds form a single web depends on the degree of
singularity that is permitted for the varieties that connect the distinct
families of smooth manifolds. If only conifolds are allowed then, since
shrinking two-spheres and three-spheres to points cannot affect the fundamental
group, manifolds with different fundamental groups will form disconnected webs.
We examine these webs for the tip of the distribution of Calabi-Yau manifolds
where the Hodge numbers (h^{11}, h^{21}) are both small. In the tip of the
distribution the quotient manifolds play an important role. We generate via
conifold transitions from these quotients a number of new manifolds. These
include a manifold with \chi =-6 and manifolds with an attractive structure
that may prove of interest for string phenomenology. We also examine the
relation of some of these manifolds to the remarkable Gross-Popescu manifolds
that have Euler number zero.
