  We show that, given a closed integral symplectic manifold $(\Sigma, \omega)$
of dimension $2n \geq 4$, for every integer $k>\int_{\Sigma}\omega^{n}$, the
Boothby-Wang bundle over $(\Sigma, k\omega)$ carries no Stein fillable contact
structure. This negatively answers a question raised by Eliashberg. A similar
result holds for Boothby-Wang orbibundles. As an application, we prove the
non-smoothability of some isolated singularities.
