  We construct examples of primitive contractions of Calabi--Yau threefolds
with exceptional locus being $ \mathbb{P}^1 \times \mathbb{P}^1$,
$\mathbb{P}^2$, and smooth del Pezzo surfaces of degrees $\leq 5$. We describe
the images of these primitive contractions and find their smoothing families.
In particular, we give a method to compute the Hodge numbers of a generic fiber
of the smoothing family of each Calabi--Yau threefold with one isolated
singularity obtained after a primitive contraction of type II. As an
application, we get examples of natural conifold transitions between some
families of Calabi--Yau threefolds.
