  Let $B$ be a smooth projective surface, and $\mathcal{L}$ an ample line
bundle on $B$. The aim of this parer is to study the families of elliptic
Calabi--Yau threefolds sitting in the bundle $\mathbb{P}(\mathcal{L}^a \oplus
\mathcal{L}^b \oplus \mathcal{O}_B)$ as anticanonical divisors. We will show
that the number of such families is finite.
